zbMATH — the first resource for mathematics

A comparison of phenomenologic growth laws for myocardial hypertrophy. (English) Zbl 1373.74026
Summary: 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.

74D10 Nonlinear constitutive equations for materials with memory
74E99 Material properties given special treatment
74L15 Biomechanical solid mechanics
Full Text: DOI
[1] Anversa, P.; Ricci, R.; Olivetti, G., Quantitative structural analysis of the myocardium during physiologic growth and induced cardiac hypertrophy: a review, J. Am. Coll. Cardiol., 7, 1140-1149, (1986)
[2] Cantor, E.J.F.; Babick, A.P.; Vasanji, Z.; Dhalla, N.S.; Netticadan, T., A comparative serial echocardiographic analysis of cardiac structure and function in rats subjected to pressure or volume overload, J. Mol. Cell. Cardiol., 38, 777-786, (2005)
[3] Frey, N.; Olson, E.N., Cardiac hypertrophy: the good, the bad, and the ugly, Annu. Rev. Physiol., 65, 45-79, (2003)
[4] Heineke, J.; Molkentin, J.D., Regulation of cardiac hypertrophy by intracellular signalling pathways, Nat. Rev. Mol. Cell Biol., 7, 589-600, (2006)
[5] Rodriguez, E.K.; Hoger, A.; McCulloch, A.D., Stress-dependent finite growth in soft elastic tissues, J. Biomech., 27, 455-467, (1994)
[6] Grossman, W.; Jones, D.; McLaurin, L.P., Wall stress and patterns of hypertrophy in the human left ventricle, J. Clin. Invest., 56, 56-64, (1975)
[7] Emery, J.L.; Omens, J.H., Mechanical regulation of myocardial growth during volume-overload hypertrophy in the rat, Am. J. Physiol., 273, 1198-1204, (1997)
[8] Holmes, J.W., Candidate mechanical stimuli for hypertrophy during volume overload, J. Appl. Physiol., 97, (2004)
[9] Lin, I.E.; Taber, L.A., A model for stress-induced growth in the developing heart, J. Biomech. Eng., 117, 343-349, (1995)
[10] Taber, L.A., Biomechanical growth laws for muscle tissue, J. Theor. Biol., 193, 201-213, (1998)
[11] Kroon, W.; Delhaas, T.; Arts, T.; Bovendeerd, P., Computational modeling of volumetric soft tissue growth: application to the cardiac left ventricle, Biomech. Model. Mechanobiol., 8, 301-309, (2009)
[12] Göktepe, S.; Abilez, O.J.; Parker, K.K.; Kuhl, E., A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis, J. Theor. Biol., 265, 433-442, (2010)
[13] Arts, T.; Delhaas, T.; Bovendeerd, P.; Verbeek, X.; Prinzen, F.W., Adaptation to mechanical load determines shape and properties of heart and circulation: the circadapt model, Am. J. Physiol., Heart Circ. Physiol., 288, 1943-1954, (2005)
[14] Kerckhoffs, R.C.P.; Omens, J.H.; McCulloch, A.D., A single strain-based growth law predicts concentric and eccentric cardiac growth during pressure and volume overload, Mech. Res. Commun., 42, 40-50, (2012)
[15] Streeter, D.D.; Spotnitz, H.M.; Patel, D.P.; Ross, J.; Sonnenblick, E.H., Fiber orientation in the canine left ventricle during diastole and systole, Circ. Res., 24, 339-347, (1969)
[16] Fomovsky, G.M.; Holmes, J.W., Evolution of scar structure, mechanics, and ventricular function after myocardial infarction in the rat, Am. J. Physiol., Heart Circ. Physiol., 298, 221-228, (2010)
[17] Villarreal, F.J.; Waldman, L.K.; Lew, W.Y., Technique for measuring regional two-dimensional finite strains in canine left ventricle, Circ. Res., 62, 711-721, (1988)
[18] Lew, W.Y.; LeWinter, M.M., Regional comparison of midwall segment and area shortening in the canine left ventricle, Circ. Res., 58, 678-691, (1986)
[19] Omens, J.H.; Farr, D.D.; McCulloch, A.D.; Waldman, L.K., Comparison of two techniques for measuring two-dimensional strain in rat left ventricles, Am. J. Physiol., 271, 1256-1261, (1996)
