Cardiac Metabolic Limitations Contribute to Diminished Performance of the Heart in Aging

Abstract

Changes in the myocardial energetics associated with aging—reductions in creatine phosphate/ATP ratio, total creatine, and ATP—mirror changes observed in failing hearts compared to healthy controls. Similarly, both aging and heart failure are associated with significant reductions in cardiac performance and maximal left ventricular cardiac power output compared with young healthy individuals. Based on these observations, we hypothesize that reductions in the concentrations of cytoplasmic adenine nucleotide, creatine, and phosphate pools that occur with aging impair the myocardial capacity to synthesize ATP at physiological free energy levels and that the resulting changes to myocardial energetic status impair the mechanical pumping ability of the heart. The purpose of this study is to test these hypotheses using an age-structured population model for myocardial metabolism in the adult female population and to determine the potential impact of reductions in key myocardial metabolite pools in causing metabolic/energetic and cardiac mechanical dysfunction associated with aging. To test these hypotheses, we developed a population model for myocardial energetics to predict myocardial ATP, ADP, creatine phosphate, creatine, and inorganic phosphate concentrations as functions of cardiac work and age in the adult female population. Model predictions support our hypotheses and are consistent with previous experimental observations. The major findings provide a novel, to our knowledge, theoretical and computational framework for further probing complex relationships between the energetics and performance of the heart with aging.

Significance

Normal mechanical function of the heart requires that ATP be continuously synthesized at a hydrolysis potential of roughly −60 kJ mol⁻¹. Yet in both the aging and diseased heart, the relationships between cardiac work rate and concentrations of ATP, ADP, and inorganic phosphate are altered. Important outstanding questions are as follows. To what extent do changes in metabolite concentrations that occur in aging and heart disease affect metabolic/molecular processes in the myocardium? How is myocardial mechanical function affected by changes in metabolite concentrations? This study addresses these questions by analyzing relationships between cardiac energy demand and supply using an age-structured population model for human myocardial energetics in women.

Introduction

Peak left ventricular (LV) cardiac power output (CPO), as an integrative measure of overall pumping capability and performance of the heart, is the strongest predictor of mortality in heart failure (1). Yet even in the absence of heart failure, maximal CPO decreases with age and thus increases the risk of cardiovascular morbidity and mortality (2). Changes in myocardial energetics with age are associated with diminished maximal CPO in older people (3, 4). These observations raise the questions of if and how age-dependent changes to myocardial metabolic energy supply influence the myocardial capacity to generate power. Previous studies have established a theoretical link between reductions in cytoplasmic adenine nucleotide, creatine, and phosphate metabolite pools and altered myocardial energetics in heart failure (5). The goals of this study are to determine whether reductions in these metabolite pools can potentially explain age-dependent changes in myocardial energetics in normal subjects and whether the resulting energetic changes can potentially explain the observed reductions in maximal CPO with age.

Left ventricular CPO is the rate at which the ventricle produces mechanical work to pump blood through the systemic circulation. CPO is calculated as left ventricular stroke work (mechanical work done per heartbeat) multiplied by the heart rate, or it is calculated as the average difference in pressure between the left atrium and the aorta multiplied by the cardiac output, expressed in units of energy per unit time. Processes such as cross-bridge cycling require that ATP is continuously synthesized (and ADP and inorganic phosphate (Pi) consumed) at sufficient concentrations such that normal functions are not kinetically or thermodynamically impaired (6, 7). Because the demand for ATP production in the myocardium is proportional to cardiac work and because ATP hydrolysis serves as the source of chemical free energy to drive myocardial contraction, it stands to reason that limitations or impairments in myocardial energy metabolism may influence overall cardiac performance represented by CPO.

It is observed that in both the aging (3, 4) and the diseased heart (8, 9, 10, 11, 12), relationships between cardiac work rate and concentrations of phosphate metabolites ATP, ADP, and creatine phosphate (CrP) are altered. In heart failure, the CrP/ATP ratio is diminished and [ATP] in myocardium is lower compared to that in healthy individuals (8, 12, 13, 14). Although heart failure is a complex syndrome, which can arise because of a variety of pathophysiological abnormalities (15), alterations to the myocardial energetics state are established hallmarks of heart failure irrespective of etiology (8, 13, 16, 17). Although a complete understanding of the mechanistic links between energy metabolism and mechanical function is lacking, energy metabolism represents an actively pursued potential target for treating heart failure (18, 19, 20, 21).

