Validation of cardiac accelerometer sensor measurements
Identifieur interne : 000614 ( Istex/Corpus ); précédent : 000613; suivant : 000615Validation of cardiac accelerometer sensor measurements
Auteurs : Espen W. Remme ; Lars Hoff ; Per Steinar Halvorsen ; Edvard Nrum ; Helge Skulstad ; Lars A. Fleischer ; Ole Jakob Elle ; Erik FosseSource :
- Physiological Measurement [ 0967-3334 ] ; 2009.
Abstract
In this study we have investigated the accuracy of an accelerometer sensor designed for the measurement of cardiac motion and automatic detection of motion abnormalities caused by myocardial ischaemia. The accelerometer, attached to the left ventricular wall, changed its orientation relative to the direction of gravity during the cardiac cycle. This caused a varying gravity component in the measured acceleration signal that introduced an error in the calculation of myocardial motion. Circumferential displacement, velocity and rotation of the left ventricular apical region were calculated from the measured acceleration signal. We developed a mathematical method to separate translational and gravitational acceleration components based on a priori assumptions of myocardial motion. The accuracy of the measured motion was investigated by comparison with known motion of a robot arm programmed to move like the heart wall. The accuracy was also investigated in an animal study. The sensor measurements were compared with simultaneously recorded motion from a robot arm attached next to the sensor on the heart and with measured motion by echocardiography and a video camera. The developed compensation method for the varying gravity component improved the accuracy of the calculated velocity and displacement traces, giving very good agreement with the reference methods.
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DOI: 10.1088/0967-3334/30/12/010
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<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title>Validation of cardiac accelerometer sensor measurements</title><author><name sortKey="Remme, Espen W" sort="Remme, Espen W" uniqKey="Remme E" first="Espen W" last="Remme">Espen W. Remme</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail:espen.remme@medisin.uio.no</mods:affiliation></affiliation></author><author><name sortKey="Hoff, Lars" sort="Hoff, Lars" uniqKey="Hoff L" first="Lars" last="Hoff">Lars Hoff</name><affiliation><mods:affiliation>Vestfold University College, Tnsberg, Norway</mods:affiliation></affiliation></author><author><name sortKey="Halvorsen, Per Steinar" sort="Halvorsen, Per Steinar" uniqKey="Halvorsen P" first="Per Steinar" last="Halvorsen">Per Steinar Halvorsen</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author><author><name sortKey="Nrum, Edvard" sort="Nrum, Edvard" uniqKey="Nrum E" first="Edvard" last="Nrum">Edvard Nrum</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author><author><name sortKey="Skulstad, Helge" sort="Skulstad, Helge" uniqKey="Skulstad H" first="Helge" last="Skulstad">Helge Skulstad</name><affiliation><mods:affiliation>Department of Cardiology, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author><author><name sortKey="Fleischer, Lars A" sort="Fleischer, Lars A" uniqKey="Fleischer L" first="Lars A" last="Fleischer">Lars A. Fleischer</name><affiliation><mods:affiliation>Vestfold University College, Tnsberg, Norway</mods:affiliation></affiliation></author><author><name sortKey="Elle, Ole Jakob" sort="Elle, Ole Jakob" uniqKey="Elle O" first="Ole Jakob" last="Elle">Ole Jakob Elle</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author><author><name sortKey="Fosse, Erik" sort="Fosse, Erik" uniqKey="Fosse E" first="Erik" last="Fosse">Erik Fosse</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8</idno><date when="2009" year="2009">2009</date><idno type="doi">10.1088/0967-3334/30/12/010</idno><idno type="url">https://api.istex.fr/document/755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">000614</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a">Validation of cardiac accelerometer sensor measurements</title><author><name sortKey="Remme, Espen W" sort="Remme, Espen W" uniqKey="Remme E" first="Espen W" last="Remme">Espen W. Remme</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail:espen.remme@medisin.uio.no</mods:affiliation></affiliation></author><author><name sortKey="Hoff, Lars" sort="Hoff, Lars" uniqKey="Hoff L" first="Lars" last="Hoff">Lars Hoff</name><affiliation><mods:affiliation>Vestfold University College, Tnsberg, Norway</mods:affiliation></affiliation></author><author><name sortKey="Halvorsen, Per Steinar" sort="Halvorsen, Per Steinar" uniqKey="Halvorsen P" first="Per Steinar" last="Halvorsen">Per Steinar Halvorsen</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author><author><name sortKey="Nrum, Edvard" sort="Nrum, Edvard" uniqKey="Nrum E" first="Edvard" last="Nrum">Edvard Nrum</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author><author><name sortKey="Skulstad, Helge" sort="Skulstad, Helge" uniqKey="Skulstad H" first="Helge" last="Skulstad">Helge Skulstad</name><affiliation><mods:affiliation>Department of Cardiology, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author><author><name sortKey="Fleischer, Lars A" sort="Fleischer, Lars A" uniqKey="Fleischer L" first="Lars A" last="Fleischer">Lars A. Fleischer</name><affiliation><mods:affiliation>Vestfold University College, Tnsberg, Norway</mods:affiliation></affiliation></author><author><name sortKey="Elle, Ole Jakob" sort="Elle, Ole Jakob" uniqKey="Elle O" first="Ole Jakob" last="Elle">Ole Jakob Elle</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author><author><name sortKey="Fosse, Erik" sort="Fosse, Erik" uniqKey="Fosse E" first="Erik" last="Fosse">Erik Fosse</name><affiliation><mods:affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Physiological Measurement</title><title level="j" type="abbrev">Physiol. Meas.</title><idno type="ISSN">0967-3334</idno><idno type="eISSN">1361-6579</idno><imprint><publisher>IOP Publishing</publisher><date type="published" when="2009">2009</date><biblScope unit="volume">30</biblScope><biblScope unit="issue">12</biblScope><biblScope unit="page" from="1429">1429</biblScope><biblScope unit="page" to="1444">1444</biblScope><biblScope unit="production">Printed in the UK</biblScope></imprint><idno type="ISSN">0967-3334</idno></series><idno type="istex">755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8</idno><idno type="DOI">10.1088/0967-3334/30/12/010</idno><idno type="PII">S0967-3334(09)21426-2</idno><idno type="articleID">321426</idno><idno type="articleNumber">010</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0967-3334</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract">In this study we have investigated the accuracy of an accelerometer sensor designed for the measurement of cardiac motion and automatic detection of motion abnormalities caused by myocardial ischaemia. The accelerometer, attached to the left ventricular wall, changed its orientation relative to the direction of gravity during the cardiac cycle. This caused a varying gravity component in the measured acceleration signal that introduced an error in the calculation of myocardial motion. Circumferential displacement, velocity and rotation of the left ventricular apical region were calculated from the measured acceleration signal. We developed a mathematical method to separate translational and gravitational acceleration components based on a priori assumptions of myocardial motion. The accuracy of the measured motion was investigated by comparison with known motion of a robot arm programmed to move like the heart wall. The accuracy was also investigated in an animal study. The sensor measurements were compared with simultaneously recorded motion from a robot arm attached next to the sensor on the heart and with measured motion by echocardiography and a video camera. The developed compensation method for the varying gravity component improved the accuracy of the calculated velocity and displacement traces, giving very good agreement with the reference methods.</div></front></TEI><istex><corpusName>iop</corpusName><author><json:item><name>Espen W Remme</name><affiliations><json:string>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</json:string><json:string>E-mail:espen.remme@medisin.uio.no</json:string></affiliations></json:item><json:item><name>Lars Hoff</name><affiliations><json:string>Vestfold University College, Tnsberg, Norway</json:string></affiliations></json:item><json:item><name>Per Steinar Halvorsen</name><affiliations><json:string>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</json:string></affiliations></json:item><json:item><name>Edvard Nrum</name><affiliations><json:string>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</json:string></affiliations></json:item><json:item><name>Helge Skulstad</name><affiliations><json:string>Department of Cardiology, Oslo University Hospital, Rikshospitalet, Oslo, Norway</json:string></affiliations></json:item><json:item><name>Lars A Fleischer</name><affiliations><json:string>Vestfold University College, Tnsberg, Norway</json:string></affiliations></json:item><json:item><name>Ole Jakob Elle</name><affiliations><json:string>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</json:string></affiliations></json:item><json:item><name>Erik Fosse</name><affiliations><json:string>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>biomedical sensor</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>accelerometer</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>cardiac surgery</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>myocardial ischaemia</value></json:item></subject><language><json:string>eng</json:string></language><abstract>In this study we have investigated the accuracy of an accelerometer sensor designed for the measurement of cardiac motion and automatic detection of motion abnormalities caused by myocardial ischaemia. The accelerometer, attached to the left ventricular wall, changed its orientation relative to the direction of gravity during the cardiac cycle. This caused a varying gravity component in the measured acceleration signal that introduced an error in the calculation of myocardial motion. Circumferential displacement, velocity and rotation of the left ventricular apical region were calculated from the measured acceleration signal. We developed a mathematical method to separate translational and gravitational acceleration components based on a priori assumptions of myocardial motion. The accuracy of the measured motion was investigated by comparison with known motion of a robot arm programmed to move like the heart wall. The accuracy was also investigated in an animal study. The sensor measurements were compared with simultaneously recorded motion from a robot arm attached next to the sensor on the heart and with measured motion by echocardiography and a video camera. The developed compensation method for the varying gravity component improved the accuracy of the calculated velocity and displacement traces, giving very good agreement with the reference methods.</abstract><qualityIndicators><score>7.9</score><pdfVersion>1.4</pdfVersion><pdfPageSize>595 x 842 pts (A4)</pdfPageSize><refBibsNative>true</refBibsNative><keywordCount>4</keywordCount><abstractCharCount>1377</abstractCharCount><pdfWordCount>7044</pdfWordCount><pdfCharCount>42696</pdfCharCount><pdfPageCount>16</pdfPageCount><abstractWordCount>200</abstractWordCount></qualityIndicators><title>Validation of cardiac accelerometer sensor measurements</title><genre.original><json:string>paper</json:string></genre.original><pii><json:string>S0967-3334(09)21426-2</json:string></pii><genre><json:string>research-article</json:string></genre><host><volume>30</volume><publisherId><json:string>PM</json:string></publisherId><pages><total>16</total><last>1444</last><first>1429</first></pages><issn><json:string>0967-3334</json:string></issn><issue>12</issue><genre><json:string>journal</json:string></genre><language><json:string>unknown</json:string></language><eissn><json:string>1361-6579</json:string></eissn><title>Physiological Measurement</title></host><publicationDate>2009</publicationDate><copyrightDate>2009</copyrightDate><doi><json:string>10.1088/0967-3334/30/12/010</json:string></doi><id>755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8</id><score>1</score><fulltext><json:item><original>true</original><mimetype>application/pdf</mimetype><extension>pdf</extension><uri>https://api.istex.fr/document/755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8/fulltext/pdf</uri></json:item><json:item><original>false</original><mimetype>application/zip</mimetype><extension>zip</extension><uri>https://api.istex.fr/document/755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8/fulltext/zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/document/755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a">Validation of cardiac accelerometer sensor measurements</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher>IOP Publishing</publisher><availability><p>IOP</p></availability><date>2009</date></publicationStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a">Validation of cardiac accelerometer sensor measurements</title><author><persName><forename type="first">Espen W</forename><surname>Remme</surname></persName><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation><affiliation>E-mail:espen.remme@medisin.uio.no</affiliation></author><author><persName><forename type="first">Lars</forename><surname>Hoff</surname></persName><affiliation>Vestfold University College, Tnsberg, Norway</affiliation></author><author><persName><forename type="first">Per Steinar</forename><surname>Halvorsen</surname></persName><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation></author><author><persName><forename type="first">Edvard</forename><surname>Nrum</surname></persName><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation></author><author><persName><forename type="first">Helge</forename><surname>Skulstad</surname></persName><affiliation>Department of Cardiology, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation></author><author><persName><forename type="first">Lars A</forename><surname>Fleischer</surname></persName><affiliation>Vestfold University College, Tnsberg, Norway</affiliation></author><author><persName><forename type="first">Ole Jakob</forename><surname>Elle</surname></persName><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation></author><author><persName><forename type="first">Erik</forename><surname>Fosse</surname></persName><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation></author></analytic><monogr><title level="j">Physiological Measurement</title><title level="j" type="abbrev">Physiol. Meas.