Research Papers

Infarcted Left Ventricles Have Stiffer Material Properties and Lower Stiffness Variation: Three-Dimensional Echo-Based Modeling to Quantify In Vivo Ventricle Material Properties

[+] Author and Article Information
Longling Fan

Department of Mathematics,
Southeast University,
Nanjing 210096, China

Jing Yao

Department of Cardiology,
First Affiliated Hospital
of Nanjing Medical University,
Nanjing 210029, China

Chun Yang

Network Technology Research Institute,
China United Network
Communications Co., Ltd.,
Beijing 100048, China

Dalin Tang

School of Biological Science & Medical
Southeast University,
Nanjing 210096, China
Mathematical Sciences Department,
Worcester Polytechnic Institute,
Worcester, MA 01609

Di Xu

Department of Cardiology,
First Affiliated Hospital
of Nanjing Medical University,
Nanjing 210029, China

1Corresponding authors.

Manuscript received December 11, 2014; final manuscript received May 11, 2015; published online June 9, 2015. Assoc. Editor: Hai-Chao Han.

J Biomech Eng 137(8), 081005 (Aug 01, 2015) (10 pages) Paper No: BIO-14-1620; doi: 10.1115/1.4030668 History: Received December 11, 2014; Revised May 11, 2015; Online June 09, 2015