[20] Omens, J.H.; MacKenna, D.A.; McCulloch, A.D., Measurement of strain and analysis of stress in resting rat left ventricular myocardium, J. Biomech., 26, 665-676, (1993)
[21] Tobita, K.; Schroder, E.A.; Tinney, J.P.; Garrison, J.B.; Keller, B.B., Regional passive ventricular stress-strain relations during development of altered loads in chick embryo, Am. J. Physiol., Heart Circ. Physiol., 282, 2386-2396, (2002)
[22] Glower, D.D.; Spratt, J.A.; Snow, N.D.; Kabas, J.S.; Davis, J.W.; Olsen, C.O.; Tyson, G.S.; Sabiston, D.C.; Rankin, J.S., Linearity of the Frank-starling relationship in the intact heart: the concept of preload recruitable stroke work, Circulation, 71, 994-1009, (1985)
[23] Sodums, M.T.; Badke, F.R.; Starling, M.R.; Little, W.C.; O’Rourke, R.A., Evaluation of left ventricular contractile performance utilizing end-systolic pressure-volume relationships in conscious dogs, Circ. Res., 54, 731-739, (1984)
[24] Rankin, J.S.; McHale, P.A.; Arentzen, C.E.; Ling, D.; Greenfield, J.C.; Anderson, R.W., The three-dimensional dynamic geometry of the left ventricle in the conscious dog, Circ. Res., 39, 304-313, (1976)
[25] Fomovsky, G.M.; Clark, S.A.; Parker, K.M.; Ailawadi, G.; Holmes, J.W., Anisotropic reinforcement of acute anteroapical infarcts improves pump function, Circ. Heart Fail., 5, 515-522, (2012)
[26] Omens, J.H.; Fung, Y.C., Residual strain in rat left ventricle, Circ. Res., 66, 37-45, (1990)
[27] Rodriguez, E.K.; Omens, J.H.; Waldman, L.K.; McCulloch, A.D., Effect of residual stress on transmural sarcomere length distributions in rat left ventricle, Am. J. Physiol., 264, 1048-1056, (1993)
[28] Alyono, D.; Ring, W.S.; Anderson, M.R.; Anderson, R.W., Left ventricular adaptation to volume overload from large aortocaval fistula, Surgery, 96, 360-367, (1984)
[29] Fujisawa, A.; Sasayama, S.; Takahashi, M.; Nakamura, M.; Ohyagi, A.; Lee, J.D.; Yui, Y.; Kawai, C., Enhancement of left ventricular contractility after opening of an arteriovenous fistula in dogs, Cardiovasc. Res., 18, 51-59, (1984)
[30] Nakano, K.; Swindle, M.M.; Spinale, F.; Ishihara, K.; Kanazawa, S.; Smith, A.; Biederman, R.W.; Clamp, L.; Hamada, Y.; Zile, M.R., Depressed contractile function due to canine mitral regurgitation improves after correction of the volume overload, J. Clin. Invest., 87, 2077-2086, (1991)
[31] Katayama, K.; Tajimi, T.; Guth, B.D.; Matsuzaki, M.; Lee, J.-D.; Seitelberger, R.; Peterson, K.L., Early diastolic filling dynamics during experimental mitral regurgitation in the conscious dog, Circulation, 78, 390-400, (1988)
[32] Kleaveland, J.P.; Kussmaul, W.G.; Vinciguerra, T.; Diters, R.; Carabello, B.A., Volume overload hypertrophy in a closed-chest model of mitral regurgitation, Am. J. Physiol., 254, 1034-1041, (1988)
[33] Carabello, B.A.; Nakano, K.; Corin, W.; Biederman, R.; Spann, J.F., Left ventricular function in experimental volume overload hypertrophy, Am. J. Physiol., 256, 974-981, (1989)
[34] Sasayama, S.; Ross, J.; Franklin, D.; Bloor, C.M.; Bishop, S.; Dilley, R.B., Adaptations of the left ventricle to chronic pressure overload, Circ. Res., 38, 172-178, (1976)
[35] Crozatier, B.; Caillet, D.; Bical, O., Left ventricular adaptation to sustained pressure overload in the conscious dog, Circ. Res., 54, 21-29, (1984)
[36] Su, J.B.; Crozatier, B., Preload-induced curvilinearity of left ventricular end-systolic pressure-volume relations. effects on derived indexes in closed-chest dogs, Circulation, 79, 431-440, (1989)