Similarities between the myocardial energetic phenotypes observed in heart failure/decompensation and aging include lower myocardial ATP and CrP/ATP compared to the healthy young heart (4, 22). Based on these similarities and similarities in terms of diminished maximal cardiac performance, we hypothesize that reductions in the concentrations of cytoplasmic adenine nucleotide, creatine, and phosphate pools that occur with aging impair the myocardial capacity to synthesize ATP at physiological free energy levels and that the resulting changes to myocardial energetic status play a causal role in contributing to reductions in cardiac performance with aging.

To explore the viability of these hypotheses, we applied a model of myocardial energetics previously used to analyze data from large animals (5, 23). An age-structured population model for myocardial metabolite pools was parameterized based on studies in humans from Köstler et al. (22) and Jakovljevic et al. (3) to represent variability and interrelationships between adenine nucleotide, creatine, and phosphate pools in the human female population. The model of population variability in metabolite pools was used in conjunction with simulations of myocardial energetics to predict the relationship between maximal CPO and age. Because of a significant difference in age-associated changes in cardiac morphology and function between men and women (2, 24, 25), our model accounts for female subjects only. Model predictions are consistent with observations on the relationships between age and maximal CPO in female subjects (3, 4) and consistent with our hypotheses. These simulations provide a theoretical/computational framework for further probing relationships between energetic status and cardiac power and for comparing predictions associated with the hypothesis and experimental data.

Methods

Overview of simulation methods

A previously developed model of myocardial energetics developed by Wu et al. (5, 23) was used to simulate how myocardial oxygen consumption (MVO₂) and cellular concentrations of ATP, ADP, inorganic phosphate, creatine, and CrP vary with changes in ATP demand. This model has been validated on the basis of its ability to match steady-state data on how these variables vary with changes in ATP demand under physiological conditions, how CrP and Pi levels change dynamically in response to acute ischemia and recovery, and how these variables are altered in response to changes in concentrations of key cytoplasmic metabolite pools. Using this underlying model framework, an age-structured population model for the total adenine nucleotide (TAN), total creatine (CRtot), and total exchangeable phosphate (TEP) metabolite pools is parameterized from data on resting myocardial CrP/ATP and [ATP] in healthy women aged 20–81 years (3, 22). The relationship between MVO₂ and CPO is determined empirically based on observations showing a linear relationship between oxygen consumption and power output over a broad range of physiological conditions in animal models and humans.

The Wu et al. model of myocardial energetics consists of 62 ordinary differential equations for state variables representing cytoplasmic and mitochondrial tricarboxylic acid cycle intermediate concentrations; phosphate metabolites ATP, ADP, AMP, Pi, creatine, and CrP; mitochondrial membrane potential; and cations K⁺, Mg²⁺, and H⁺ (5). The full set of equations is provided in the supporting material for Wu et al. (5), and MATLAB (The MathWorks, Natick, MA) codes for the model are disseminated (http://virtualrat.org/models/steady-state-cardiac-energetics-control-left-ventricular-hypertrophy-lvh-hearts). For applications described here, default normal parameter values are used, with conserved TAN, CRtot, and TEP metabolite pools varied as described below. Steady-state cytoplasmic energetic state (concentrations of ATP, ADP, Pi, etc.) are computed as functions of cytoplasmic ATP hydrolysis rate to compute relationships between metabolite concentrations and oxygen consumption rate.

