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Hybrid mathematical model of cardiomyocyte turnover in the adult human heart.

Elser JA, Margulies KB - PLoS ONE (2012)

Bottom Line: However, estimates of cardiomyocyte turnover rates conflict greatly, with a study employing C14 pulse-chase methodology concluding 1% annual turnover in youth declining to 0.5% with aging and another using cell population dynamics indicating substantial, age-increasing turnover (4% increasing to 20%).Incorporating considerations of primary variable sensitivity and controversial model assumptions, an unbiased numerical solver identified a scenario of significant, age-increasing turnover (4-6% increasing to 15-22% with age) that was compatible with data from both studies, provided that successive generations of cardiomyocytes experienced higher attrition rates than predecessors.Nevertheless, discrepancies among recent cell turnover estimates can be explained and reconciled.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, USA.

ABSTRACT

Rationale: The capacity for cardiomyocyte regeneration in the healthy adult human heart is fundamentally relevant for both myocardial homeostasis and cardiomyopathy therapeutics. However, estimates of cardiomyocyte turnover rates conflict greatly, with a study employing C14 pulse-chase methodology concluding 1% annual turnover in youth declining to 0.5% with aging and another using cell population dynamics indicating substantial, age-increasing turnover (4% increasing to 20%).

Objective: Create a hybrid mathematical model to critically examine rates of cardiomyocyte turnover derived from alternative methodologies.

Methods and results: Examined in isolation, the cell population analysis exhibited severe sensitivity to a stem cell expansion exponent (20% variation causing 2-fold turnover change) and apoptosis rate. Similarly, the pulse-chase model was acutely sensitive to assumptions of instantaneous incorporation of atmospheric C14 into the body (4-fold impact on turnover in young subjects) while numerical restrictions precluded otherwise viable solutions. Incorporating considerations of primary variable sensitivity and controversial model assumptions, an unbiased numerical solver identified a scenario of significant, age-increasing turnover (4-6% increasing to 15-22% with age) that was compatible with data from both studies, provided that successive generations of cardiomyocytes experienced higher attrition rates than predecessors.

Conclusions: Assignment of histologically-observed stem/progenitor cells into discrete regenerative phenotypes in the cell population model strongly influenced turnover dynamics without being directly testable. Alternatively, C14 trafficking assumptions and restrictive models in the pulse-chase model artificially eliminated high-turnover solutions. Nevertheless, discrepancies among recent cell turnover estimates can be explained and reconciled. The hybrid mathematical model provided herein permits further examination of these and forthcoming datasets.

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Simulations Derived from Applying Pre-specified Annual CM Turnover Rates to Bergmann Model Analysis Method.A model was produced for each of the 12 Bergmann subjects (defined by their lifespans and birth years). Instead of cycling dynamics parameters from the Kajstura manuscript, true constant annual turnover was specified as input. The category “Older Subjects” includes ND60, ND67, ND73, ND61, and ND51 from the Bergmann study, while the category “Young Subjects” includes ND56, ND68, ND50, ND69, ND71, ND54, and ND74. When true turnover input is high (beginning at 4%/year and fully apparent by 10%/year), the resulting ΛC14 has two numerical solutions—a low solution (plotted in A) and a high solution (plotted in B). The high solution tracks the true (ideal) input whereas the low solution asymptotes at 0.75%/year. Although the ΛC14 levels obtained by Bergmann for older subjects (∼20 per mil) are too low for the high solution to be enabled (∼60 per mil, not shown), this graph illustrates that, for measured ΛC14 exceeding a certain discrete threshold, a bifurcation point exists such that adoption of the low solution leads to insensitivity.
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pone-0051683-g003: Simulations Derived from Applying Pre-specified Annual CM Turnover Rates to Bergmann Model Analysis Method.A model was produced for each of the 12 Bergmann subjects (defined by their lifespans and birth years). Instead of cycling dynamics parameters from the Kajstura manuscript, true constant annual turnover was specified as input. The category “Older Subjects” includes ND60, ND67, ND73, ND61, and ND51 from the Bergmann study, while the category “Young Subjects” includes ND56, ND68, ND50, ND69, ND71, ND54, and ND74. When true turnover input is high (beginning at 4%/year and fully apparent by 10%/year), the resulting ΛC14 has two numerical solutions—a low solution (plotted in A) and a high solution (plotted in B). The high solution tracks the true (ideal) input whereas the low solution asymptotes at 0.75%/year. Although the ΛC14 levels obtained by Bergmann for older subjects (∼20 per mil) are too low for the high solution to be enabled (∼60 per mil, not shown), this graph illustrates that, for measured ΛC14 exceeding a certain discrete threshold, a bifurcation point exists such that adoption of the low solution leads to insensitivity.

Mentions: In addition, for subjects born before the atmospheric C14 spike, at a certain subject-specific value of measured ΛC14, the numerical solution bifurcates creating low and high solutions. Beyond the bifurcation point, the low solution reports a turnover estimate of 0.75%/year even as higher turnover rates are used as the sole input parameter, whereas the high solution remains approximately truthful to the ideal at all turnover levels (Figure 3). The hybrid model then computes estimated ΛC14 for each subject under each turnover input scenario and then solves for a best-fit constant turnover solution using either using either the low or high solution. While the measured ΛC14 for subjects born before the C14 spike is below the threshold needed to make a high solution viable, the high solution becomes viable at surprisingly low ΛC14 measurements (approximately 60 per mil), lower than the ΛC14 measurement that could have been expected in these subjects from the global Scenario A best-fit data (by which Bergmann concluded 1% annual turnover).


Hybrid mathematical model of cardiomyocyte turnover in the adult human heart.

