A mathematical model of the impact of novel treatments on the A β burden in the Alzheimer’s brain, CSF and plasma
Identifieur interne : 000112 ( Istex/Corpus ); précédent : 000111; suivant : 000113A mathematical model of the impact of novel treatments on the A β burden in the Alzheimer’s brain, CSF and plasma
Auteurs : David L. Craft ; Lawrence M. Wein ; Dennis J. SelkoeSource :
- Bulletin of Mathematical Biology [ 0092-8240 ] ; 2002-09-01.
Abstract
Abstract: With the advent of novel therapies for Alzheimer’s disease, there is a pressing need for biomarkers that are easy to monitor, such as the amyloid-beta (Aβ) levels in the cerebrospinal fluid (CSF) and plasma. To gain a better understanding of the explanatory power of these biomarkers, we formulate and analyze a compartmental mathematical model for the Aβ accumulation in the brain, CSF and plasma, throughout the course of Alzheimer’s treatment. Our analysis reveals that the total Aβ burden in the brain is dictated by a unitless quantity called the polymerization ratio, which is the product of the production and elongation rates divided by the product of the fragmentation and loss rates. In this ratio, the production rate and loss rate include a source and sink term, respectively, related to the intercompartmental transport. Our results suggest that production inhibitors are likely to reduce the Aβ levels in all three compartments. In contrast, agents that ingest monomers off of polymers, or that increase fragmentation or block elongation, may also reduce Aβ burden in the brain, but may produce little change in—or even transiently increase—CSF and plasma Aβ levels. Hence, great care must be taken when interpreting these biomarkers.
Url:
DOI: 10.1006/bulm.2002.0304
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Our analysis reveals that the total Aβ burden in the brain is dictated by a unitless quantity called the polymerization ratio, which is the product of the production and elongation rates divided by the product of the fragmentation and loss rates. In this ratio, the production rate and loss rate include a source and sink term, respectively, related to the intercompartmental transport. Our results suggest that production inhibitors are likely to reduce the Aβ levels in all three compartments. In contrast, agents that ingest monomers off of polymers, or that increase fragmentation or block elongation, may also reduce Aβ burden in the brain, but may produce little change in—or even transiently increase—CSF and plasma Aβ levels. 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To gain a better understanding of the explanatory power of these biomarkers, we formulate and analyze a compartmental mathematical model for the A<Emphasis Type="Italic">β</Emphasis> accumulation in the brain, CSF and plasma, throughout the course of Alzheimer’s treatment. Our analysis reveals that the total A<Emphasis Type="Italic">β</Emphasis> burden in the brain is dictated by a unitless quantity called the polymerization ratio, which is the product of the production and elongation rates divided by the product of the fragmentation and loss rates. In this ratio, the production rate and loss rate include a source and sink term, respectively, related to the intercompartmental transport. Our results suggest that production inhibitors are likely to reduce the A<Emphasis Type="Italic">β</Emphasis> levels in all three compartments. In contrast, agents that ingest monomers off of polymers, or that increase fragmentation or block elongation, may also reduce A<Emphasis Type="Italic">β</Emphasis> burden in the brain, but may produce little change in—or even transiently increase—CSF and plasma A<Emphasis Type="Italic">β</Emphasis> levels. Hence, great care must be taken when interpreting these biomarkers.</Para></Abstract></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>A mathematical model of the impact of novel treatments on the A β burden in the Alzheimer’s brain, CSF and plasma</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>A mathematical model of the impact of novel treatments on the A β burden in the Alzheimer’s brain, CSF and plasma</title></titleInfo><name type="personal"><namePart type="given">David</namePart><namePart type="given">L.</namePart><namePart type="family">Craft</namePart><affiliation>Operations Research Center, MIT, 02139, Cambridge, MA, USA</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal" displayLabel="corresp"><namePart type="given">Lawrence</namePart><namePart type="given">M.</namePart><namePart type="family">Wein</namePart><affiliation>Sloan School of Management, MIT, 02139, Cambridge, MA, USA</affiliation><affiliation>E-mail: lwein@mit.edu</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Dennis</namePart><namePart type="given">J.</namePart><namePart type="family">Selkoe</namePart><affiliation>Center for Neurologic Diseases, Harvard Medical School, Brigham and Women’s Hospital, 02115, Boston, MA, USA</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">New York</placeTerm></place><dateCreated encoding="w3cdtf">2002-01-22</dateCreated><dateIssued encoding="w3cdtf">2002-09-01</dateIssued><copyrightDate encoding="w3cdtf">2002</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: With the advent of novel therapies for Alzheimer’s disease, there is a pressing need for biomarkers that are easy to monitor, such as the amyloid-beta (Aβ) levels in the cerebrospinal fluid (CSF) and plasma. To gain a better understanding of the explanatory power of these biomarkers, we formulate and analyze a compartmental mathematical model for the Aβ accumulation in the brain, CSF and plasma, throughout the course of Alzheimer’s treatment. Our analysis reveals that the total Aβ burden in the brain is dictated by a unitless quantity called the polymerization ratio, which is the product of the production and elongation rates divided by the product of the fragmentation and loss rates. In this ratio, the production rate and loss rate include a source and sink term, respectively, related to the intercompartmental transport. Our results suggest that production inhibitors are likely to reduce the Aβ levels in all three compartments. In contrast, agents that ingest monomers off of polymers, or that increase fragmentation or block elongation, may also reduce Aβ burden in the brain, but may produce little change in—or even transiently increase—CSF and plasma Aβ levels. 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