</title><idno type="pISSN">0967-3334</idno><idno type="eISSN">1361-6579</idno><imprint><publisher>IOP Publishing</publisher><date type="published" when="2009"></date><biblScope unit="volume">30</biblScope><biblScope unit="issue">12</biblScope><biblScope unit="page" from="1429">1429</biblScope><biblScope unit="page" to="1444">1444</biblScope><biblScope unit="production">Printed in the UK</biblScope></imprint></monogr><idno type="istex">755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8</idno><idno type="DOI">10.1088/0967-3334/30/12/010</idno><idno type="PII">S0967-3334(09)21426-2</idno><idno type="articleID">321426</idno><idno type="articleNumber">010</idno></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2009</date></creation><langUsage><language ident="en">en</language></langUsage><abstract><p>In this study we have investigated the accuracy of an accelerometer sensor designed for the measurement of cardiac motion and automatic detection of motion abnormalities caused by myocardial ischaemia. The accelerometer, attached to the left ventricular wall, changed its orientation relative to the direction of gravity during the cardiac cycle. This caused a varying gravity component in the measured acceleration signal that introduced an error in the calculation of myocardial motion. Circumferential displacement, velocity and rotation of the left ventricular apical region were calculated from the measured acceleration signal. We developed a mathematical method to separate translational and gravitational acceleration components based on a priori assumptions of myocardial motion. The accuracy of the measured motion was investigated by comparison with known motion of a robot arm programmed to move like the heart wall. The accuracy was also investigated in an animal study. The sensor measurements were compared with simultaneously recorded motion from a robot arm attached next to the sensor on the heart and with measured motion by echocardiography and a video camera. The developed compensation method for the varying gravity component improved the accuracy of the calculated velocity and displacement traces, giving very good agreement with the reference methods.</p></abstract><textClass><keywords scheme="keyword"><list><head>keywords</head><item><term>biomedical sensor</term></item><item><term>accelerometer</term></item><item><term>cardiac surgery</term></item><item><term>myocardial ischaemia</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2009">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><original>false</original><mimetype>text/plain</mimetype><extension>txt</extension><uri>https://api.istex.fr/document/755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8/fulltext/txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus iop not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="ISO-8859-1"</istex:xmlDeclaration><istex:docType SYSTEM="http://ej.iop.org/dtd/iopv1_5_2.dtd" name="istex:docType"></istex:docType><istex:document><article artid="pm321426"><article-metadata><jnl-data jnlid="pm"><jnl-fullname>Physiological Measurement</jnl-fullname><jnl-abbreviation>Physiol. Meas.</jnl-abbreviation><jnl-shortname>PM</jnl-shortname><jnl-issn>0967-3334</jnl-issn><jnl-coden>PMEAE3</jnl-coden><jnl-imprint>IOP Publishing</jnl-imprint><jnl-web-address>stacks.iop.org/PM</jnl-web-address></jnl-data><volume-data><year-publication>2009</year-publication><volume-number>30</volume-number></volume-data><issue-data><issue-number>12</issue-number><coverdate>December 2009</coverdate></issue-data><article-data><article-type type="paper" sort="regular"></article-type><type-number type="paper" artnum="010">10</type-number><article-number>321426</article-number><first-page>1429</first-page><last-page>1444</last-page><length>16</length><pii>S0967-3334(09)21426-2</pii><doi>10.1088/0967-3334/30/12/010</doi><copyright>2009 Institute of Physics and Engineering in Medicine</copyright><ccc>0967-3334/09/121429+16$30.00</ccc><printed>Printed in the UK</printed><features colour="none" mmedia="no" suppdata="yes"></features><definition></definition></article-data></article-metadata><header><title-group><title>Validation of cardiac accelerometer sensor measurements</title><short-title>Validation of cardiac accelerometer sensor measurements</short-title><ej-title>Validation of cardiac accelerometer sensor measurements</ej-title></title-group><author-group><author address="pm321426ad1" email="pm321426ea1"><first-names>Espen W</first-names><second-name>Remme</second-name></author><author address="pm321426ad2"><first-names>Lars</first-names><second-name>Hoff</second-name></author><author address="pm321426ad1"><first-names>Per Steinar</first-names><second-name>Halvorsen</second-name></author><author address="pm321426ad1"><first-names>Edvard</first-names><second-name>Nærum</second-name></author><author address="pm321426ad3"><first-names>Helge</first-names><second-name>Skulstad</second-name></author><author address="pm321426ad2"><first-names>Lars A</first-names><second-name>Fleischer</second-name></author><author address="pm321426ad1"><first-names>Ole Jakob</first-names><second-name>Elle</second-name></author><author address="pm321426ad1"><first-names>Erik</first-names><second-name>Fosse</second-name></author></author-group><address-group><address id="pm321426ad1"><orgname>The Interventional Centre, Oslo University Hospital, Rikshospitalet</orgname>, Oslo, <country>Norway</country></address><address id="pm321426ad2"><orgname>Vestfold University College</orgname>, Tønsberg, <country>Norway</country></address><address id="pm321426ad3"><orgname>Department of Cardiology, Oslo University Hospital, Rikshospitalet</orgname>, Oslo, <country>Norway</country></address><e-address id="pm321426ea1"><email mailto="espen.remme@medisin.uio.no">espen.remme@medisin.uio.no</email></e-address></address-group><history received="11 June 2009" accepted="2 October 2009" online="12 November 2009"></history><abstract-group><abstract><heading>Abstract</heading><p indent="no">In this study we have investigated the accuracy of an accelerometer sensor designed for the measurement of cardiac motion and automatic detection of motion abnormalities caused by myocardial ischaemia. The accelerometer, attached to the left ventricular wall, changed its orientation relative to the direction of gravity during the cardiac cycle. This caused a varying gravity component in the measured acceleration signal that introduced an error in the calculation of myocardial motion. Circumferential displacement, velocity and rotation of the left ventricular apical region were calculated from the measured acceleration signal. We developed a mathematical method to separate translational and gravitational acceleration components based on <italic>a priori</italic> assumptions of myocardial motion. The accuracy of the measured motion was investigated by comparison with known motion of a robot arm programmed to move like the heart wall. The accuracy was also investigated in an animal study. The sensor measurements were compared with simultaneously recorded motion from a robot arm attached next to the sensor on the heart and with measured motion by echocardiography and a video camera. The developed compensation method for the varying gravity component improved the accuracy of the calculated velocity and displacement traces, giving very good agreement with the reference methods.</p></abstract></abstract-group><classifications><keywords><keyword>biomedical sensor</keyword><keyword>accelerometer</keyword><keyword>cardiac surgery</keyword><keyword>myocardial ischaemia</keyword></keywords></classifications></header><body numbering="bysection" refstyle="alphabetic"><sec-level1 id="pm321426s1" label="1"><heading>Introduction</heading><p indent="no">Patients undergoing cardiac surgery may experience myocardial dysfunction or ischaemia during surgery or the first few days following the operation (Comunale <italic>et al</italic> <cite linkend="pm321426bib02" show="year">1998</cite>). Myocardial ischaemia is associated with increased risk of myocardial infarction and increased mortality (Landesberg <cite linkend="pm321426bib14" show="year">2005</cite>). Therefore, a sensor that continuously monitors cardiac function and automatically detects ischaemia during this period could be beneficial. Myocardial dysfunction and ischaemia are associated with motion abnormalities (Tennant and Wiggers <cite linkend="pm321426bib17" show="year">1935</cite>, Urheim <italic>et al</italic> <cite linkend="pm321426bib18" show="year">2000</cite>). A miniaturized motion sensor attached to the cardiac wall may continuously monitor myocardial motion and automatically detect abnormalities. Myocardial displacement, velocity and acceleration may be used as measures of cardiac motion. By measuring one of these, the two others may be derived by integration or derivation, e.g. velocity and displacement may be calculated from the time integral and double time integral, respectively, of a measured acceleration signal with known initial conditions.</p><p>We have previously developed and tested a prototype three-axis accelerometer sensor for the measurement of cardiac motion. The tests were performed both in animals and humans during baseline and ischaemic conditions. The measurements from the accelerometer showed qualitative and quantitative differences that could be used to distinguish the different conditions (Elle <italic>et al</italic> <cite linkend="pm321426bib04" show="year">2005</cite>, Halvorsen <italic>et al</italic> <cite linkend="pm321426bib06" show="year">2008</cite>, <cite linkend="pm321426bib07" show="year">2009</cite>).</p><p>However, a validation test of the accelerometer's ability to measure true myocardial motion has not been systematically performed. In this respect the influence of gravity on the measurements has not been studied. Acceleration and gravitation cannot be distinguished. An axis of the accelerometer that has a component along the vertical direction, i.e. not strictly horizontal, will measure an acceleration equal to its component of gravity, which comes in addition to acceleration resulting from translational motion of the accelerometer. As the accelerometer approximately starts at and returns to the same position during one cardiac cycle, it is assumed that the average translational acceleration is zero over one cardiac cycle. A static component of gravity along an axis will result in a non-zero average acceleration. The pure translational acceleration may then be found by subtracting the non-zero average. This is the principle used in the high-pass filter and integration method to obtain velocity and displacement curves from accelerometers on the heart described by Hoff <italic>et al</italic> (<cite linkend="pm321426bib10" show="year">2004</cite>). However, a static component of gravity requires the axes of the accelerometer to maintain the same orientation relative to the vertical direction throughout the cardiac cycle. Hoff <italic>et al</italic> (<cite linkend="pm321426bib10" show="year">2004</cite>) mentioned that rotation of the sensor in the gravitational field may influence the measurements, but did not make any attempt to investigate this quantitatively. The myocardial motion is a complex three-dimensional movement that varies regionally around the heart wall. The heart surface is not flat, but shaped approximately as a truncated ellipsoid that is almost circular in the short axis. Thus, during large deformations, an accelerometer that is attached to the myocardial surface will move along a curved path and rotate its axes with respect to the vertical direction (figure <figref linkend="pm321426fig01">1</figref>). Hence, the gravity component along one axis is generally not static during the cardiac cycle, and the axes that change their vertical direction component will show a corresponding change in acceleration. Subtraction of the average acceleration over one cardiac cycle from the measured acceleration signal will then equal the pure translational acceleration plus the change in the gravity component during the cycle. Thus, the time-varying gravity component during the cardiac cycle introduces an error that has not been quantified.