[37] Karunanithi, M.K.; Feneley, M.P., Single-beat determination of preload recruitable stroke work relationship: derivation and evaluation in conscious dogs, J. Am. Coll. Cardiol., 35, 502-513, (2000)
[38] Zile, M.R.; Tomita, M.; Ishihara, K.; Nakano, K.; Lindroth, J.; Spinale, F.; Swindle, M.; Carabello, B.A., Changes in diastolic function during development and correction of chronic LV volume overload produced by mitral regurgitation, Circulation, 87, 1378-1388, (1993)
[39] Sabri, A.; Rafiq, K.; Seqqat, R.; Kolpakov, M.A.; Dillon, R.; Dell’italia, L.J., Sympathetic activation causes focal adhesion signaling alteration in early compensated volume overload attributable to isolated mitral regurgitation in the dog, Circ. Res., 102, 1127-1136, (2008)
[40] Lee, J.D.; Sasayama, S.; Kihara, Y.; Ohyagi, A.; Fujisawa, A.; Yui, Y.; Kawai, C., Adaptations of the left ventricle to chronic volume overload induced by mitral regurgitation in conscious dogs, Heart Vessels, 1, 9-15, (1985)
[41] Newman, W.H.; Webb, J.G., Adaptation of left ventricle to chronic pressure overload: response to inotropic drugs, Am. J. Physiol., 238, 134-143, (1980)
[42] Wojciechowski, P.; Juric, D.; Louis, X.L.; Thandapilly, S.J.; Yu, L.; Taylor, C.; Netticadan, T., Resveratrol arrests and regresses the development of pressure overload- but not volume overload-induced cardiac hypertrophy in rats, J. Nutr., 140, 962-968, (2010)
[43] Pawlush, D.G.; Moore, R.L.; Musch, T.I.; Davidson, W.R., Echocardiographic evaluation of size, function, and mass of normal and hypertrophied rat ventricles, J. Appl. Physiol., 74, 2598-2605, (1993)
[44] Guido, M.C.; Carvalho Frimm, C.; Koike, M.K.; Cordeiro, F.F.; Moretti, A.I.S.; Godoy, L.C., Low coronary driving pressure is associated with subendocardial remodelling and left ventricular dysfunction in aortocaval fistula, Clin. Exp. Pharmacol. Physiol., 34, 1165-1172, (2007)
[45] Melenovsky, V.; Benes, J.; Skaroupkova, P.; Sedmera, D.; Strnad, H.; Kolar, M.; Vlcek, C.; Petrak, J.; Benes, J.; Papousek, F.; Oliyarnyk, O.; Kazdova, L.; Cervenka, L., Metabolic characterization of volume overload heart failure due to aorto-caval fistula in rats, Mol. Cell. Biochem., 354, 83-96, (2011)
[46] Ryan, T.D.; Rothstein, E.C.; Aban, I.; Tallaj, J.A.; Husain, A.; Lucchesi, P.A.; Dell’Italia, L.J., Left ventricular eccentric remodeling and matrix loss are mediated by bradykinin and precede cardiomyocyte elongation in rats with volume overload, J. Am. Coll. Cardiol., 49, 811-821, (2007)
[47] Chen, Y.W.; Pat, B.; Gladden, J.D.; Zheng, J.; Powell, P.; Wei, C.C.; Cui, X.; Husain, A.; Dell’Italia, L.J., Dynamic molecular and histopathological changes in the extracellular matrix and inflammation in the transition to heart failure in isolated volume overload, Am. J. Physiol., Heart Circ. Physiol., 300, 2251-2260, (2011)
[48] Wilson, K.; Guggilam, A.; West, T.A.; Zhang, X.; Trask, A.J.; Cismowski, M.J.; Tombe, P.; Sadayappan, S.; Lucchesi, P.A., Effects of a myofilament calcium sensitizer on left ventricular systolic and diastolic function in rats with volume overload heart failure, Am. J. Physiol., Heart Circ. Physiol., 307, 1605-1617, (2014)
[49] Gladden, J.D.; Zelickson, B.R.; Guichard, J.L.; Ahmed, M.I.; Yancey, D.M.; Ballinger, S.; Shanmugam, M.; Babu, G.J.; Johnson, M.S.; Darley-Usmar, V.; Dell’Italia, L.J., Xanthine oxidase inhibition preserves left ventricular systolic but not diastolic function in cardiac volume overload, Am. J. Physiol., Heart Circ. Physiol., 305, 1440-1450, (2013)