Population myocardial energetics model

The model of Wu et al. (5, 23) was used to simulate myocardial oxygen transport, mitochondrial tricarboxylic acid cycle kinetics and oxidative phosphorylation, and cytoplasmic adenylate kinase, creatine kinase, and ATP hydrolysis. Model predictions of how phosphate metabolite levels vary with MVO₂ are illustrated in Fig. 1 for 20-year-old subjects. For these steady-state model simulations, the ATP hydrolysis and ATP synthesis rates are equal and proportional to the rate of oxygen consumption. To obtain these results, the ATP demand (the cellular ATP hydrolysis rate) is varied from 0.36 to 1.52 mmol · s⁻¹ · (L cell)⁻¹. This range of ATP hydrolysis rate yields a range of MVO₂ of 3.5–13.5 mmol · min⁻¹ · g⁻¹ (or 78–302 μLO₂ · min⁻¹ · g⁻¹). Because MVO₂ = 3.5 mmol · min⁻¹ · g⁻¹ is the mean value of LV MVO₂ observed in anesthetized dogs under baseline conditions in the data sets analyzed by Wu et al. (23) and MVO₂ = 13.5 mmol · min⁻¹ · g⁻¹ represents the upper limit of LV oxygen consumption in conscious exercising dogs (26), we use this range of ATP demand to capture upper and lower limits of the physiological range. Simulations summarized in Fig. 1 show that mean cytoplasmic Pi concentration ([Pi]_c) increases from 0.43 mM under resting conditions (MVO₂ = 5.1 mmol · min⁻¹ · g⁻¹ (27)) to 2.0 mM at a moderate exercise intensity (MVO₂ = 10 mmol · min⁻¹ · g⁻¹) to 4.3 mM at maximal exercise conditions (MVO₂ = 13.5 mmol · min⁻¹ · g⁻¹), whereas the CrP/ATP ratio decreases from ∼2.06 at rest to 1.80 at MVO₂ = 10 mmol · min⁻¹ · g⁻¹ and to 1.50 at maximal exercise. These concentration ranges correspond to the expected ranges based on available in vivo data (23, 28).

Figure 1.

Myocardial cellular energetics. Population model predictions of myocardial energy metabolite levels are plotted as functions of MVO₂. Model-predicted CrP/ATP (A), cytoplasmic inorganic phosphate concentration [Pi]_c (B), cytoplasmic ATP concentration [ATP]_c (C), and cytoplasmic ADP concentration [ADP]_c (D) are plotted for a population of 20-year-old female subjects. The light shaded areas represent the 90% confidence range from the population prediction for each variable; the dark shaded areas represent the 50% confidence range; and the solid line represents the population mean.

Predictions of the Wu et al. model depend on the levels of the three conserved metabolite pools: the TAN, TEP, and CR_tot (5, 23). These pools are defined as follows:

$$\begin{array}{l}\begin{array}{c}TAN=V_{cyto}{W}_c\left({\left[ATP\right]}_c+{\left[ADP\right]}_c+{\left[AMP\right]}_c\right)\\ +V_{mito}{W}_i\left({\left[ATP\right]}_i+{\left[ADP\right]}_i+{\left[AMP\right]}_i\right)\\ +V_{mito}{W}_x\left({\left[ATP\right]}_x+{\left[ADP\right]}_x\right),\end{array}\\ \begin{array}{c}TEP=V_{cyto}{W}_c\left(2{\left[ATP\right]}_c+{\left[ADP\right]}_c+{\left[Pi\right]}_c+{\left[CrP\right]}_c\right)\\ +V_{mito}{W}_i\left(2{\left[ATP\right]}_i+{\left[ADP\right]}_i+{\left[Pi\right]}_i+{\left[CrP\right]}_i\right)\\ +V_{mito}{W}_x\left({\left[ATP\right]}_x+{\left[Pi\right]}_x+{\left[GTP\right]}_x\right),\end{array}\\ \begin{array}{c}{\text{CR}}_{\text{tot}}=V_{cyto}{W}_c\left({\left[Cr\right]}_c+{\left[CrP\right]}_c\right),\end{array}\end{array}$$ (1)

where V_cyto and V_mito are the cellular volume fraction of cytoplasm and mitochondria, respectively; W_c, W_i, and W_x are the water volume fraction in cytoplasm, mitochondrial intermembrane space, and mitochondrial matrix, respectively; solute concentration in different cellular region is represented by the solute name in a square bracket together with a subscript “c,” “i,” or “x,” indicating cytoplasm, mitochondrial intermembrane space, and mitochondrial matrix, respectively. The values of volume fractions used in this study are from Wu et al. (23).