<figure id="pm321426fig01"><graphic><graphic-file version="print" colour="yes" format="EPS" filename="images/pm321426fig01.eps" width="31pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/pm321426fig01.jpg"></graphic-file></graphic><caption id="pm321426fc01" label="Figure 1"><p indent="no">Placement and orientation of the accelerometer sensor. Panel (a) shows a picture from the animal study with the accelerometer placed in the anterior apical region of the left ventricle. The calculated motion of the accelerometer was compared with the recorded motion of the robot arm which was attached next to the sensor. Panels (b) and (c) show schematic drawings of the right (RV) and left ventricles (LV) with the orientation of the axes of the accelerometer indicated. Cardiac motion is referred to in an elliptic axis notation as demonstrated in (b). The accelerometer <italic>x</italic>-axis is aligned with the longitudinal direction, the <italic>y</italic>-axis with the circumferential and the <italic>z</italic>-axis with the radial. The myocardial contraction during systole causes a counter-clockwise rotation of the apical region when viewed from the apex as indicated in (c).</p></caption></figure></p><p>The purpose of this study was to validate the measurements derived from the accelerometer recordings and quantify the accuracy of the calculated velocities and displacements. A mathematical model was constructed to investigate the influence of gravity. In this theoretical model, we developed a method to separate translational and gravitational acceleration components using <italic>a priori</italic> assumptions of myocardial motion. The accelerometer was then tested in two experimental setups. First, it was attached to a robot that was programmed to move as a point on the left ventricular wall. Rotations and translations of the robot were specified with high accuracy and facilitated a means to investigate measurements from the accelerometer in a controlled environment. Secondly, the accelerometer was tested on pig hearts. The accelerometer obtained velocities and displacements were compared to measurements obtained by three other methods: (1) simultaneously recorded motion of a robot arm connected on the heart wall next to the accelerometer, (2) echocardiographically measured wall motion and (3) video recording of the cardiac motion.</p></sec-level1><sec-level1 id="pm321426s2" label="2"><heading>Methods</heading><sec-level2 id="pm321426s2-1" label="2.1"><heading>Accelerometer information</heading><p indent="no">In this study we applied an acceleration sensor constructed using a Kionix KXM52-1050 triple-axis microaccelerometer (Kionix Inc., Itacha, NY, USA). This accelerometer was mounted on an alumina substrate and encapsulated in silicone. To reduce noise, the bandwidth was limited to 100 Hz by adding 47 nF capacitors to the outputs. The manufacturing and characterization of these sensors have been described in detail previously (Imenes <italic>et al</italic> <cite linkend="pm321426bib11" show="year">2007</cite>). Selected sensors were calibrated by rotating them slowly in the gravitational field finding the highest and lowest reading, corresponding to +1 <italic>g</italic> and −1 <italic>g</italic>, and assuming a linear relation between acceleration and output voltage. This provided estimates for sensitivity, measured as mV/<italic>g</italic>, and offset, defined as the voltage at zero acceleration. The results are given in table <tabref linkend="pm321426tab01">1</tabref>. Some variation was found between the accelerometer axes, while much smaller variations were observed between the individual accelerometers. We believe that the measured variations between sensors were mainly a consequence of our calibration procedure, rather than reflecting real variations between the accelerometers. The data in table <tabref linkend="pm321426tab01">1</tabref> were used to calibrate all our measurements.
<table id="pm321426tab01" frame="topbot"><caption id="pm321426tc01" label="Table 1"><p indent="no">Calibration results from five accelerometers.</p></caption><tgroup cols="5"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><colspec colnum="5" colname="col5" align="left"></colspec><spanspec spanname="2to3" namest="col2" nameend="col3" align="center"></spanspec><spanspec spanname="4to5" namest="col4" nameend="col5" align="center"></spanspec><thead><row><entry></entry><entry spanname="2to3">Sensitivity (mV/<italic>g</italic>)</entry><entry spanname="4to5">Offset (mV)</entry></row><row><entry></entry><entry spanname="2to3"></entry><entry spanname="4to5"></entry></row><row><entry>Axis</entry><entry>Mean</entry><entry>SD</entry><entry>Mean</entry><entry>SD</entry></row></thead><tbody><row><entry><italic>x</italic></entry><entry>914</entry><entry>8</entry><entry>2380</entry><entry>40</entry></row><row><entry><italic>y</italic></entry><entry>903</entry><entry>2</entry><entry>2400</entry><entry>10</entry></row><row><entry><italic>z</italic></entry><entry>817</entry><entry>3</entry><entry>2570</entry><entry>30</entry></row></tbody></tgroup></table></p></sec-level2><sec-level2 id="pm321426s2-2" label="2.2"><heading>Heart geometry and cardiac motion</heading><p indent="no">Knowledge of the geometry and typical motion patterns of the heart is a prerequisite for understanding cardiac accelerometer measurements and designing realistic tests for the accelerometer. Figure <figref linkend="pm321426fig01">1</figref> demonstrates typical placement of the accelerometer on the anterior surface in the apical region of the left ventricle (LV). The motion of the myocardium is decomposed into longitudinal, circumferential and radial motion as illustrated in the figure. The axes of the accelerometer are aligned with the cardiac coordinate system with the <italic>x</italic>-axis parallel to the longitudinal direction, the <italic>y</italic>-axis parallel to the circumferential direction and the <italic>z</italic>-axis parallel to the radial direction. Note that circumferential motion corresponds to a rotation of the left ventricle around its long axis. The rotation of the LV apical region is homogenous and about 11 ± 5° in the <italic>in situ</italic> healthy human heart, while rotation may be significantly reduced and vary regionally in the ischaemic heart (Helle-Valle <italic>et al</italic> <cite linkend="pm321426bib09" show="year">2009</cite>). In addition to rotation, normal myocardial motion is characterized by longitudinal and circumferential shortening and wall thickening. Normally, longitudinal shortening is seen by a descent of the valve plane towards the apex. However, during bypass surgery, the heart is taken out of the pericardium and the apex and base may sometimes move towards each other and effectively cause less longitudinal displacement of the region in between (Skulstad <italic>et al</italic> <cite linkend="pm321426bib16" show="year">2004</cite>). Ejection of blood out of the ventricle is facilitated by a contraction of the longitudinal and radial cavity dimensions. The radial dimension is reduced by both circumferential shortening and wall thickening. The endocardial surface exhibits large radial motions during the contraction and expansion cycle of the ventricle. In comparison, the radial motion on the epicardial surface is reduced due to the wall thickening and thinning that occur during the phases when the endocardial surface moves inward and outward, respectively. Consequently, the dominant motion of the LV epicardial apical region, where the accelerometer is placed, is circumferential displacement or rotation.</p><p>During cardiac surgery, the patient normally lies in a supine position. A similar position was obtained in the animal study with the LV longitudinal axis approximately in the horizontal direction. Thus, the <italic>y</italic> and <italic>z</italic> axes will change their orientation relative to the vertical direction by the rotational motion of the LV apex resulting in a varying gravitational component during the cardiac cycle along the <italic>y</italic> and <italic>z</italic> axes. The longitudinal motion is relatively small compared to the radius of curvature in the longitudinal direction and hence, the change of the <italic>x</italic>-axis relative to the vertical axis is small.</p></sec-level2><sec-level2 id="pm321426s2-3" label="2.3"><heading>Theoretical model of myocardial motion measured by the accelerometer</heading><p indent="no">Since rotation is the major motion component in the LV apical region, we developed a theoretical model of measured acceleration from a sensor moving along a circular path as illustrated in figure <figref linkend="pm321426fig02">2</figref>. The model assumes that the rotation at the point where the accelerometer is fastened can be described as a translational movement around a fixed centre point, with constant radius of curvature. The resulting measured accelerations in the three axes of the sensor are shown in equation (<eqnref linkend="pm321426eqn01a">1<italic>a</italic></eqnref>) (Resnick and Halliday <cite linkend="pm321426bib15" show="year">1966</cite>) as a function of radius (<italic>R</italic>), gravity (<italic>g</italic>), rotation angle (α(<italic>t</italic>)) and the angle β which is the angle between the long axis/rotational axis and the horizontal direction as shown in the right panel of figure <figref linkend="pm321426fig02">2</figref>:
<eqn-group id="pm321426eqngrp01"><display-eqn id="pm321426eqn01a" eqnnum="1a"></display-eqn><display-eqn id="pm321426eqn01b" eqnnum="1b"></display-eqn><display-eqn id="pm321426eqn01c" eqnnum="1c"></display-eqn></eqn-group>The first term in the <italic>y</italic> acceleration is the translational acceleration while the second term is the time-varying gravitational component caused by the rotation of the accelerometer in the gravitational field. The negative and positive sign of the gravitational component in equation (<eqnref linkend="pm321426eqn01a">1<italic>a</italic></eqnref>) may be derived from examples of no movement and free fall motion. An accelerometer at rest oriented with its <italic>y</italic>-axis aligned downwards in the direction of <italic>g</italic> (α = β = 0°) will measure <italic>a<sub>y</sub></italic> = −<italic>g</italic> because it ‘feels’ that it is accelerated upwards (i.e. in the negative <italic>y</italic>-direction) as opposed to a free fall when it would ‘feel’ weightless and measure <italic>a<sub>y</sub></italic> = 0 <italic>g</italic>.