[50] Wei, C.C.; Chen, Y.; Powell, L.C.; Zheng, J.; Shi, K.; Bradley, W.E.; Powell, P.C.; Ahmad, S.; Ferrario, C.M.; Dell’Italia, L.J., Cardiac kallikrein-kinin system is upregulated in chronic volume overload and mediates an inflammatory induced collagen loss, PLoS ONE, 7, 1-14, (2012)
[51] Miyamoto, M.I.; Monte, F.; Schmidt, U.; DiSalvo, T.S.; Kang, Z.B.; Matsui, T.; Guerrero, J.L.; Gwathmey, J.K.; Rosenzweig, A.; Hajjar, R.J., Adenoviral gene transfer of SERCA2a improves left-ventricular function in aortic-banded rats in transition to heart failure, Proc. Natl. Acad. Sci. USA, 97, 793-798, (2000)
[52] Litwin, S.E.; Katz, S.E.; Weinberg, E.O.; Lorell, B.H.; Aurigemma, G.P.; Douglas, P.S., Serial echocardiographic-Doppler assessment of left ventricular geometry and function in rats with pressure-overload hypertrophy: chronic angiotensin-converting enzyme inhibition attenuates the transition to heart failure, Circulation, 91, 2642-2654, (1995)
[53] Kobayashi, S.; Yano, M.; Kohno, M.; Obayashi, M.; Hisamatsu, Y.; Ryoke, T.; Ohkusa, T.; Yamakawa, K.; Matsuzaki, M., Influence of aortic impedance on the development of pressure-overload left ventricular hypertrophy in rats, Circulation, 94, 3362-3368, (1996)
[54] Hao, J.; Kim, C.H.; Ha, T.S.; Ahn, H.Y., Epigallocatechin-3 gallate prevents cardiac hypertrophy induced by pressure overload in rats, J. Vet. Sci., 8, 121, (2007)
[55] Doenst, T.; Pytel, G.; Schrepper, A.; Amorim, P.; Färber, G.; Shingu, Y.; Mohr, F.W.; Schwarzer, M., Decreased rates of substrate oxidation ex vivo predict the onset of heart failure and contractile dysfunction in rats with pressure overload, Cardiovasc. Res., 86, 461-470, (2010)
[56] Shyu, K.G.; Liou, J.Y.; Wang, B.W.; Fang, W.J.; Chang, H., Carvedilol prevents cardiac hypertrophy and overexpression of hypoxia-inducible factor-1alpha and vascular endothelial growth factor in pressure-overloaded rat heart, J. Biomed. Sci., 12, 409-420, (2005)
[57] Derumeaux, G.; Mulder, P.; Richard, V.; Chagraoui, A.; Nafeh, C.; Bauer, F.; Henry, J.P.; Thuillez, C., Tissue Doppler imaging differentiates physiological from pathological pressure-overload left ventricular hypertrophy in rats, Circulation, 105, 1602-1608, (2002)
[58] Hwang, H.S.; Bleske, B.E.; Ghannam, M.M.J.; Converso, K.; Russell, M.W.; Hunter, J.C.; Boluyt, M.O., Effects of hawthorn on cardiac remodeling and left ventricular dysfunction after 1 month of pressure overload-induced cardiac hypertrophy in rats, Cardiovasc. Drugs Ther., 22, 19-28, (2008)
[59] Ma, Y.; Chen, B.; Liu, D.; Yang, Y.; Xiong, Z.; Zeng, J.; Dong, Y., MG132 treatment attenuates cardiac remodeling and dysfunction following aortic banding in rats via the NF-\(κ\mbox{B/TGF}β 1\) pathway, Biochem. Pharmacol., 81, 1228-1236, (2011)
[60] Xu, R.; Lin, F.; Zhang, S.; Chen, X.; Hu, S.; Zheng, Z., Signal pathways involved in reverse remodeling of the hypertrophic rat heart after pressure unloading, Int. J. Cardiol., 143, 414-423, (2010)
[61] Li, J.; Li, P.; Feng, X.; Li, Z.; Hou, R.; Han, C.; Zhang, Y., Effects of losartan on pressure overload-induced cardiac gene expression profiling in rats, Clin. Exp. Pharmacol. Physiol., 30, 827-832, (2003)
[62] Kume, O.; Takahashi, N.; Wakisaka, O.; Nagano-Torigoe, Y.; Teshima, Y.; Nakagawa, M.; Yufu, K.; Hara, M.; Saikawa, T.; Yoshimatsu, H., Pioglitazone attenuates inflammatory atrial fibrosis and vulnerability to atrial fibrillation induced by pressure overload in rats, Heart Rhythm, 8, 278-285, (2011)
[63] Phrommintikul, A.; Tran, L.; Kompa, A.; Wang, B.; Adrahtas, A.; Cantwell, D.; Kelly, D.J.; Krum, H., Effects of a rho kinase inhibitor on pressure overload induced cardiac hypertrophy and associated diastolic dysfunction, Am. J. Physiol., Heart Circ. Physiol., 294, 1804-1814, (2008)