Elser JA, Margulies KB - PLoS ONE (2012)

Simulations Derived from Applying Pre-specified Annual CM Turnover Rates to Bergmann Model Analysis Method.A model was produced for each of the 12 Bergmann subjects (defined by their lifespans and birth years). Instead of cycling dynamics parameters from the Kajstura manuscript, true constant annual turnover was specified as input. The category “Older Subjects” includes ND60, ND67, ND73, ND61, and ND51 from the Bergmann study, while the category “Young Subjects” includes ND56, ND68, ND50, ND69, ND71, ND54, and ND74. When true turnover input is high (beginning at 4%/year and fully apparent by 10%/year), the resulting ΛC14 has two numerical solutions—a low solution (plotted in A) and a high solution (plotted in B). The high solution tracks the true (ideal) input whereas the low solution asymptotes at 0.75%/year. Although the ΛC14 levels obtained by Bergmann for older subjects (∼20 per mil) are too low for the high solution to be enabled (∼60 per mil, not shown), this graph illustrates that, for measured ΛC14 exceeding a certain discrete threshold, a bifurcation point exists such that adoption of the low solution leads to insensitivity.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3526650&req=5

pone-0051683-g003: Simulations Derived from Applying Pre-specified Annual CM Turnover Rates to Bergmann Model Analysis Method.A model was produced for each of the 12 Bergmann subjects (defined by their lifespans and birth years). Instead of cycling dynamics parameters from the Kajstura manuscript, true constant annual turnover was specified as input. The category “Older Subjects” includes ND60, ND67, ND73, ND61, and ND51 from the Bergmann study, while the category “Young Subjects” includes ND56, ND68, ND50, ND69, ND71, ND54, and ND74. When true turnover input is high (beginning at 4%/year and fully apparent by 10%/year), the resulting ΛC14 has two numerical solutions—a low solution (plotted in A) and a high solution (plotted in B). The high solution tracks the true (ideal) input whereas the low solution asymptotes at 0.75%/year. Although the ΛC14 levels obtained by Bergmann for older subjects (∼20 per mil) are too low for the high solution to be enabled (∼60 per mil, not shown), this graph illustrates that, for measured ΛC14 exceeding a certain discrete threshold, a bifurcation point exists such that adoption of the low solution leads to insensitivity.
Mentions: In addition, for subjects born before the atmospheric C14 spike, at a certain subject-specific value of measured ΛC14, the numerical solution bifurcates creating low and high solutions. Beyond the bifurcation point, the low solution reports a turnover estimate of 0.75%/year even as higher turnover rates are used as the sole input parameter, whereas the high solution remains approximately truthful to the ideal at all turnover levels (Figure 3). The hybrid model then computes estimated ΛC14 for each subject under each turnover input scenario and then solves for a best-fit constant turnover solution using either using either the low or high solution. While the measured ΛC14 for subjects born before the C14 spike is below the threshold needed to make a high solution viable, the high solution becomes viable at surprisingly low ΛC14 measurements (approximately 60 per mil), lower than the ΛC14 measurement that could have been expected in these subjects from the global Scenario A best-fit data (by which Bergmann concluded 1% annual turnover).

Bottom Line: However, estimates of cardiomyocyte turnover rates conflict greatly, with a study employing C14 pulse-chase methodology concluding 1% annual turnover in youth declining to 0.5% with aging and another using cell population dynamics indicating substantial, age-increasing turnover (4% increasing to 20%).Incorporating considerations of primary variable sensitivity and controversial model assumptions, an unbiased numerical solver identified a scenario of significant, age-increasing turnover (4-6% increasing to 15-22% with age) that was compatible with data from both studies, provided that successive generations of cardiomyocytes experienced higher attrition rates than predecessors.Nevertheless, discrepancies among recent cell turnover estimates can be explained and reconciled.

View Article: PubMed Central - PubMed

Affiliation: Department of Bioengineering, University of Pennsylvania, Philadelphia, PA, USA.

ABSTRACT

Rationale: The capacity for cardiomyocyte regeneration in the healthy adult human heart is fundamentally relevant for both myocardial homeostasis and cardiomyopathy therapeutics. However, estimates of cardiomyocyte turnover rates conflict greatly, with a study employing C14 pulse-chase methodology concluding 1% annual turnover in youth declining to 0.5% with aging and another using cell population dynamics indicating substantial, age-increasing turnover (4% increasing to 20%).

Objective: Create a hybrid mathematical model to critically examine rates of cardiomyocyte turnover derived from alternative methodologies.

Methods and results: Examined in isolation, the cell population analysis exhibited severe sensitivity to a stem cell expansion exponent (20% variation causing 2-fold turnover change) and apoptosis rate. Similarly, the pulse-chase model was acutely sensitive to assumptions of instantaneous incorporation of atmospheric C14 into the body (4-fold impact on turnover in young subjects) while numerical restrictions precluded otherwise viable solutions. Incorporating considerations of primary variable sensitivity and controversial model assumptions, an unbiased numerical solver identified a scenario of significant, age-increasing turnover (4-6% increasing to 15-22% with age) that was compatible with data from both studies, provided that successive generations of cardiomyocytes experienced higher attrition rates than predecessors.

Conclusions: Assignment of histologically-observed stem/progenitor cells into discrete regenerative phenotypes in the cell population model strongly influenced turnover dynamics without being directly testable. Alternatively, C14 trafficking assumptions and restrictive models in the pulse-chase model artificially eliminated high-turnover solutions. Nevertheless, discrepancies among recent cell turnover estimates can be explained and reconciled. The hybrid mathematical model provided herein permits further examination of these and forthcoming datasets.

Show MeSH
Related in: MedlinePlus