<figure id="pm321426fig02"><graphic><graphic-file version="print" format="EPS" filename="images/pm321426fig02.eps" width="26pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/pm321426fig02.jpg"></graphic-file></graphic><caption id="pm321426fc02" label="Figure 2"><p indent="no">Schematic drawing of the motion path of an accelerometer sensor placed in the apical region of the left ventricle (LV). As the apex rotates about its long axis (typically ∼10°) the sensor follows a circular path. In the left panel, the LV is oriented with its long axis in the horizontal direction pointing out of the drawing, representative of a patient lying in a supine position. The direction of gravity is indicated by <italic>g</italic>, <italic>R</italic> is the short-axis radius and α(<italic>t</italic>) is the time-varying angle of the orientation of the accelerometer <italic>z</italic>-axis, which varies with apical rotation. The right panel illustrates a situation where the long axis is oriented with an angle β with respect to the horizontal plane, representative of a sitting patient. Positive β defined as indicated.</p></caption></figure></p><p>If α(<italic>t</italic>) and β are known, the true translational motion may be found by subtracting the last term from the measured acceleration in equation (<eqnref linkend="pm321426eqn01b">1<italic>b</italic></eqnref>). In the general <italic>in vivo</italic> case where α(<italic>t</italic>) is unknown, an initial estimate of α and β may be made based on average accelerations during the cardiac cycle:
<eqn-group id="pm321426eqngrp02"><display-eqn id="pm321426eqn02a" eqnnum="2a"></display-eqn><display-eqn id="pm321426eqn02b" eqnnum="2b"></display-eqn></eqn-group>where <inline-eqn></inline-eqn> and <inline-eqn></inline-eqn> denote averaging over one cardiac cycle. The angle β<sub>0</sub> is assumed to be constant while α<sub>0</sub> is the average angle over one cardiac cycle between the horizontal axis and the accelerometer <italic>z</italic>-axis. Since the rotation angle is relatively small (11 ± 5°; Helle-Valle <italic>et al</italic> <cite linkend="pm321426bib09" show="year">2009</cite>), we may describe α(<italic>t</italic>) as a small variation around the average angle and derive a Taylor expansion for cos(α(<italic>t</italic>)):
<eqn-group id="pm321426eqngrp03"><display-eqn id="pm321426eqn03a" lines="multiline" eqnnum="3a"></display-eqn><display-eqn id="pm321426eqn03b" eqnnum="3b"></display-eqn><display-eqn id="pm321426eqn03c" eqnnum="3c"></display-eqn></eqn-group>This is inserted into equation (<eqnref linkend="pm321426eqn01b">1<italic>b</italic></eqnref>), giving
<display-eqn id="pm321426eqn04" lines="multiline" eqnnum="4"></display-eqn>where <italic>g<sub>p</sub></italic> is the static component of gravity parallel to the <italic>y</italic>-direction and <italic>g<sub>n</sub></italic> is the static component normal to the <italic>y</italic>-direction, defined by
<eqn-group id="pm321426eqngrp04"><display-eqn id="pm321426eqn05a" eqnnum="5a"></display-eqn><display-eqn id="pm321426eqn05b" eqnnum="5b"></display-eqn></eqn-group>We may now solve for γ(<italic>t</italic>) by first adding <italic>g<sub>p</sub></italic> to equation (<eqnref linkend="pm321426eqn04">4</eqnref>). Subsequently, the differential equation is most easily solved in the frequency domain through a Fourier transform (the symbol <inline-eqn></inline-eqn> denotes the Fourier transform of the quantity <italic>x</italic>: <inline-eqn></inline-eqn>):
<eqn-group id="pm321426eqngrp05"><display-eqn id="pm321426eqn06a" eqnnum="6a"></display-eqn><display-eqn id="pm321426eqn06b" eqnnum="6b"></display-eqn><display-eqn id="pm321426eqn06c" eqnnum="6c"></display-eqn><display-eqn id="pm321426eqn06d" eqnnum="6d"></display-eqn></eqn-group></p><p indent="no">Equation (<eqnref linkend="pm321426eqn06c">6<italic>c</italic></eqnref>) introduces a transfer function <italic>H</italic>(ω) between the acceleration <italic>a<sub>yg</sub></italic> and the angle γ. The transfer function <italic>H</italic>(ω) can be interpreted by noticing that 1/ω<sup>2</sup> corresponds to integration with time twice, and <italic>g<sub>n</sub></italic>/<italic>R</italic> is a simple scaling. Hence, 1/ω<sup>2</sup> represents the translational part, integrated twice to obtain the position <italic>R</italic>γ, while <italic>g<sub>n</sub></italic>/<italic>R</italic> represents the contribution from the rotation of the accelerometer. Equation (<eqnref linkend="pm321426eqn06c">6<italic>c</italic></eqnref>) is not stable when <italic>g<sub>n</sub></italic> approaches zero. This situation corresponds to no variation in the orientation of the gravitational vector through the motion. Since we are only interested in movements at the heart rate, around 1 Hz, frequencies substantially lower than this can safely be filtered out. A stable model was achieved by removing all frequency components below 0.5 Hz, having no influence at the frequencies present in the heart's motion, but eliminating instability artefacts for <italic>g<sub>n</sub></italic> approaching zero. The angle α(<italic>t</italic>) may be estimated (α<sub>est</sub>(<italic>t</italic>)) by inserting the solution of equation (<eqnref linkend="pm321426eqn06d">6<italic>d</italic></eqnref>) into equation (<eqnref linkend="pm321426eqn03a">3<italic>a</italic></eqnref>). Furthermore, the estimated rotation angle may be used in order to compensate for the time-varying gravity component. The pure translational acceleration of the accelerometer (<italic>a<sub>yt</sub></italic>) may be found by subtracting an approximation of the last term from the measured acceleration in equation (<eqnref linkend="pm321426eqn01b">1<italic>b</italic></eqnref>):
<display-eqn id="pm321426eqn07" lines="multiline" eqnnum="7"></display-eqn>Velocity and displacement are found by integration. Due to the cyclic motion we assume that a point on the heart returns to the same position after one heart cycle. Hence, average acceleration, velocity and displacement over one cycle or a number of cycles are assumed to be zero. This assumption is used as an initial condition in the integration procedure by subtracting the mean acceleration and mean velocity prior to integration to velocity and displacement, respectively.</p><sec-level3 id="pm321426s2-3-1" label="2.3.1"><heading>Analysis of the accelerometer accuracy using the theoretical model</heading><p indent="no">The theoretical accuracy and the artefact due to the rotation of the accelerometer in the gravitational field may be tested by the developed mathematical model of measured acceleration. We used a rotation trace measured by speckle tracking echocardiography from the animal study (solid line in figure <figref linkend="pm321426fig03" override="yes">3(a)</figref>) as an input for α(<italic>t</italic>) in equation (<eqnref linkend="pm321426eqn01a">1<italic>a</italic></eqnref>) to calculate a simulated measured acceleration signal. The rotation trace was scaled in time or amplitude to generate different signals with different heart rates and rotations. From the simulated measured acceleration signals, we calculated peak systolic rotation, displacement and velocity. The accuracies of these measurements were investigated during variations of heart rate, rotation amplitude, radius and the angles α<sub>0</sub> and β, and the results with and without the proposed compensation for the varying gravity component were compared. In addition, the accuracies of the measurements were investigated when the accelerometer was misaligned relative to the cardiac coordinate axes to simulate a situation when the sensor was incorrectly sutured onto the heart. Misalignment of the accelerometer <italic>y</italic>-axis relative to the circumferential axis was achieved by rotating the accelerometer by 15° around the radial axis and in another case by rotating it by 15° around the longitudinal axis.
<figure id="pm321426fig03"><graphic><graphic-file version="print" format="EPS" filename="images/pm321426fig03.eps" width="31pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/pm321426fig03.jpg"></graphic-file></graphic><caption id="pm321426fc03" label="Figure 3"><p indent="no">Robot experiment: traces from the comparison of the accelerometer derived measurements with the known motion of the robot. Robot motion is shown with dashed lines. The accelerometer rotation (α(<italic>t</italic>)) and the displacement and velocity traces with compensation for the varying gravity component are shown with solid lines. The results without compensation substantially overestimated the true motion and are indicated with dotted lines that go outside the scale of this figure. The traces correspond to the test in the first row of table <tabref linkend="pm321426tab03">3</tabref>.</p></caption></figure></p></sec-level3></sec-level2><sec-level2 id="pm321426s2-4" label="2.4"><heading>Comparison of accelerometer measurements with known motion of a robot</heading><p indent="no">We tested the accuracy of the accelerometer in an experimental setup where the accelerometer was mounted as to reproduce the motion described in the theoretical model. The accelerometer was attached to an arm of a programmable robot (PHANTOM Omni haptic device, Sensable Technologies, Woburn, MA, USA). The robot arm was programmed to follow a circular path with a rotation angle, α(<italic>t</italic>), similar to the one used in the theoretical model and hence as if the arm moved like a point on the LV epicardial apical region. The accelerometer was attached with the <italic>y</italic>-axis aligned tangential to the circumferential motion of the robot arm. We recorded the robot motion at a sample rate of 1000 Hz. According to the specification data of the robot, its nominal position resolution was ∼0.055 mm. The calculated rotation, displacement and velocity of the accelerometer sensor were compared to the recorded motion of the robot arm. The accelerometer measurements were acquired at a sample rate of 500 Hz, so the robot recordings were decimated by a factor of 2 prior to comparisons. We compared peak systolic values of the different measures. To evaluate similarity of curve shapes between the robot and accelerometer, we calculated the root mean square error (RMSE) between the curves over one heart cycle as
<display-eqn id="pm321426eqn08" eqnnum="8"></display-eqn>where <italic>x<sub>nR</sub></italic> is the quantity <italic>x</italic> measured by the robot, and <italic>x<sub>nA</sub></italic> is <italic>x</italic> estimated from the accelerometer measurements using the described model, and the sum is taken over the <italic>N</italic> samples in one heart cycle. The comparisons were carried out for different values of heart rate, rotation amplitude, radius and the angles α<sub>0</sub> and β with and without the compensation for the varying gravity component.</p></sec-level2><sec-level2 id="pm321426s2-5" label="2.5"><heading>Animal study</heading><p indent="no">Five pigs were anaesthetized and surgically prepared as previously described (Halvorsen <italic>et al</italic> <cite linkend="pm321426bib07" show="year">2009</cite>). The study was approved by the Institutional Animal Care and Use Committee. The animals were supplied by the Centre for Comparative Medicine, Rikshospitalet University Hospital, Oslo, Norway. An accelerometer was fixed by sutures on the epicardial surface in the LV apical anterior region with its axes oriented as described above. The tip of a robot arm (the same robot as previously described) was fixed by sutures next to the accelerometer as shown in figure <figref linkend="pm321426fig01" override="yes">1(a)</figref>. The three-dimensional position of the robot arm was recorded simultaneously with the accelerometer measurements. The motion along the accelerometer <italic>y</italic>-axis was compared with the recorded motion of the robot. The comparison was performed along the horizontal robot axis that was parallel to the LV short-axis plane. This axis of the robot was visually aligned to be as parallel as possible with the <italic>y</italic>-axis of the accelerometer which followed a more circular path and was hence not parallel with the straight robot axis during the whole cardiac cycle.</p><p>A digital video camera was used to record the rotational motion of the accelerometer as seen from an apical view, recording at 25 frames per second. A small needle was inserted into the silicone casing of the accelerometer, approximately aligned with the <italic>z</italic>-axis. On the captured images, the orientation of the needle through the cardiac cycle was manually tracked and quantified by custom-made software developed in Matlab (The MathWorks, Natick, MA, USA). The time-varying angle of the needle with respect to the horizontal direction represented the changing orientation of the accelerometer and hence the underlying apical rotation, i.e. α(<italic>t</italic>). Apical rotation was also measured using speckle tracking echocardiography (STE) of LV short-axis images obtained at the level of the accelerometer, at 70–85 frames per second (Vivid 7 and EchoPac, GE Vingmed Ultrasound, Horten, Norway). Rotations derived from needle measurements and STE were obtained in four of the animals and compared with rotation derived from the accelerometer measurements.</p><p>A video recording of the experimental setup is provided as an online supplement to this paper (available from <stacks article="this" jnl="PM" vol="30" page="1429">stacks.iop.org/PM/30/1429</stacks>). The video shows the accelerometer attached to the heart with the robot arm next to it and the inserted plastic needle pointing up in the accelerometer <italic>z</italic>-direction.</p></sec-level2></sec-level1><sec-level1 id="pm321426s3" label="3"><heading>Results</heading><sec-level2 id="pm321426s3-1" label="3.1"><heading>Analysis of the accelerometer accuracy using the theoretical model</heading><p indent="no">In the theoretical analysis, the motion along a circular path was accurately predicted when the estimated rotation angle was used to compensate for the angle-dependent gravitational component. As shown in table <tabref linkend="pm321426tab02">2</tabref>, the peak systolic rotation angle was correctly estimated in most cases with an error less than 1%. There were two cases where the error was more than 1%. If the assumed radius (i.e. the assumed short-axis radius, <italic>R</italic><sub>est</sub>) was 33% different from the true radius, the rotation angle estimate was about 10% wrong. If the initial α (α<sub>start</sub>) was around 0°, the rotation estimate was off by about 7%. The estimated displacement and velocities were accurate with the same two exceptions due to their dependence on an accurately estimated rotation angle.