Methods to quantify ventricle material properties noninvasively using in vivo data are of great important in clinical applications. An ultrasound echo-based computational modeling approach was proposed to quantify left ventricle (LV) material properties, curvature, and stress/strain conditions and find differences between normal LV and LV with infarct. Echo image data were acquired from five patients with myocardial infarction (I-Group) and five healthy volunteers as control (H-Group). Finite element models were constructed to obtain ventricle stress and strain conditions. Material stiffening and softening were used to model ventricle active contraction and relaxation. Systolic and diastolic material parameter values were obtained by adjusting the models to match echo volume data. Young's modulus (YM) value was obtained for each material stress–strain curve for easy comparison. LV wall thickness, circumferential and longitudinal curvatures (C- and L-curvature), material parameter values, and stress/strain values were recorded for analysis. Using the mean value of H-Group as the base value, at end-diastole, I-Group mean YM value for the fiber direction stress–strain curve was 54% stiffer than that of H-Group (136.24 kPa versus 88.68 kPa). At end-systole, the mean YM values from the two groups were similar (175.84 kPa versus 200.2 kPa). More interestingly, H-Group end-systole mean YM was 126% higher that its end-diastole value, while I-Group end-systole mean YM was only 29% higher that its end-diastole value. This indicated that H-Group had much greater systole–diastole material stiffness variations. At beginning-of-ejection (BE), LV ejection fraction (LVEF) showed positive correlation with C-curvature, stress, and strain, and negative correlation with LV volume, respectively. At beginning-of-filling (BF), LVEF showed positive correlation with C-curvature and strain, but negative correlation with stress and LV volume, respectively. Using averaged values of two groups at BE, I-Group stress, strain, and wall thickness were 32%, 29%, and 18% lower (thinner), respectively, compared to those of H-Group. L-curvature from I-Group was 61% higher than that from H-Group. Difference in C-curvature between the two groups was not statistically significant. Our results indicated that our modeling approach has the potential to determine in vivo ventricle material properties, which in turn could lead to methods to infer presence of infarct from LV contractibility and material stiffness variations. Quantitative differences in LV volume, curvatures, stress, strain, and wall thickness between the two groups were provided.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Desmond-Hellmann, S., Sawyers, C. L., Cox, D. R., Fraser-Liggett, C., Galli, S. J., Goldstein, D. B., Hunter, D., Kohane, I. S., Lo, B., Misteli, T., Morrison, S. J., Nichols, D. G., Olson, M. V., Royal, C. D., and Yamamoto, K. R., 2011, “Toward Precision Medicine: Building a Knowledge Network for Biomedical Research and a New Taxonomy of Disease,” Committee on a Framework for Development a New Taxonomy of Disease, National Research Council, The National Academies Press. http://www.nap.edu/catalog.php?record_id=13284
McCulloch, A., Waldman, L., Rogers, J., and Guccione, J., 1992, “Large-Scale Finite Element Analysis of the Beating Heart,” Crit. Rev. Biomed. Eng., 20(5–6), pp. 427–449. [PubMed]
Guccione, J. M., McCulloch, A. D., and Waldman, L. K., 1991, “Passive Material Properties of Intact Ventricular Myocardium Determined From a Cylindrical Model,” ASME J. Biomech. Eng., 113(1), pp. 42–55. [CrossRef]
Guccione, J. M., Waldman, L. K., and McCulloch, A. D., 1993, “Mechanics of Active Contraction in Cardiac Muscle: Part II—Cylindrical Models of the Systolic Left Ventricle,” ASME J. Biomech. Eng., 115(1), pp. 82–90. [CrossRef]
Krishnamurthy, A., Villongco, C. T., Chuang, J., Frank, L. R., Nigam, V., Belezzuoli, E., Stark, P., Krummen, D. E., Narayan, S., Omens, J. H., McCulloch, A. D., and Kerckhoffs, R. C., 2013, “Patient-Specific Models of Cardiac Biomechanics,” J. Comput. Phys., 244, pp. 4–21. [CrossRef] [PubMed]
Holmes, J. W., and Costa, K. D., 2006, “Imaging Cardiac Mechanics: What Information Do We Need to Extract From Cardiac Images?,” Conf. Proc. IEEE Eng. Med. Biol. Soc., 1, pp. 1545–1547. [CrossRef] [PubMed]
Moyer, C. B., Norton, P. T., Ferguson, J. D., and Holmes, J. W., “Changes in Global and Regional Mechanics Due to Atrial Fibrillation: Insights From a Coupled Finite-Element and Circulation Model,” Ann. Biomed. Eng. (in press). [CrossRef]
Fomovsky, G. M., Macadangdang, J. R., Ailawadi, G., and Holmes, J. W., 2011, “Model-Based Design of Mechanical Therapies for Myocardial Infarction,” J. Cardiovasc. Trans. Res., 4(1), pp. 82–91. [CrossRef]
Emond, M., Mock, M. B., Davis, K. B., Fisher, L. D., Holmes, D. R., Jr., Chaitman, B. R., Kaiser, G. C., Alderman, E., and Killip, T., III, 1994, “Long-Term Survival of Medically Treated Patients in the Coronary Artery Surgery Study (CASS) Registry,” Circulation, 90(6), pp. 2645–2657. [CrossRef] [PubMed]
Møller, J. E., Hillis, G. S., Oh, J. K., Reeder, G. S., Gersh, B. J., and Pellikka, P. A., 2006, “Wall Motion Score Index and Ejection Fraction for Risk Stratification After Acute Myocardial Infarction,” Am. Heart J., 151(2), pp. 419–425. [CrossRef] [PubMed]