It is assumed that the mean level of each metabolite pool varies linearly with human age, and the distribution of pool level at each specific age follows the normal distribution. Thus, for an individual subject, the metabolite pool is defined with a linear model as follows:

$$\begin{array}{ccc}\text{TAN}& =& \left(A_0-a\times age\right)\times \left(1+{\epsilon }_a\right),\\ \text{TEP}& =& \left(P_0-p\times age\right)\times \left(1+{\epsilon }_p\right),\\ {\text{CR}}_{\text{tot}}& =& \left(C_0-c\times age\right)\times \left(1+{\epsilon }_c\right),\end{array}$$ (2)

where A₀, P₀, C₀, a, p, and c are parameters, and ε_a, ε_p, and ε_c are random variables assumed to follow normal distributions with a mean of zero and variances defined as follows:

$$\langle \left[\begin{array}{c}{\epsilon }_a\\ {\epsilon }_p\\ {\epsilon }_c\end{array}\right]\times \left[\begin{array}{ccc}{\epsilon }_a& {\epsilon }_p& {\epsilon }_c\end{array}\right]\rangle =\left[\begin{array}{ccc}{\sigma }_a^2& 0& 0\\ 0& {\sigma }_p^2& {\sigma }_{pc}^2\\ 0& {\sigma }_{pc}^2& {\sigma }_c^2\end{array}\right].$$ (3)

Equation 3 assumes that the variability in the phosphate and creatine pools are correlated (with correlation coefficient σ_pc), whereas the adenine nucleotide pool varies independently of the other pools.

Values of parameters A₀, P₀, C₀, a, p, c, σ_a, σ_p, σ_c, and σ_pc are listed in Table 1. Values of these parameters were estimated as follows. The mean levels for all three metabolite pools in the 20-year-old population were assumed to be equal to the normal levels determined by Wu et al. (5) as follows:

$$\begin{array}{ccc}\langle \text{TAN}\left(20\mathrm{year}.\right)\rangle & =& A_0-20a=8.62\text{mmol}{\left(\text{L}\text{cell}\right)}^{-1},\\ \langle \text{TEP}\left(20\mathrm{year}.\right)\rangle & =& P_0-20p=29.78\text{mmol}{\left(\text{L}\text{cell}\right)}^{-1},\\ \langle {\text{CR}}_{\text{tot}}\left(20\mathrm{year}.\right)\rangle & =& C_0-20c=35.04\text{mmol}{\left(\text{L}\text{cell}\right)}^{-1}.\end{array}$$ (4)

Table 1.

Population Model Parameters

	Definition	Value	Units
A0	reference TAN value, assigned from Eq. 4	8.62	mmol (L cell)−1
P0	reference TEP value, assigned from Eq. 4	29.78	mmol (L cell)−1
C0	reference CRtot value, assigned from Eq. 4	35.04	mmol (L cell)−1
a	slope of relationship between mean TAN and age, estimated by fitting data in Fig. 2	0.082	mmol (L cell·year.)−1
p	slope of relationship between mean TEP and age, determined by Eq. 5	0.283	mmol (L cell·year.)−1
c	slope of relationship between mean CRtot and age, estimated by fitting data in Fig. 2	0.39837	mmol (L cell·year.)−1
σa	relative variance in TAN pool, estimated by fitting data in Fig. 2	0.12	unitless
σp	relative variance in TEP pool, estimated by fitting data in Fig. 2	0.06	unitless
σc	relative variance in CRtot pool, estimated by fitting data in Fig. 2	0.12	unitless
σpc	covariance between TEP and CRtot pool, estimated by fitting data in Fig. 2	0.08	unitless

Furthermore, the relationship between a and p was fixed to maintain the average proportion between TAN and TEP determined by Wu et al. (5) as follows:

$$p=\left(\frac{29.78}{8.62}\right)\times a.$$ (5)

Using the relationships defined in Eqs. 4 and 5, values of A₀, P₀, C₀, and p are calculated from estimates of a and c. The six adjustable parameters (a, c, σ_a, σ_p, σ_c, and σ_pc) defining the age-dependent variability in the metabolite pools are estimated by fitting model predictions to data from Köstler et al. (22) and Jakovljevic et al. (3), as detailed below.

Population model results were obtained by randomly sampling the distributions of TAN, TEP, and CR_tot governed by Eqs. 2 and 3. Results below were obtained by simulating 13 fixed-age groups representing ages from 20 to 80 years. Within each age group, 1000 independently determined individuals were simulated. Simulations representing the resting state are obtained setting the cellular ATP hydrolysis rate to 0.547 mmol·s⁻¹·(L cell)⁻¹, which yields a resting-state MVO₂ = 5.1 mmol·min⁻¹·(g tissue)⁻¹.