<table id="pm321426tab02" frame="topbot"><caption id="pm321426tc02" label="Table 2"><p indent="no">Results from the theoretical analysis of accelerometer accuracy for motion along a circular path.</p></caption><tgroup cols="13"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><colspec colnum="5" colname="col5" align="left"></colspec><colspec colnum="6" colname="col6" align="left"></colspec><colspec colnum="7" colname="col7" align="left"></colspec><colspec colnum="8" colname="col8" align="left"></colspec><colspec colnum="9" colname="col9" align="left"></colspec><colspec colnum="10" colname="col10" align="left"></colspec><colspec colnum="11" colname="col11" align="left"></colspec><colspec colnum="12" colname="col12" align="left"></colspec><colspec colnum="13" colname="col13" align="left"></colspec><spanspec spanname="1to6" namest="col1" nameend="col6" align="center"></spanspec><spanspec spanname="8to10" namest="col8" nameend="col10" align="center"></spanspec><spanspec spanname="11to13" namest="col11" nameend="col13" align="center"></spanspec><spanspec spanname="1to13" namest="col1" nameend="col13" align="center"></spanspec><thead><row><entry spanname="1to6">Input parameters</entry><entry>Rot</entry><entry spanname="8to10">Displacement</entry><entry spanname="11to13">Velocity</entry></row><row><entry spanname="1to6"></entry><entry></entry><entry spanname="8to10"></entry><entry spanname="11to13"></entry></row><row><entry><italic>R</italic><sub>true</sub></entry><entry><italic>R</italic><sub>est</sub></entry><entry>dα</entry><entry>α<sub>start</sub></entry><entry>β</entry><entry><italic>T<sub>p</sub></italic></entry><entry>dα<sub>est</sub></entry><entry>Disp</entry><entry>Disp1</entry><entry>Disp2</entry><entry>Vel</entry><entry>Vel1</entry><entry>Vel2</entry></row><row><entry>(cm)</entry><entry>(cm)</entry><entry>(°)</entry><entry>(°)</entry><entry>(°)</entry><entry>(s)</entry><entry>(°)</entry><entry>(mm)</entry><entry>(mm)</entry><entry>(mm)</entry><entry>(cm s<sup>−1</sup>)</entry><entry>(cm s<sup>−1</sup>)</entry><entry>(cm s<sup>−1</sup>)</entry></row></thead><tbody><row><entry>3</entry><entry>3</entry><entry>10</entry><entry>90</entry><entry>0</entry><entry>0.6</entry><entry>10.0</entry><entry>−5.2</entry><entry>−5.2</entry><entry>−20.1</entry><entry>−4.5</entry><entry>−4.5</entry><entry>−13.9</entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry>3</entry><entry>3</entry><entry><inline-eqn></inline-eqn></entry><entry>90</entry><entry>0</entry><entry>0.6</entry><entry> 5.0</entry><entry>−2.6</entry><entry>−2.6</entry><entry>−10.0</entry><entry>−2.3</entry><entry>−2.3</entry><entry>−7.0</entry></row><row><entry>3</entry><entry>3</entry><entry><inline-eqn></inline-eqn></entry><entry>90</entry><entry>0</entry><entry>0.6</entry><entry>14.9</entry><entry>−7.9</entry><entry>−7.8</entry><entry>−30.0</entry><entry>−6.8</entry><entry>−6.7</entry><entry>−20.8</entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry>3</entry><entry>3</entry><entry>10</entry><entry>90</entry><entry><inline-eqn></inline-eqn></entry><entry>0.6</entry><entry>10.0</entry><entry>−5.2</entry><entry>−5.2</entry><entry>−15.7</entry><entry>−4.5</entry><entry>−4.5</entry><entry>−11.1</entry></row><row><entry>3</entry><entry>3</entry><entry>10</entry><entry>90</entry><entry><inline-eqn></inline-eqn></entry><entry>0.6</entry><entry>10.0</entry><entry>−5.2</entry><entry>−5.2</entry><entry>−5.2</entry><entry>−4.5</entry><entry>−4.5</entry><entry>−4.5</entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row></tbody><tfoot>Rot = rotation; <italic>R</italic><sub>true</sub> = true radius from centre to accelerometer sensor; <italic>R</italic><sub>est</sub> = estimated/assumed radius; dα = peak systolic rotation; α<sub>start</sub> = angle of accelerometer at beginning of heart cycle; β = constant angle of accelerometer <italic>x</italic>-axis relative to horizontal axis; <italic>T<sub>p</sub></italic> = cycle period; dα<sub>est</sub> = estimated peak systolic rotation; Disp/Disp1/Disp2 = peak systolic displacement (true/calculated using compensation for the time-varying gravity component/calculated assuming a constant gravity component); Vel/Vel1/Vel2 = peak systolic velocity (true/calculated using compensation for the time-varying gravity component/calculated assuming a constant gravity component).</tfoot></tgroup></table></p><p>In contrast, without compensation for the varying gravity component, the calculated displacements and velocities were substantially overestimated by three to four times in most cases (table <tabref linkend="pm321426tab02">2</tabref>). When α was varied around 0° (i.e. corresponding to a lateral position of the accelerometer), the overestimation was reduced to less than 20%. This is explained by the cosine function in the gravitational component; see the last term in equation (<eqnref linkend="pm321426eqn01b">1<italic>b</italic></eqnref>). An angle variation around 0° causes only minor changes in the value of the cosine, while the cosine function varies the most around 90°. Hence, the error introduced by a varying gravitational component was reduced at α<sub>start</sub> = 0° as the gravitational component varied less during the heart cycle. As β was increased from 0 to 90°, the error of the estimated displacement and velocity was reduced to 0. This is consistent with the rotational motion occurring in the horizontal plane where the gravity component is reduced to 0 in the <italic>y</italic>-direction and hence the gravitational artefact vanishes. The magnitude of the error was highly dependent on heart rate. The first term in equation (<eqnref linkend="pm321426eqn01b">1<italic>b</italic></eqnref>) is proportional to the second derivative of the rotation, hence, proportional to the square of the heart rate. This term is the true translational acceleration and as heart rate was increased the first term increased relative to the gravity component in the second term which is independent of heart rate. Therefore, the error was less at higher heart rates as the measured acceleration became dominated by the first term.</p><p>Misaligning the accelerometer <italic>y</italic>-axis by 15° with respect to the circumferential axis introduced an error ⩽4% of measured peak systolic rotation, circumferential displacement and velocity when using compensation for the time-varying gravity component. Misalignment had only a minor effect on measured peak systolic displacement and velocity derived assuming a constant gravity component which were still overestimated by three to four times.</p></sec-level2><sec-level2 id="pm321426s3-2" label="3.2"><heading>Comparison of accelerometer measurements with known robot motion</heading><p indent="no">The estimated rotation, displacements and velocities derived from the accelerometer measurements using the compensation for the varying gravity component corresponded very well with the recorded motion of the robot arm in all test cases. A representative example is shown in figure <figref linkend="pm321426fig03">3</figref>. The robot was attached to a tripod which allowed alteration of the angles α<sub>0</sub> and β. The inertia of the robot arm caused minor vibration of its attachment to the tripod as the robot arm rapidly accelerated or decelerated in order to follow the programmed rotation trace. This vibration was not recorded by the robot as the whole robot was moving and hence also the origin of its reference coordinate system. However, the accelerometer registered both the rotation of the arm and the vibration of the entire robot. The oscillations in the accelerometer measurements relative to the recorded rotation trace of the robot arm in figure <figref linkend="pm321426fig03">3</figref> are probably a result of this vibration. The oscillations were small but may have contributed to a falsely increased error when comparing the peak values. Calculated peak values are shown in table <tabref linkend="pm321426tab03">3</tabref>. The deviation between the estimated and prescribed robot rotation traces (RMSE) was 3 ± 1% of the rotation amplitude. The errors of the estimated peak rotation and peak displacement were in most cases less than 5%. The errors in peak velocity were greater, on average −0.6 ± 0.3 cm s<sup>−1</sup> or 18 ± 7%. The greater error may have been a result of the oscillation artefact as velocity is the derivative of displacement and the derivative amplifies higher frequency oscillations and noise, probably causing the larger velocity oscillations as seen in the example in figure <figref linkend="pm321426fig03">3</figref>.
<table id="pm321426tab03" frame="topbot"><caption id="pm321426tc03" label="Table 3"><p indent="no">Results from the comparison between accelerometer measurements and known robot motion.</p></caption><tgroup cols="13"><colspec colnum="1" colname="col1" align="left"></colspec><colspec colnum="2" colname="col2" align="left"></colspec><colspec colnum="3" colname="col3" align="left"></colspec><colspec colnum="4" colname="col4" align="left"></colspec><colspec colnum="5" colname="col5" align="left"></colspec><colspec colnum="6" colname="col6" align="left"></colspec><colspec colnum="7" colname="col7" align="left"></colspec><colspec colnum="8" colname="col8" align="left"></colspec><colspec colnum="9" colname="col9" align="left"></colspec><colspec colnum="10" colname="col10" align="left"></colspec><colspec colnum="11" colname="col11" align="left"></colspec><colspec colnum="12" colname="col12" align="left"></colspec><colspec colnum="13" colname="col13" align="left"></colspec><spanspec spanname="1to5" namest="col1" nameend="col5" align="center"></spanspec><spanspec spanname="8to10" namest="col8" nameend="col10" align="center"></spanspec><spanspec spanname="11to13" namest="col11" nameend="col13" align="center"></spanspec><spanspec spanname="1to13" namest="col1" nameend="col13" align="center"></spanspec><thead><row><entry spanname="1to5">Input parameters</entry><entry></entry><entry></entry><entry spanname="8to10">Displacement</entry><entry spanname="11to13">Velocity</entry></row><row><entry spanname="1to5"></entry><entry></entry><entry></entry><entry spanname="8to10"></entry><entry spanname="11to13"></entry></row><row><entry><italic>R</italic></entry><entry>dα</entry><entry>α<sub>start</sub></entry><entry>β</entry><entry><italic>T</italic><sub>p</sub></entry><entry>dα<sub>est</sub></entry><entry>α<sub>RMSE</sub></entry><entry>Disp</entry><entry>Disp1</entry><entry>Disp2</entry><entry>Vel</entry><entry>Vel1</entry><entry>Vel2</entry></row><row><entry>(cm)</entry><entry>(°)</entry><entry>(°)</entry><entry>(°)</entry><entry>(s)</entry><entry>(°)</entry><entry>(°)</entry><entry>(mm)</entry><entry>(mm)</entry><entry>(mm)</entry><entry>(cm s<sup>−1</sup>)</entry><entry>(cm s<sup>−1</sup>)</entry><entry>(cm s<sup>−1</sup>)</entry></row></thead><tbody><row><entry>2.5</entry><entry>21</entry><entry>90</entry><entry>0</entry><entry>1.0</entry><entry>21.6</entry><entry>0.3</entry><entry>−9.0</entry><entry>−9.4</entry><entry>−82.5</entry><entry>−3.5</entry><entry>−4.2</entry><entry>−27.2</entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry>2.5</entry><entry><inline-eqn></inline-eqn></entry><entry>90</entry><entry>0</entry><entry>1.0</entry><entry>11.3</entry><entry>0.3</entry><entry>−4.7</entry><entry>−4.9</entry><entry>−49.5</entry><entry>−2.3</entry><entry>−2.7</entry><entry>−17.3</entry></row><row><entry>2.5</entry><entry><inline-eqn></inline-eqn></entry><entry>90</entry><entry>0</entry><entry>1.0</entry><entry>28.6</entry><entry>0.6</entry><entry>−12.1</entry><entry>−12.5</entry><entry>−106.1</entry><entry>−4.8</entry><entry>−5.2</entry><entry>−34.7</entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry>2.5</entry><entry>21</entry><entry>90</entry><entry><inline-eqn></inline-eqn></entry><entry>1.0</entry><entry>21.9</entry><entry>0.4</entry><entry>−9.0</entry><entry>−9.5</entry><entry>−74.6</entry><entry>−3.6</entry><entry>−4.2</entry><entry>−24.5</entry></row><row><entry>2.5</entry><entry>20</entry><entry>90</entry><entry><inline-eqn></inline-eqn></entry><entry>1.0</entry><entry>22.2</entry><entry>0.5</entry><entry>−8.8</entry><entry>−9.7</entry><entry>−48.4</entry><entry>−3.5</entry><entry>−4.1</entry><entry>−16.2</entry></row><row><entry>2.5</entry><entry>19</entry><entry>90</entry><entry><inline-eqn></inline-eqn></entry><entry>1.0</entry><entry>22.1</entry><entry>0.9</entry><entry>−8.3</entry><entry>−9.7</entry><entry>−6.3</entry><entry>−3.4</entry><entry>−3.9</entry><entry>−3.7</entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row><row><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry><entry><inline-eqn></inline-eqn></entry></row></tbody><tfoot><italic>R</italic> = radius from rotation centre to accelerometer sensor; dα = peak systolic rotation; α<sub>start</sub> = angle of accelerometer at beginning of heart cycle; β = constant angle of accelerometer <italic>x</italic>-axis relative to horizontal axis; <italic>T<sub>p</sub></italic> = cycle period; dα<sub>est</sub> = peak systolic rotation; α<sub>RMSE</sub> = root mean square difference between measured and estimated rotation curves over one heart cycle; Disp/Disp1/Disp2 = peak systolic displacement (robot/calculated using compensation for the time-varying gravity component/calculated assuming a constant gravity component); Vel/Vel1/Vel2 = peak systolic velocity (robot/calculated using compensation for the time-varying gravity component/calculated assuming a constant gravity component).</tfoot></tgroup></table></p><p>Without compensation for the time-varying gravity component, displacement and velocity were several times overestimated compared to the recorded robot motion. The cycle time in this experiment was longer than in the theoretical model, 1.0 versus 0.6 s, corresponding to 60 BPM versus 100 BPM. Thus, the overestimation was higher due to the dependence of the error on heart rate. Consistent with the theoretical analysis, the error was reduced when β or α<sub>start</sub> was reduced. It was not possible with the robot setup to decrease α<sub>start</sub> to less than 45°.</p></sec-level2><sec-level2 id="pm321426s3-3" label="3.3"><heading>Animal study</heading><p indent="no">The measured displacement and velocity traces from the pig hearts obtained by the accelerometer using compensation for the time-varying gravity component showed good agreement with the recorded traces from the robot as illustrated in figure <figref linkend="pm321426fig04">4</figref>. Figure <figref linkend="pm321426fig05">5</figref> shows peak systolic values from each of the five animals. The average difference of peak systolic displacement and velocity was 7 ± 6% and 3 ± 17%, respectively. The average of the root mean square difference between the displacement curves was 1.1 ± 0.4 mm. Accelerometer displacements and velocities calculated assuming a constant gravity component were substantially overestimated as shown in figures <figref linkend="pm321426fig04">4</figref> and <figref linkend="pm321426fig05">5</figref>.
