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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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Hybrid Model Automaton Algorithm.Subject hearts are modeled by initiating a “Starting CM Count” for the subject at the “Start Age” of the simulation (typically birth) and a “Subject Lifespan” that determines the number of year-repetitions. An age distribution of CM at the time of subject autopsy is produced either via Mode A or Mode B. Mode A uses variables and formulas from the Kajstura methodology to perform iterations of CM creation and destruction throughout each year-iteration according to the duration and frequency of these cycles. In this formulation, NCSC = Number of Cardiac Stem Cells, %Cyc = Fraction of CSCs cycling, and E = Number of CSC divisions occurring before loss of pluripotency. Alternatively, Mode B uses input annual creation and destruction values directly and these values may be dependent on either the patient age (at time of CM formation or at current iteration of production/destruction) or on the age of the CM undergoing destruction. There are two main outputs: (1) a distribution of surviving CM by CM age and (2) an end average C14 measurement, modeling the Bergmann methodology applied to model hearts, which is produced by incorporation of the CM age distribution with atmospheric C14 timecourse data and human polyploidization magnitudes/rates.
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pone-0051683-g001: Hybrid Model Automaton Algorithm.Subject hearts are modeled by initiating a “Starting CM Count” for the subject at the “Start Age” of the simulation (typically birth) and a “Subject Lifespan” that determines the number of year-repetitions. An age distribution of CM at the time of subject autopsy is produced either via Mode A or Mode B. Mode A uses variables and formulas from the Kajstura methodology to perform iterations of CM creation and destruction throughout each year-iteration according to the duration and frequency of these cycles. In this formulation, NCSC = Number of Cardiac Stem Cells, %Cyc = Fraction of CSCs cycling, and E = Number of CSC divisions occurring before loss of pluripotency. Alternatively, Mode B uses input annual creation and destruction values directly and these values may be dependent on either the patient age (at time of CM formation or at current iteration of production/destruction) or on the age of the CM undergoing destruction. There are two main outputs: (1) a distribution of surviving CM by CM age and (2) an end average C14 measurement, modeling the Bergmann methodology applied to model hearts, which is produced by incorporation of the CM age distribution with atmospheric C14 timecourse data and human polyploidization magnitudes/rates.

Mentions: While these two studies both indicate that new CM formation exists in the healthy, adult human heart, the discrepancy in magnitude and age progression is perplexingly large. Accordingly, we developed a hybrid mathematical model designed to evaluate the two models simultaneously. The hybrid model agent-based algorithm is described in Figure 1 and is programmed to accept turnover rate (CM formation, apoptosis rate, and polyploidization) parameters that vary with subject age and sex, such as those found in the Kajstura paper (Mode A); however, these variables may be substituted by time-varying CM formation and destruction rates as employed by Bergmann (Mode B). By applying this model to the two data sets, we have identified explanations for their discrepancies and defined whether differences can be reconciled, while providing a tool for modeling data derived from subsequent inquiries.


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

Elser JA, Margulies KB - PLoS ONE (2012)

Hybrid Model Automaton Algorithm.Subject hearts are modeled by initiating a “Starting CM Count” for the subject at the “Start Age” of the simulation (typically birth) and a “Subject Lifespan” that determines the number of year-repetitions. An age distribution of CM at the time of subject autopsy is produced either via Mode A or Mode B. Mode A uses variables and formulas from the Kajstura methodology to perform iterations of CM creation and destruction throughout each year-iteration according to the duration and frequency of these cycles. In this formulation, NCSC = Number of Cardiac Stem Cells, %Cyc = Fraction of CSCs cycling, and E = Number of CSC divisions occurring before loss of pluripotency. Alternatively, Mode B uses input annual creation and destruction values directly and these values may be dependent on either the patient age (at time of CM formation or at current iteration of production/destruction) or on the age of the CM undergoing destruction. There are two main outputs: (1) a distribution of surviving CM by CM age and (2) an end average C14 measurement, modeling the Bergmann methodology applied to model hearts, which is produced by incorporation of the CM age distribution with atmospheric C14 timecourse data and human polyploidization magnitudes/rates.
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pone-0051683-g001: Hybrid Model Automaton Algorithm.Subject hearts are modeled by initiating a “Starting CM Count” for the subject at the “Start Age” of the simulation (typically birth) and a “Subject Lifespan” that determines the number of year-repetitions. An age distribution of CM at the time of subject autopsy is produced either via Mode A or Mode B. Mode A uses variables and formulas from the Kajstura methodology to perform iterations of CM creation and destruction throughout each year-iteration according to the duration and frequency of these cycles. In this formulation, NCSC = Number of Cardiac Stem Cells, %Cyc = Fraction of CSCs cycling, and E = Number of CSC divisions occurring before loss of pluripotency. Alternatively, Mode B uses input annual creation and destruction values directly and these values may be dependent on either the patient age (at time of CM formation or at current iteration of production/destruction) or on the age of the CM undergoing destruction. There are two main outputs: (1) a distribution of surviving CM by CM age and (2) an end average C14 measurement, modeling the Bergmann methodology applied to model hearts, which is produced by incorporation of the CM age distribution with atmospheric C14 timecourse data and human polyploidization magnitudes/rates.
Mentions: While these two studies both indicate that new CM formation exists in the healthy, adult human heart, the discrepancy in magnitude and age progression is perplexingly large. Accordingly, we developed a hybrid mathematical model designed to evaluate the two models simultaneously. The hybrid model agent-based algorithm is described in Figure 1 and is programmed to accept turnover rate (CM formation, apoptosis rate, and polyploidization) parameters that vary with subject age and sex, such as those found in the Kajstura paper (Mode A); however, these variables may be substituted by time-varying CM formation and destruction rates as employed by Bergmann (Mode B). By applying this model to the two data sets, we have identified explanations for their discrepancies and defined whether differences can be reconciled, while providing a tool for modeling data derived from subsequent inquiries.

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