Summary of model assumptions

In summary, simulations are based on the previously published model of Wu et al. (23) of cardiac energy metabolism, which is validated in comparison to steady-state and transient data on phosphate metabolites from normal canine hearts in vivo and from steady-state data on phosphate metabolites measured in vivo in a canine model of hypertrophy and decompensation after pressure overload (5). Previously reported analyses of myocardial energetics in heart disease revealed that the observed reductions in ATP and CrP/ATP ratio may be explained by measured reductions in the TAN, CRtot, and TEP metabolite pools. Here, similar change in metabolic pools were imposed based on Eq. 2 to determine if and how changes in metabolite pools with age can explain changes in myocardial energetics and maximal cardiac power output with aging. Furthermore, to simulate the relationship between energetics cardiac power, we use the assumption of constant cardiac efficiency (see below.) Thus, there is no explicit model of myocardial mechanics, and it is assumed that cardiac mechanical efficiency is constant and independent of age. The validity of this assumption is discussed in the Discussion.

Results

Steady-state phosphate metabolite levels for healthy young individuals

The model predictions show in Fig. 1 (corresponding to a population of 20-year-old female subjects) reveal the expected trends of increasing ADP and inorganic phosphate with increasing ATP/oxygen demand. This in vivo relationship between ATP hydrolysis products and ATP synthesis rate has been shown to be effectively captured by an apparent random bi-bi mechanism (29) with apparent Michaelis-Menten constants for ADP and Pi of approximately K_ADP = 21 μM and K_Pi = 1.1 mM (30, 31). Thus, the predicted ADP concentration is several-fold higher than the apparent Michaelis-Menten constants for ADP over the whole range of in vivo ATP/oxygen demand, whereas ([Pi]_c) increases from approximately half its apparent Michaelis-Menten constant at resting conditions (MVO₂ = 5.1 mmol · min⁻¹ · g⁻¹). Thus, the inorganic phosphate concentration is the more important of ATP hydrolysis products in feedback stimulation of ATP synthesis (5, 23, 30, 31, 32). Increasing cytoplasmic Pi with increasing ATP demand leads to increased matrix Pi, which leads to a greater diving force for phosphorylation of ADP in the matrix, which leads to a greater ATP/ADP level, which increases flux through the mitochondrial ATP/ADP translocator, meeting the increased demand.

Parameterization of population model

The six adjustable parameters (a, c, σ_a, σ_p, σ_c, and σ_pc) in the population model are estimated by matching model predictions to data on resting-state myocardial energetics from Köstler et al. (22) and Jakovljevic et al. (3) in Fig. 2. The mean model outputs are plotted as solid black lines. The light shaded areas represent the 90% confidence range from the population prediction for each variable, and the dark shaded areas represent the 50% confidence range. The nonzero value of σ_pc, the covariance between TEP and CR_tot pool, indicates that higher-than-average CR_tot tends to be accompanied by higher-than-average total phosphate. In fact, the estimated σ_pc is roughly equal to the geometric mean of σ_p and σ_c, the relative variances in the TEP and CR_tot pools, suggesting that these two metabolite pools are regulated to vary in proportion.

Figure 2.

Changes in resting-state myocardial cellular energetics with age. Population model predictions of resting-state myocardial energy metabolite levels are plotted as functions of age. Model-predicted CrP/ATP (A), total ATP (B), total CrP (C), Gibbs free energy of ATP hydrolysis (D), cytoplasmic ADP concentration [ADP]_c (E), and cytoplasmic inorganic phosphate concentration [Pi]_c (F) are compared to data from Köstler et al. (22) and Jakovljevic et al. (3). The light shaded areas represent the 90% confidence range from the population prediction for each variable; the dark shaded areas represent the 50% confidence range; and the solid line represents population mean. Data from individual subjects are plotted as red dots. To see this figure in color, go online.