<figure id="pm321426fig04"><graphic><graphic-file version="print" format="EPS" filename="images/pm321426fig04.eps" width="31pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/pm321426fig04.jpg"></graphic-file></graphic><caption id="pm321426fc04" label="Figure 4"><p indent="no">Animal study: traces from the comparison of the accelerometer-derived measurements with the known recorded motion of the robot attached to the heart. The root mean square difference between the displacement curves was 1.2 mm for this animal (animal #II in figure <figref linkend="pm321426fig05">5</figref>). Robot displacement and velocity are shown with dashed lines. The accelerometer displacement and velocity traces with compensation for the varying gravity component are shown with solid lines and without compensation with dotted lines. The right panel shows acceleration measured by the accelerometer: the raw signal from the accelerometer is shown with a dotted line, the estimated slowly varying gravity component is shown with a dashed line and the acceleration after compensation for the estimated varying gravity component is shown with a solid line. The slowly varying gravity component has roughly the shape of a half sinusoidal wave and has lower amplitude than the other two acceleration signals which go outside the scale of this plot.</p></caption></figure><figure id="pm321426fig05"><graphic><graphic-file version="print" format="EPS" filename="images/pm321426fig05.eps" width="21pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/pm321426fig05.jpg"></graphic-file></graphic><caption id="pm321426fc05" label="Figure 5"><p indent="no">Animal study: peak systolic displacement and velocity in the five different animals as measured by the robot (Robot), accelerometer using compensation for the varying gravity component (Comp) and accelerometer without the compensation (Not comp). The accelerometer motion calculated by applying the compensation agreed very well with the robot, while without the compensation the motion was substantially overestimated.</p></caption></figure></p><p>A regression analysis showed a moderate correlation (<italic>R</italic> = 0.61) between peak systolic rotations measured by the accelerometer and speckle tracking echocardiography and a very good correlation (<italic>R</italic> = 0.99) between the accelerometer and the video needle measurements. On average the accelerometer underestimated peak systolic rotation by 4.3 ± 5.4 and 0.8 ± 0.2° compared to rotation obtained by the two methods, respectively. Measurements of the time to peak systolic rotation from the start of the ECG QRS complex showed that the peak was on average delayed for 38 ± 76 ms compared to the ultrasound recording. The comparison of time to peak systolic rotation was not performed between the accelerometer and needle rotation due to the lack of the ECG signal on the video-camera-recorded needle motion and the long sampling interval (40 ms) of the camera. Figure <figref linkend="pm321426fig06">6</figref> shows measured rotation traces by the three different methods.
<figure id="pm321426fig06"><graphic><graphic-file version="print" format="EPS" filename="images/pm321426fig06.eps" width="12pc"></graphic-file><graphic-file version="ej" format="JPEG" filename="images/pm321426fig06.jpg"></graphic-file></graphic><caption id="pm321426fc06" label="Figure 6"><p indent="no">Animal study: left ventricular apical rotation traces from the accelerometer measurement (solid line), speckle tracking echocardiography (dotted line) and the video recordings of the needle inserted into the silicone casing of the accelerometer (dashed line).</p></caption></figure></p></sec-level2></sec-level1><sec-level1 id="pm321426s4" label="4"><heading>Discussion</heading><p indent="no">In this study we have investigated the accuracy of the accelerometer sensor to measure myocardial motion, specifically circumferential displacement (rotation) and velocity of the LV epicardial apical region. The derived displacements and velocities showed very good agreement with the reference methods as long as the gravitational component was correctly accounted for in the acceleration measurements.</p><p>The axes of the accelerometer changed their orientation with respect to the vertical direction during the cardiac cycle and the time-varying gravity component looked roughly like a half sinusoidal wave over one cardiac cycle (figure <figref linkend="pm321426fig04">4</figref>, right panel). The variation in the gravity component occurred at a low frequency relative to the rapidly oscillating translational acceleration. In the circumferential direction the slowly varying gravity component caused a substantial effect when it was integrated to velocity and displacement, resulting in typically three to four times overestimation of these measures. The magnitude or the error was highly sensitive to heart rate, decreasing with increasing heart rate. The error was also reduced when the angle β was increased, i.e. when the long axis of the left ventricle was aligned more in the vertical direction, and when the angle α<sub>0</sub> was around 0°, corresponding to a lateral placement of the accelerometer in the normal supine position of a patient. In the typical clinical situation, the patient lies in a supine position with the accelerometer placed in the LV apical antero-lateral region. In this situation, the changing gravity component will dominate the calculation of circumferential displacement and velocity and effectively amplify these measures.</p><p>We developed an algorithm that removed the varying gravity component from the accelerometer measurements by assuming that the accelerometer was moving along a part of the perimeter of a circle. The results from the theoretical analysis and the results from the test where the accelerometer was attached to a robot arm moving along a circular path showed that the motion was accurately measured using this compensation. The theoretical analysis and robot test showed that the compensation should work also if the patient is oriented in other positions than in the supine, e.g. if the patient is sitting or standing. This was facilitated through equation (<eqnref linkend="pm321426eqn02a">2<italic>a</italic></eqnref>) which estimates the orientation of the accelerometer (and patient). This estimation is based on the assumption that the average translational acceleration is zero over one heart beat and a non-zero average acceleration is equal to the average gravity component over the cardiac cycle. However, the assumption requires that the patient is not moving as movement of the patient during the recording may violate the assumption of a non-zero average translational acceleration. The accelerometer measured circumferential displacement and velocity with high accuracy also in the pig hearts. This indicates that the gravity compensation worked in the real heart and supports the assumption that the LV epicardial apical region moves approximately along a circular path. However, this study was limited to five animals during baseline conditions and a general validity of this assumption requires a quantitative study in hearts with different loading and disease states.</p><p>The main purpose of the accelerometer sensor is to work as an automatic ischaemia detector. Its ability to measure displacement and velocity exactly is of secondary importance. The varying gravity component amplifies the calculated displacement and velocity in the circumferential direction. Hence, these measures may be more sensitive to variations in apical rotation when they are calculated without compensation for the varying gravity component. For example, the results in table <tabref linkend="pm321426tab02">2</tabref> showed that a reduction in the rotation amplitude from 10° to 5° (rows 1 and 4) decreased the true displacement and velocity by 2.6 mm and 2.2 cm s<sup>−1</sup>, respectively, while without the compensation they changed by 10.1 mm and 6.9 cm s<sup>−1</sup>, i.e. the magnitude of the change was three to four times larger without the compensation, perhaps making it more sensitive to changes in rotation. Previous studies have demonstrated a reduction of apical rotation during acute ischaemia both in animals (Kroeker <italic>et al</italic> <cite linkend="pm321426bib13" show="year">1995</cite>) and humans (Knudtson <italic>et al</italic> <cite linkend="pm321426bib12" show="year">1997</cite>). This indicates that a sensor which measures rotation may be suitable for the detection of ischaemia and could possibly work both with and without the compensation. Our current study clarifies the components of the measured accelerometer signal which is a combination of translational motion and rotation of the sensor in the gravitational field. In our ongoing development of a fully automated ischaemia detection system, we will investigate its performance using calculated motion both with and without the proposed compensation for the time-varying gravity component.</p><p>In this study the accelerometer-measured motion was validated against three reference methods: the recorded motion of a robot, rotation measured by speckle tracking echocardiography and rotation derived from video recordings of the varying angle of a needle inserted into the accelerometer. The robot recorded motion with high accuracy. However, in the animal study, the motion of the <italic>y</italic>-direction of the accelerometer, which presumably followed a curved path during the cardiac cycle, was compared to motion along a straight axis of the robot. Thus, these axes were generally not 100% parallel. Additionally, the sutures that fixated the rigid tip of the robot arm to the heart wall may have allowed some slack to occur during the cardiac cycle, effectively moving the robot arm relative to the accelerometer. Despite these inaccuracies, the measured motion traces and peak values showed very good agreement. The ultrasound speckle tracking was performed in the subendocardial region as the open chest situation caused poorer image quality and hence tracking in the subepicardial region. Rotation is highest in the endocardium and is reduced towards the epicardium where the accelerometer is placed (Buchalter <italic>et al</italic> <cite linkend="pm321426bib01" show="year">1990</cite>, Goffinet <italic>et al</italic> <cite linkend="pm321426bib05" show="year">2008</cite>). This may partly explain the underestimation of the accelerometer measurement relative to the ultrasound measurements. In our open-chest experiments the ultrasound probe was placed on the heart wall with an ultrasound gel stand-off. The gel allowed the heart wall to glide under the ultrasound probe as the heart rotated. However, the wall motion was somewhat dampened as a result of the contact with the ultrasound probe through the gel. This may have resulted in an abnormal motion situation. The rotation of the needle showed better agreement with the accelerometer-derived rotation, probably because it directly reflected the varying orientation of the accelerometer <italic>y</italic>-axis.</p><sec-level2 id="pm321426s4-1" label="4.1"><heading>Limitations</heading><p indent="no">A prerequisite for the analysis of the measurements was that the axes of the accelerometer were aligned with the cardiac coordinate system and particularly that the <italic>y</italic>-axis was parallel to the circumferential direction. This was not a problem with the large prototype accelerometer used in this study (5 × 3 × 5 mm). However, a miniaturized sensor may be more difficult to align and measurement errors may be caused by misalignment. A theoretical investigation of the effect of misaligning the orientation of the accelerometer by 15° with respect to the cardiac coordinate axes showed that the introduced error was modest (⩽4%).