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A Comparison of Phenomenologic Growth Laws for Myocardial Hypertrophy

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Abstract

The heart grows in response to changes in hemodynamic loading during normal development and in response to valve disease, hypertension, and other pathologies. In general, a left ventricle subjected to increased afterload (pressure overloading) exhibits concentric growth characterized by thickening of individual myocytes and the heart wall, while one experiencing increased preload (volume overloading) exhibits eccentric growth characterized by lengthening of myocytes and dilation of the cavity. Predictive models of cardiac growth could be important tools in evaluating treatments, guiding clinical decision making, and designing novel therapies for a range of diseases. Thus, in the past 20 years there has been considerable effort to simulate growth within the left ventricle. While a number of published equations or systems of equations (often termed “growth laws”) can capture some aspects of experimentally observed growth patterns, no direct comparisons of the various published models have been performed. Here we examine eight of these laws and compare them in a simple test-bed in which we imposed stretches measured during in vivo pressure and volume overload. Laws were compared based on their ability to predict experimentally measured patterns of growth in the myocardial fiber and radial directions as well as the ratio of fiber-to-radial growth. Three of the eight laws were able to reproduce most key aspects of growth following both pressure and volume overload. Although these three growth laws utilized different approaches to predict hypertrophy, they all employed multiple inputs that were weakly correlated during in vivo overload and therefore provided independent information about mechanics.

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Acknowledgements

This study was supported by the Hartwell Foundation (CMW) and the National Institutes of Health (U01 HL127654, JWH).

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Authors and Affiliations

  1. Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA

    Colleen M. Witzenburg & Jeffrey W. Holmes

  2. Department of Medicine, University of Virginia, Charlottesville, VA, USA

    Jeffrey W. Holmes

  3. Robert M. Berne Cardiovascular Research Center, University of Virginia, Charlottesville, VA, USA

    Jeffrey W. Holmes

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  1. Colleen M. Witzenburg
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Correspondence to Jeffrey W. Holmes.

Electronic Supplementary Material

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Table S1: Summary of LV Radius and Thickness Changes in Response to Overload in Dogs and Rats (PDF 249 kB)

Table S2: Summary Myocyte Radius and Thickness Changes in Response to Overload in Dogs and Rats (PDF 214 kB)

10659_2017_9631_MOESM3_ESM.pdf

Figure S1: For each law we varied the maximum elastic fiber or cross-fiber stretch (i.e. end-diastolic stretch) or the minimum elastic fiber or cross-fiber stretch (i.e. the end-systolic stretch) over the ranges covered by our simulations and determined the growth rate that would occur in our simplified biaxial slab model. This turns out to be more straightforward for some laws than for others. KFR and KUR (A) predict isotropic growth based on end-diastolic fiber strain, but the growth rate for KUR is insensitive any previous growth (i.e. the y-axis is simply \({F_{g}^{i+1}} / {1}\)). For both KOM (B) and LT2 (C) the rates of fiber growth and cross-fiber growth are determined from inputs at different time points within the cardiac cycle. ART uses the ratio of maximum to minimum fiber stretch, so the behavior while varying one depends strongly on the value of the other (D). Finally, GEG and GCG laws use growth-limiting terms that alter the entire stretch-growth curve as growth progresses (F and G) (TIF 255 kB)

10659_2017_9631_MOESM4_ESM.pdf

Figure S2: The end-diastolic pressure (EDP) and end-diastolic segment length data from Fomovsky et al. [25] were used to estimate end-diastolic circumferential stretch relative to the unloaded state in normal dogs. A linear fit (solid line) was used to extrapolate segment length at an EDP of 1 mmHg. This value was considered the end-diastolic stretch in reference to the unloaded state. Only extrapolations with coefficients of variation <5.0% were used (TIF 231 kB)

10659_2017_9631_MOESM5_ESM.pdf

Figure S3: The number of growth time steps at which L&T, KFR, KUR, GEG and KOM all achieved steady state growth. LT2, GCG, and ART (dashed bars) produced divergent growth (\(F_{g} >20\) or \(F_{g} <0.05\)). Simulations for these laws were stopped early (at 2, 4, and 2 growth time steps, respectively) in order to match the mean radius-to-thickness ratio observed experimentally (TIF 43 kB)

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Witzenburg, C.M., Holmes, J.W. A Comparison of Phenomenologic Growth Laws for Myocardial Hypertrophy. J Elast 129, 257–281 (2017). https://doi.org/10.1007/s10659-017-9631-8

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