Fig. 2 A compares results on resting CrP to ATP ratio to data from Jakovljevic et al. (3) obtained from 55 healthy, untrained women with ages ranging from 21 to 81 years. The population model, defined based on Eqs. 2 and 3 effectively captures the trends observed by Jakovljevic et al. (3). Data from 29 of the 55 individuals fall within the 50% confidence range. Data from 3 of the 55 individual fall outside of the 90% confidence range. Fig. 2, B and C compare results on resting myocardial ATP and CrP levels to data from Köstler et al. (22) from 12 healthy women ranging from 21 to 64 years old. In Fig. 2, B and C, simulations and data are reported in terms of total ATP and CrP per mass of myocardium. The predicted decreases in CrP and ATP and with increasing age are in good agreement with the trends in the data from Köstler et al. (22).

Fig. 2, E and F plot the associated model predictions of cytoplasmic ADP ([ADP]_c) and [Pi]_c, which are reported here in units of millimoles per liter of myocyte cytoplasmic water space. As the TAN decreases with age, both the cytoplasmic ATP and ADP decrease. The median resting [ADP]_c is predicted to decrease from 78 μM for a typical 20-year-old to 17 μM for a typical 80-year-old. Because ATP synthesis is primarily controlled by concentrations of ADP and Pi, lower ADP levels in older individuals is balanced by higher concentrations of free phosphate compared to younger individuals. The population model predicts that resting-state cytoplasmic Pi increases from ∼0.5 mM in 20–40-year-old individuals to 1.0 mM in the mean 65-year-old and to greater than 1 mM in most individuals aged 70 years and older. Thus, the population model predicts that because of differences in conserved metabolite pool levels, the same resting ATP synthesis rate is associated with substantially different phosphate metabolite concentrations in young versus old individuals. The prediction of higher free phosphate, associated with lower ADP, in older compared to younger individuals, is intriguing in light of a potential link between increased plasma free phosphate levels and aging and cardiovascular disease risk (33, 34, 35). Lower ATP and ADP levels are also predicted to be associated with lower AMP and thus diminished AMP-dependent signaling in older individuals.

Predicted impacts of changes to cytoplasmic metabolic pools on the resting Gibbs free energy of ATP hydrolysis are shown in Fig. 2 D. For the age range of 20–40 years, the estimated ΔG_ATP is approximately −65.5 kJ mol⁻¹, equivalent to that estimated by Bazil et al. (17). As free phosphate levels increase with age, the magnitude of the resting ΔG_ATP decreases, reflecting the higher [Pi]_c required to maintain the same resting ATP demand in older compared to younger women.

Prediction of maximal cardiac power output

To predict maximal CPO, the maximal MVO₂ was estimated for each individual in the virtual populations by increasing cytoplasmic ATP demand until the cytoplasmic inorganic phosphate concentration reached 4.4 mM, the value associated with the maximal MVO₂ in the mean 30-year-old individual. The maximal MVO₂ was converted to maximal CPO based on the proportionality between MVO₂ and work as follows:

$$\text{CPO}=\epsilon \times {\text{M}\dot{\text{V}}\text{O}}_2\times 20\times \text{LVM}$$ (6)

where the myocardial external efficiency ε is set to 0.25 (36), MVO₂ is expressed in units of mL×(second g tissue)^-1, the caloric equivalent of 1 mL of O₂ is taken to be 20 J, and LVM is the LV mass set to 150 g.

Fig. 3 compares model-predicted maximal CPO to data from Jakovljevic et al. (3). Both panels plot the model predictions as in Figs. 1 and 2 with the light shaded areas representing the 90% confidence range from the population prediction for each variable and the dark shaded areas representing the 50% confidence range. The left panel plots the individual data points as red dots. The right panel plots statistical summaries of the data for three age groups, showing mean age and mean maximal CPO, and with error bars indicating ±1 SD. The model predicts that from age 20 to 80, the mean maximal CPO drops from 3.87 to 2.83 W, in agreement with the trend observed by Jakovljevic et al. (3) and Nathania et al. (4).

Figure 3.

Predicted maximal left ventricular CPO as function of age. Both panels plot the population model predictions of maximal left-ventricular power output as functions of age. The left panel shows observations from Jakovljevic et al. (3), with data from individual subjects plotted as individual data points. The right panel plots the means (open squares) and SDs (red lines) for the three age groups observed by Jakovljevic et al. (3). To see this figure in color, go online.