</p><p>The developed algorithms to calculate rotation, velocity and displacement over the cardiac cycle require detection of the start and end of each cardiac cycle. This may be achieved by recording an ECG signal simultaneously with the accelerometer measurements via an external limb lead as in the current study or more elegantly the accelerometer sensor could include an electrode for intramyocardial ECG registration. Automatic detection of ECG R-peaks is common in several medical applications (Hamilton and Tompkins <cite linkend="pm321426bib08" show="year">1986</cite>) and will provide the timing of the cardiac cycle required for automatic analysis of the accelerometer signal.</p><p>In this study we have focused on measurements along the <italic>y</italic>-axis of the accelerometer that corresponded to circumferential motion/rotation. This is the dominant type of motion in the LV apical region. However, clinical valuable information may also exist in the other two directions. Possible compensation for the influence of gravity and centripetal acceleration in the radial <italic>z</italic>-axis may be developed similar to the method described here. The accuracy and value of such a method should be investigated in further studies.</p></sec-level2><sec-level2 id="pm321426s4-2" label="4.2"><heading>Conclusions</heading><p indent="no">The validation of the accelerometer showed that the measured circumferential displacement and velocity were significantly overestimated due to addition of a time-varying gravity component to the translational acceleration, which was caused by rotation of the accelerometer as it moved with the curved left ventricular surface. When the time-varying gravity component was correctly accounted for, the accelerometer measured myocardial motion with high accuracy. The proposed algorithm for removal of the time-varying gravity component from the accelerometer signal worked well in the animal study involving healthy hearts and the estimated circumferential displacement and velocity showed good agreement with the reference methods. This indicates that the method may be used for accurate monitoring of cardiac rotational motion.</p></sec-level2></sec-level1><noteadded id="pm321426not"><heading>Disclosure</heading><p indent="no">The three-axis accelerometer is patented by Oslo University Hospital, Rikshospitalet, Oslo, Norway, for the use of monitoring myocardial function during and after cardiac surgery (Elle <italic>et al</italic> <cite linkend="pm321426bib03" show="year">2003</cite>). Engineer Ole Jakob Elle and Drs Erik Fosse and Per Steinar Halvorsen are patent holders. The company Bio-Medisinsk Innovasjon AS has the rights to commercially exploit this idea. The other authors report no conflicts of interest.</p></noteadded></body><back><references><heading>References</heading><reference-list type="alphabetic"><journal-ref id="pm321426bib01" author="Buchalter et al" year-label="1990"><authors><au><second-name>Buchalter</second-name><first-names>M B</first-names></au><au><second-name>Weiss</second-name><first-names>J L</first-names></au><au><second-name>Rogers</second-name><first-names>W J</first-names></au><au><second-name>Zerhouni</second-name><first-names>E A</first-names></au><au><second-name>Weisfeldt</second-name><first-names>M L</first-names></au><au><second-name>Beyar</second-name><first-names>R</first-names></au><au><second-name>Shapiro</second-name><first-names>E P</first-names></au></authors><year>1990</year><art-title>Noninvasive quantification of left ventricular rotational deformation in normal humans using magnetic resonance imaging myocardial tagging</art-title><jnl-title>Circulation</jnl-title><volume>81</volume><pages>1236–44</pages></journal-ref><journal-ref id="pm321426bib02" author="Comunale et al" year-label="1998"><authors><au><second-name>Comunale</second-name><first-names>M E</first-names></au><au><second-name>Body</second-name><first-names>S C</first-names></au><au><second-name>Ley</second-name><first-names>C</first-names></au><au><second-name>Koch</second-name><first-names>C</first-names></au><au><second-name>Roach</second-name><first-names>G</first-names></au><au><second-name>Mathew</second-name><first-names>J P</first-names></au><au><second-name>Herskowitz</second-name><first-names>A</first-names></au><au><second-name>Mangano</second-name><first-names>D T Multicenter Study of Perioperative Ischemia (McSPI) Research Group</first-names></au></authors><year>1998</year><art-title>The concordance of intraoperative left ventricular wall-motion abnormalities and electrocardiographic S-T segment changes: association with outcome after coronary revascularization</art-title><jnl-title>Anesthesiology</jnl-title><volume>88</volume><pages>945–54</pages><crossref><cr_doi>http://dx.doi.org/10.1097/00000542-199804000-00014</cr_doi><cr_issn type="print">00033022</cr_issn></crossref></journal-ref><misc-ref id="pm321426bib03" author="Elle et al" year-label="2003"><authors><au><second-name>Elle</second-name><first-names>O J</first-names></au><au><second-name>Fosse</second-name><first-names>E</first-names></au><au><second-name>Gulbrandsen</second-name><first-names>MG</first-names></au></authors><year>2003</year><patent>International Patent</patent><patent-number code="WO">Application with International Publication Number WO 03/061473</patent-number></misc-ref><journal-ref id="pm321426bib04" author="Elle et al" year-label="2005"><authors><au><second-name>Elle</second-name><first-names>O J</first-names></au><au><second-name>Halvorsen</second-name><first-names>S</first-names></au><au><second-name>Gulbrandsen</second-name><first-names>M G</first-names></au><au><second-name>Aurdal</second-name><first-names>L</first-names></au><au><second-name>Bakken</second-name><first-names>A</first-names></au><au><second-name>Samset</second-name><first-names>E</first-names></au><au><second-name>Dugstad</second-name><first-names>H</first-names></au><au><second-name>Fosse</second-name><first-names>E</first-names></au></authors><year>2005</year><art-title>Early recognition of regional cardiac ischemia using a 3-axis accelerometer sensor</art-title><jnl-title>Physiol. Meas.</jnl-title><volume>26</volume><pages>429–40</pages><crossref><cr_doi>http://dx.doi.org/10.1088/0967-3334/26/4/009</cr_doi><cr_issn type="print">09673334</cr_issn><cr_issn type="electronic">13616579</cr_issn></crossref></journal-ref><journal-ref id="pm321426bib05" author="Goffinet et al" year-label="2009"><authors><au><second-name>Goffinet</second-name><first-names>C</first-names></au><au><second-name>Chenot</second-name><first-names>F</first-names></au><au><second-name>Robert</second-name><first-names>A</first-names></au><au><second-name>Pouleur</second-name><first-names>A C</first-names></au><au><second-name>de Waroux</second-name><first-names>J B</first-names></au><au><second-name>Vancrayenest</second-name><first-names>D</first-names></au><au><second-name>Gerard</second-name><first-names>O</first-names></au><au><second-name>Pasquet</second-name><first-names>A</first-names></au><au><second-name>Gerber</second-name><first-names>B L</first-names></au><au><second-name>Vanoverschelde</second-name><first-names>J L</first-names></au></authors><year>2009</year><art-title>Assessment of subendocardial vs subepicardial left ventricular rotation and twist using two-dimensional speckle tracking echocardiography: comparison with tagged cardiac magnetic resonance</art-title><jnl-title>Eur. Heart. J.</jnl-title><volume>30</volume><pages>608–17</pages><crossref><cr_doi>http://dx.doi.org/10.1093/eurheartj/ehn511</cr_doi><cr_issn type="print">0195668X</cr_issn><cr_issn type="electronic">15229645</cr_issn></crossref></journal-ref><journal-ref id="pm321426bib06" author="Halvorsen et al" year-label="2008"><authors><au><second-name>Halvorsen</second-name><first-names>P S</first-names></au><au><second-name>Espinoza</second-name><first-names>A</first-names></au><au><second-name>Fleischer</second-name><first-names>L A</first-names></au><au><second-name>Elle</second-name><first-names>O J</first-names></au><au><second-name>Hoff</second-name><first-names>L</first-names></au><au><second-name>Lundblad</second-name><first-names>R</first-names></au><au><second-name>Skulstad</second-name><first-names>H</first-names></au><au><second-name>Edvardsen</second-name><first-names>T</first-names></au><au><second-name>Ihlen</second-name><first-names>H</first-names></au><au><second-name>Fosse</second-name><first-names>E</first-names></au></authors><year>2008</year><art-title>Feasibility of a three-axis epicardial accelerometer in detecting myocardial ischemia in cardiac surgical patients</art-title><jnl-title>J. Thorac. Cardiovasc. Surg.</jnl-title><volume>136</volume><pages>1496–502</pages><crossref><cr_doi>http://dx.doi.org/10.1016/j.jtcvs.2008.08.043</cr_doi><cr_issn type="print">00225223</cr_issn></crossref></journal-ref><journal-ref id="pm321426bib07" author="Halvorsen et al" year-label="2009"><authors><au><second-name>Halvorsen</second-name><first-names>P S</first-names></au><au><second-name>Fleischer</second-name><first-names>L A</first-names></au><au><second-name>Espinoza</second-name><first-names>A</first-names></au><au><second-name>Elle</second-name><first-names>O J</first-names></au><au><second-name>Hoff</second-name><first-names>L</first-names></au><au><second-name>Skulstad</second-name><first-names>H</first-names></au><au><second-name>Edvardsen</second-name><first-names>T</first-names></au><au><second-name>Fosse</second-name><first-names>E</first-names></au></authors><year>2009</year><art-title>Detection of myocardial ischaemia by epicardial accelerometers in the pig</art-title><jnl-title>Br. J. Anaesth.</jnl-title><volume>102</volume><pages>29–37</pages><crossref><cr_doi>http://dx.doi.org/10.1093/bja/aen331</cr_doi><cr_issn type="print">00070912</cr_issn><cr_issn type="electronic">14716771</cr_issn></crossref></journal-ref><journal-ref id="pm321426bib08" author="Hamilton and Tompkins" year-label="1986"><authors><au><second-name>Hamilton</second-name><first-names>P S</first-names></au><au><second-name>Tompkins</second-name><first-names>W J</first-names></au></authors><year>1986</year><art-title>Quantitative investigation of QRS detection rules using the MIT/BIH arrhythmia database</art-title><jnl-title>IEEE Trans. Biomed. Eng.</jnl-title><volume>33</volume><pages>1157–65</pages><crossref><cr_doi>http://dx.doi.org/10.1109/TBME.1986.325695</cr_doi><cr_issn type="print">00189294</cr_issn><cr_issn type="electronic">15582531</cr_issn></crossref></journal-ref><journal-ref id="pm321426bib09" author="Helle-Valle et al" year-label="2009"><authors><au><second-name>Helle-Valle</second-name><first-names>T</first-names></au><au><second-name>Remme</second-name><first-names>E W</first-names></au><au><second-name>Lyseggen</second-name><first-names>E</first-names></au><au><second-name>Pettersen</second-name><first-names>E</first-names></au><au><second-name>Vartdal</second-name><first-names>T</first-names></au><au><second-name>Opdahl</second-name><first-names>A</first-names></au><au><second-name>Smith</second-name><first-names>H J</first-names></au><au><second-name>Osman</second-name><first-names>N</first-names></au><au><second-name>Ihlen</second-name><first-names>H</first-names></au><au><second-name> Edvardsen</second-name><first-names>T</first-names></au><au><second-name>Smiseth</second-name><first-names>O A</first-names></au></authors><year>2009</year><art-title>Clinical assessment of left ventricular apical rotation and strain—a novel approach for quantification of function in infarcted myocardium and its border zones</art-title><jnl-title>Am. J. Physiol.