[64] Spinale, F.G.; Ishihra, K.; Zile, M.; DeFryte, G.; Crawford, F.A.; Carabello, B.A., Structural basis for changes in left ventricular function and geometry because of chronic mitral regurgitation and after correction of volume overload, J. Thorac. Cardiovasc. Surg., 106, 1147-1157, (1993)
[65] Tsutsui, H.; Urabe, Y.; Mann, D.L.; Tagawa, H.; Carabello, B.A.; Cooper, G.; Zile, M.R., Effects of chronic mitral regurgitation on diastolic function in isolated cardiocytes, Circ. Res., 72, 1110-1123, (1993)
[66] Gerdes, A.M.; Campbell, S.E.; Hilbelink, D.R., Structural remodeling of cardiac myocytes in rats with arteriovenous fistulas, Lab. Invest., 59, 857-861, (1988)
[67] Liu, Z.; Hilbelink, D.R.; Crockett, W.B.; Gerdes, A.M., Regional changes in hemodynamics and cardiac myocyte size in rats with aortocaval fistulas. 1. developing and established hypertrophy, Circ. Res., 69, 52-58, (1991)
[68] Gerdes, A.M.; Clark, L.C.; Capasso, J.M., Regression of cardiac hypertrophy after closing an aortocaval fistula in rats, Am. J. Physiol., 268, 2345-2351, (1995)
[69] Zierhut, W.; Zimmer, H.G.; Gerdes, A.M., Effect of angiotensin converting enzyme inhibition on pressure-induced left ventricular hypertrophy in rats, Circ. Res., 69, 609-617, (1991)
[70] Wang, X.; Li, F.; Gerdes, A.M., Chronic pressure overload cardiac hypertrophy and failure in guinea pigs: I. regional hemodynamics and myocyte remodeling, J. Mol. Cell. Cardiol., 31, 307-317, (1999)
[71] Campbell, S.E.; Rakusan, K.; Gerdes, A.M., Change in cardiac myocyte size distribution in aortic-constricted neonatal rats, Basic Res. Cardiol., 84, 247-258, (1989)
[72] Korecky, B.; Rakusan, K., Normal and hypertrophic growth of the rat heart: changes in cell dimensions and number, Am. J. Physiol., 234, 123-128, (1978)
[73] Campbell, S.E.; Korecky, B.; Rakusan, K., Remodeling of myocyte dimensions in hypertrophic and atrophic rat hearts, Circ. Res., 68, 984-996, (1991)
[74] Degens, H.; Brouwer, K.F.J.; Gilde, A.J.; Lindhout, M.; Willemsen, P.H.M.; Janssen, B.J.; Vusse, G.J.; Bilsen, M., Cardiac fatty acid metabolism is preserved in the compensated hypertrophic rat heart, Basic Res. Cardiol., 101, 17-26, (2006)
[75] Mohammed, S.F.; Storlie, J.R.; Oehler, E.A.; Bowen, L.A.; Korinek, J.; Lam, C.S.P.; Simari, R.D.; Burnett, J.C.; Redfield, M.M., Variable phenotype in murine transverse aortic constriction, Cardiovasc. Pathol., 21, 188-198, (2012)
[76] Humphrey, J.D.; Rajagopal, K.R., A constrained mixture model for growth and remodeling of soft tissues, Math. Models Methods Appl. Sci., 12, 407-430, (2002) · Zbl 1021.74026
[77] Freeman, G.L.; LeWinter, M.M., Pericardial adaptations during chronic cardiac dilation in dogs, Circ. Res., 54, 294-300, (1984)
[78] Rodriguez, E.K.; Hunter, W.C.; Royce, M.J.; Leppo, M.K.; Douglas a, S.; Weisman, H.F., A method to reconstruct myocardial sarcomere lengths and orientations at transmural sites in beating canine hearts, Am. J. Physiol., 263, 293-306, (1992)
[79] Guccione, J.M.; O’Dell, W.G.; McCulloch, A.D.; Hunter, W.C., Anterior and posterior left ventricular sarcomere lengths behave similarly during ejection, Am. J. Physiol., 272, 469-477, (1997)
[80] Spotnitz, H.M.; Sonnenblick, E.H.; Spiro, D., Relation of ultrastructure to function in the intact heart: sarcomere structure relative to pressure volume curves of intact left ventricles of dog and cat, Circ. Res., 18, 49-66, (1966)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.