Similar to the resting-state simulations in Fig. 2, the majority of the data in Fig. 3 falls within the 90% confidence range, with 8 of the 55 individuals falling outside of the 90% range and 20 of 55 data points falling within the 50% confidence range. The population model predicts an average drop of 0.48 W in maximal CPO from the middle age group (mean 44 years) to old group (mean 71 years) compared to an observed difference of 0.79 W. Maximal CPO falls below 2.2 W for roughly 25% of the simulated 80-year-old population, close to the value of 1.96 W that has been identified as the cutoff associated with maximal relative risk ratio for mortality (1). Maximal CPO falls below 1.96 W for 15.5% of the simulated 80-year-old population.

Discussion

Using an age-structured population model, our study tested hypotheses that reductions in key cytosolic metabolite pools that occur with aging impair the myocardial capacity to synthesize ATP at physiological free energy levels and that the resulting metabolic changes impair the mechanical pumping ability of the heart and its performance. Results support these hypotheses, as the model parameterized based on resting-state data predicts the observed relationships between age and mechanical and energetic performance of the heart in exercise. Specifically, the population-level model of human cardiac energetics was parametrized to match data on resting-state energetics in healthy women aged 21–81.

Similar approaches to generating populations of model parameterizations have been used by Britton et al. (37) and Sobie (38) to generate model populations representing variability in cardiomyocyte electrophysiology kinetics. Sobie (38) introduced a method of sensitivity analysis combining random sampling of parameter values with least-squares regressions models mapping parameter variability to variability in model outputs. Britton et al. (37) used Latin hypercube sampling to generate uncorrelated random variability in parameters representing channel conductances and time constant, and then used comparisons to experimental data to explore relationships between variability in experimentally measured variables and the statistical structure of variability in the parameter space. Here, instead of first generating an unbiased uncorrelated parameter population and then later culling the parameter space based on comparisons to data, as done by Britton et al. (37), we have assumed an a priori statistical structure for the variability in metabolite pools, governed by parameters a, c, σ_a, σ_p, σ_c, and σ_pc. The statistical model is identified and validated based on comparison to data in Fig. 2. The validated virtual model population that is associated with parameter sets sampled from this statistical model is then used to explore how resting and exercise-state myocardial energetics varies in the population.

Model simulations predict that metabolic supply capacity decreases with age, driven by changes in metabolic pools. Applying the assumption that maximal cardiac power output is limited by maximal metabolic supply yields predictions that are consistent with available data on reductions in maximal CPO with age and are consistent with the following specific hypotheses:

• 1)Reductions in cytoplasmic adenine nucleotide, creatine, and phosphate pools that occur with aging impair the myocardial capacity to synthesize ATP at physiological free energy levels; and
• 2)The resulting changes to myocardial energetic status play a causal role in contributing to reductions in maximal cardiac power output with aging.

The potential importance of the link between energetic status and mechanical function is highlighted by the fact that maximal CPO is the strongest predictor of mortality in heart failure (1). Indeed, the hypotheses for mechanisms underlying age-dependent changes to myocardial mechano-energetic function tested here were formulated based on previous theoretical analysis of the link between energy metabolite levels and mechanical function of the heart in cardiac decomposition and failure (6, 7). Although these results do not suggest that the phenotypes are identical, they do suggest fundamental similarities in terms of mechanisms impeding myocardial energetics and mechanical-energetic coupling.

Because our model lacks an explicit representation of the mechanistic effects of metabolic/energetic state on myocardial mechanics, predictions of maximal cardiac power hinge on the simplifying assumption of constant efficiency (Eq. 6). An alternative to the second hypothesis above would be that cardiac efficiency decreases with age. However, our simulations suggest that this alternative may not be a major contributor to reductions in maximal CPO with aging. If mechanical efficiency were to markedly go down with age, then maximal CPO would drop with age even more than predicted by our model, which assumes constant efficiency. Future studies investigating the direct mechanistic link between energetics and muscle dynamics will require the development of a cardiomyocyte mechanics model that accounts for the effects of energetic state and is parameterized to represent human myocytes.

Author Contributions

X.G. and D.A.B. designed the study and conducted the analysis. All authors contributed to interpreting the results and writing the manuscript.

Editor: Eric Sobie.