</jnl-title><volume>297</volume><pages>H257–67</pages></journal-ref><conf-ref id="pm321426bib10" author="Hoff et al" year-label="2004"><authors><au><second-name>Hoff</second-name><first-names>L</first-names></au><au><second-name>Elle</second-name><first-names>O J</first-names></au><au><second-name>Grimnes</second-name><first-names>M</first-names></au><au><second-name>Halvorsen</second-name><first-names>P S</first-names></au><au><second-name>Alker</second-name><first-names>H J</first-names></au><au><second-name>Fosse</second-name><first-names>E</first-names></au></authors><year>2004</year><art-title>Measurements of heart motion using accelerometers</art-title><conf-title>Conf. Proc. IEEE Eng. Med. Biol. Soc.</conf-title><pages>pp 2049–51</pages></conf-ref><journal-ref id="pm321426bib11" author="Imenes et al" year-label="2007"><authors><au><second-name>Imenes</second-name><first-names>K</first-names></au><au><second-name>Aasmundtveit</second-name><first-names>K</first-names></au><au><second-name>Husa</second-name><first-names>E M</first-names></au><au><second-name>Høgetveit</second-name><first-names>J O</first-names></au><au><second-name>Halvorsen</second-name><first-names>S</first-names></au><au><second-name>Elle</second-name><first-names>O J</first-names></au><au><second-name>Mirtaheri</second-name><first-names>P</first-names></au><au><second-name>Fosse</second-name><first-names>E</first-names></au><au><second-name>Hoff</second-name><first-names>L</first-names></au></authors><year>2007</year><art-title>Assembly and packaging of a three-axis micro accelerometer used for detection of heart infarction</art-title><jnl-title>Biomed. Microdevices</jnl-title><volume>9</volume><pages>951–7</pages><crossref><cr_doi>http://dx.doi.org/10.1007/s10544-007-9082-2</cr_doi><cr_issn type="print">13872176</cr_issn><cr_issn type="electronic">15728781</cr_issn></crossref></journal-ref><journal-ref id="pm321426bib12" author="Knudtson et al" year-label="1997"><authors><au><second-name>Knudtson</second-name><first-names>M L</first-names></au><au><second-name>Galbraith</second-name><first-names>P D</first-names></au><au><second-name>Hildebrand</second-name><first-names>K L</first-names></au><au><second-name>Tyberg</second-name><first-names>J V</first-names></au><au><second-name>Beyar</second-name><first-names>R</first-names></au></authors><year>1997</year><art-title>Dynamics of left ventricular apex rotation during angioplasty: a sensitive index of ischemic dysfunction</art-title><jnl-title>Circulation</jnl-title><volume>96</volume><pages>801–8</pages></journal-ref><journal-ref id="pm321426bib13" author="Kroeker et al" year-label="1995"><authors><au><second-name>Kroeker</second-name><first-names>C A</first-names></au><au><second-name>Tyberg</second-name><first-names>J V</first-names></au><au><second-name>Beyar</second-name><first-names>R</first-names></au></authors><year>1995</year><art-title>Effects of ischemia on left ventricular apex rotation. An experimental study in anesthetized dogs</art-title><jnl-title>Circulation</jnl-title><volume>92</volume><pages>3539–48</pages></journal-ref><journal-ref id="pm321426bib14" author="Landesberg" year-label="2005"><authors><au><second-name>Landesberg</second-name><first-names>G.</first-names></au></authors><year>2005</year><art-title>Monitoring for myocardial ischemia</art-title><jnl-title>Best Pract. Res. Clin. Anaesthesiol.</jnl-title><volume>19</volume><pages>77–95</pages></journal-ref><book-ref id="pm321426bib15" author="Resnick and Halliday" year-label="1966"><authors><au><second-name>Resnick</second-name><first-names>R</first-names></au><au><second-name>Halliday</second-name><first-names>D</first-names></au></authors><year>1966</year><book-title>Physics</book-title><publication><place>Tokyo</place><publisher>Toppan</publisher></publication><pages>pp 251–6</pages></book-ref><journal-ref id="pm321426bib16" author="Skulstad et al" year-label="2004"><authors><au><second-name>Skulstad</second-name><first-names>H</first-names></au><au><second-name>Andersen</second-name><first-names>K</first-names></au><au><second-name>Edvardsen</second-name><first-names>T</first-names></au><au><second-name>Rein</second-name><first-names>K A</first-names></au><au><second-name>Tønnessen</second-name><first-names>T I</first-names></au><au><second-name>Hol</second-name><first-names>P K</first-names></au><au><second-name>Fosse</second-name><first-names>E</first-names></au><au><second-name>Ihlen</second-name><first-names>H</first-names></au></authors><year>2004</year><art-title>Detection of ischemia and new insight into left ventricular physiology by strain Doppler and tissue velocity imaging: assessment during coronary bypass operation of the beating heart</art-title><jnl-title>J. Am. Soc. Echocardiogr.</jnl-title><volume>17</volume><pages>1225–33</pages><crossref><cr_doi>http://dx.doi.org/10.1016/j.echo.2004.07.014</cr_doi><cr_issn type="print">08947317</cr_issn></crossref></journal-ref><journal-ref id="pm321426bib17" author="Tennant and Wiggers" year-label="1935"><authors><au><second-name>Tennant</second-name><first-names>R</first-names></au><au><second-name>Wiggers</second-name><first-names>C J</first-names></au></authors><year>1935</year><art-title>The effect of coronary occlusion on myocardial contraction</art-title><jnl-title>Am. J. Physiol.</jnl-title><volume>112</volume><pages>351–61</pages></journal-ref><journal-ref id="pm321426bib18" author="Urheim et al" year-label="2000"><authors><au><second-name>Urheim</second-name><first-names>S</first-names></au><au><second-name>Edvardsen</second-name><first-names>T</first-names></au><au><second-name>Torp</second-name><first-names>H</first-names></au><au><second-name>Angelsen</second-name><first-names>B</first-names></au><au><second-name>Smiseth</second-name><first-names>OA</first-names></au></authors><year>2000</year><art-title>Myocardial strain by Doppler echocardiography. Validation of a new method to quantify regional myocardial function</art-title><jnl-title>Circulation</jnl-title><volume>102</volume><pages>1158–64</pages></journal-ref></reference-list></references></back></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo><title>Validation of cardiac accelerometer sensor measurements</title></titleInfo><titleInfo type="abbreviated"><title>Validation of cardiac accelerometer sensor measurements</title></titleInfo><titleInfo type="alternative"><title>Validation of cardiac accelerometer sensor measurements</title></titleInfo><name type="personal"><namePart type="given">Espen W</namePart><namePart type="family">Remme</namePart><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation><affiliation>E-mail:espen.remme@medisin.uio.no</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Lars</namePart><namePart type="family">Hoff</namePart><affiliation>Vestfold University College, Tnsberg, Norway</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Per Steinar</namePart><namePart type="family">Halvorsen</namePart><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Edvard</namePart><namePart type="family">Nrum</namePart><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Helge</namePart><namePart type="family">Skulstad</namePart><affiliation>Department of Cardiology, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Lars A</namePart><namePart type="family">Fleischer</namePart><affiliation>Vestfold University College, Tnsberg, Norway</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Ole Jakob</namePart><namePart type="family">Elle</namePart><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Erik</namePart><namePart type="family">Fosse</namePart><affiliation>The Interventional Centre, Oslo University Hospital, Rikshospitalet, Oslo, Norway</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="paper"></genre><originInfo><publisher>IOP Publishing</publisher><dateIssued encoding="w3cdtf">2009</dateIssued><copyrightDate encoding="w3cdtf">2009</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><internetMediaType>text/html</internetMediaType><note type="production">Printed in the UK</note></physicalDescription><abstract>In this study we have investigated the accuracy of an accelerometer sensor designed for the measurement of cardiac motion and automatic detection of motion abnormalities caused by myocardial ischaemia. The accelerometer, attached to the left ventricular wall, changed its orientation relative to the direction of gravity during the cardiac cycle. This caused a varying gravity component in the measured acceleration signal that introduced an error in the calculation of myocardial motion. Circumferential displacement, velocity and rotation of the left ventricular apical region were calculated from the measured acceleration signal. We developed a mathematical method to separate translational and gravitational acceleration components based on a priori assumptions of myocardial motion. The accuracy of the measured motion was investigated by comparison with known motion of a robot arm programmed to move like the heart wall. The accuracy was also investigated in an animal study. The sensor measurements were compared with simultaneously recorded motion from a robot arm attached next to the sensor on the heart and with measured motion by echocardiography and a video camera. The developed compensation method for the varying gravity component improved the accuracy of the calculated velocity and displacement traces, giving very good agreement with the reference methods.</abstract><subject><genre>keywords</genre><topic>biomedical sensor</topic><topic>accelerometer</topic><topic>cardiac surgery</topic><topic>myocardial ischaemia</topic></subject><relatedItem type="host"><titleInfo><title>Physiological Measurement</title></titleInfo><titleInfo type="abbreviated"><title>Physiol. Meas.</title></titleInfo><genre type="journal">journal</genre><identifier type="ISSN">0967-3334</identifier><identifier type="eISSN">1361-6579</identifier><identifier type="PublisherID">PM</identifier><identifier type="CODEN">PMEAE3</identifier><identifier type="URL">stacks.iop.org/PM</identifier><part><date>2009</date><detail type="volume"><caption>vol.</caption><number>30</number></detail><detail type="issue"><caption>no.</caption><number>12</number></detail><extent unit="pages"><start>1429</start><end>1444</end><total>16</total></extent></part></relatedItem><identifier type="istex">755203A072AAC6BCE0B34D3AA0E716CB90B6CBE8</identifier><identifier type="DOI">10.1088/0967-3334/30/12/010</identifier><identifier type="PII">S0967-3334(09)21426-2</identifier><identifier type="articleID">321426</identifier><identifier type="articleNumber">010</identifier><accessCondition type="use and reproduction" contentType="copyright">2009 Institute of Physics and Engineering in Medicine</accessCondition><recordInfo><recordContentSource>IOP</recordContentSource><recordOrigin>2009 Institute of Physics and Engineering in Medicine</recordOrigin></recordInfo></mods></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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