Quinones, M. A., Greenberg, B. H., Kopelen, H. A., Koilpillai, C., Limacher, M. C., Shindler, D. M., Shelton, B. J., and Weiner, D. H., 2000, “Echocardiographic Predictors of Clinical Outcome in Patients With Left Ventricular Dysfunction Enrolled in the SOLVD Registry and Trials: Significance of Left Ventricular Hypertrophy,” J. Am. Coll. Cardiol., 35(5), pp. 1237–1244. [CrossRef] [PubMed]
Sabia, P., Afrookteh, A., Touchstone, D. A., Keller, M. W., Esquivel, L., and Kaul, S., 1991, “Value of Regional Wall Motion Abnormality in the Emergency Room Diagnosis of Acute Myocardial Infarction: A Prospective Study Using Two Dimensional Echocardiography,” Circulation, 84(3 Suppl.), pp. I85–I92. [PubMed]
Thune, J. J., Kober, L., Pfeffer, M. A., Skali, H., Anavekar, N. S., Bourgoun, M., Ghali, J. K., Arnold, J. M., Velazquez, E. J., and Solomon, S. D., 2006, “Comparison of Regional Versus Global Assessment of Left Ventricular Function in Patients With Left Ventricular Dysfunction, Heart Failure, or Both After Myocardial Infarction: The Valsartan in Acute Myocardial Infarction Echocardiographic Study,” J. Am. Soc. Echocardiogr., 19(12), pp. 1462–1465. [CrossRef] [PubMed]
Gopal, A. S., Shen, Z., Sapin, P. M., Keller, A. M., Schnellbaecher, M. J., Leibowitz, D. W., Akinboboye, O. O., Rodney, R. A., Blood, D. K., and King, D. L., 1995, “Assessment of Cardiac Function by Three-Dimensional Echocardiography Compared With Conventional Noninvasive Methods,” Circulation, 92(4), pp. 842–853. [CrossRef] [PubMed]
Mondelli, J. A., Di Luzio, S., Nagaraj, A., Kane, B. J., Smulevitz, B., Nagaraj, A. V., Greene, R., McPherson, D. D., and Rigolin, V. H., 2001, “The Validation of Volumetric Real-Time 3-Dimensional Echocardiography for the Determination of Left Ventricular Function,” J. Am. Soc. Echocardiogr., 14(10), pp. 994–1000. [CrossRef] [PubMed]
Edvardsen, T., Gerber, B. L., Garot, J., Bluemke, D. A., Lima, J. A., and Smiseth, O. A., 2002, “Quantitative Assessment of Intrinsic Regional Myocardial Deformation by Doppler Strain Rate Echocardiography in Humans: Validation Against Three Dimensional Tagged Magnetic Resonance Imaging,” Circulation, 106(1), pp. 50–56. [CrossRef] [PubMed]
Urheim, S., Edvardsen, T., Torp, H., Angelsen, B., and Smiseth, O. A., 2000, “Myocardial Strain by Doppler Echocardiography: Validation of a New Method to Quantify Regional Myocardial Function,” Circulation, 102(1), pp. 1158–1164. [CrossRef] [PubMed]
Sutherland, G. R., Di Salvo, G., Claus, P., D'hooge, J., and Bijnens, B., 2004, “Strain and Strain Rate Imaging: A New Clinical Approach to Quantifying Regional Myocardial Function,” J. Am. Soc. Echocardiogr., 17(7), pp. 788–802. [CrossRef] [PubMed]
Amundsen, B. H., Helle-Valle, T., Edvardsen, T., Torp, H., Crosby, J., Lyseggen, E., Støylen, A., Ihlen, H., Lima, J. A., Smiseth, O. A., and Slørdahl, S. A., 2006, “Noninvasive Myocardial Strain Measurement by Speckle Tracking Echocardiography: Validation Against Sonomicrometry and Tagged Magnetic Resonance Imaging,” J. Am. Coll. Cardiol., 47(4), pp. 789–793. [CrossRef] [PubMed]
Peskin, C. S., 1975, Mathematical Aspects of Heart Physiology (Lecture Notes of Courant Institute of Mathematical Sciences), New York University, New York.
Costa, K. D., Takayama, Y., McCulloch, A. D., and Covell, J. W., 1999, “Laminar Fiber Architecture and Three-Dimensional Systolic Mechanics in Canine Ventricular Myocardium,” Am. J. Physiol., 276(2 Pt. 2), pp. H595–H607. [PubMed]
Nash, M. P., and Hunter, P. J., 2000, “Computational Mechanics of the Heart, From Tissue Structure to Ventricular Function,” J. Elasticity, 61(1–3), pp. 113–141. [CrossRef]
Rogers, J. M., and McCulloch, A. D., 1994, “Nonuniform Muscle Fiber Orientation Causes Spiral Wave Drift in a Finite Element Model of Cardiac Action Potential Propagation,” J. Cardiovasc. Electrophysiol., 5(6), pp. 496–509. [CrossRef] [PubMed]
Sacks, M. S., and Chuong, C. J., 1993, “Biaxial Mechanical Properties of Passive Right Ventricular Free Wall Myocardium,” ASME J. Biomech. Eng., 115(2), pp. 202–205. [CrossRef]
Takayama, Y., Costa, K. D., and Covell, J. W., 2002, “Contribution of Laminar Myofiber Architecture to Load-Dependent Changes in Mechanics of LV Myocardium,” Am. J. Physiol. Heart Circ. Physiol., 282(4), pp. H1510–H1520. [CrossRef] [PubMed]
Humphrey, J. D., Strumpf, R. K., and Yin, F. C., 1999, “Biaxial Mechanical Behavior of Excised Ventricular Epicardium,” Am. J. Physiol., 259(1 Pt. 2), pp. H101–H108.
Mojsejenko, D., McGarvey, J. R., Dorsey, S. M., Gorman, J. H., III, Burdick, J. A., Pilla, J. J., Gorman, R. C., and Wenk, J. F., 2015, “Estimating Passive Mechanical Properties in a Myocardial Infarction Using MRI and Finite Element Simulations,” Biomech. Model. Mechanobiol., 14(3), pp. 633–647. [CrossRef] [PubMed]
Hassaballah, A. I., Hassan, M. A., Mardi, A. N., and Hamdi, M., 2013, “An Inverse Finite Element Method for Determining the Tissue Compressibility of Human Left Ventricular Wall During the Cardiac Cycle,” PLoS One, 8(12), p. e82703. [CrossRef] [PubMed]
Humphrey, J. D., 2002, Cardiovascular Solid Mechanics, Springer-Verlag, New York. [CrossRef]
Axel, L., 2002, “Biomechanical Dynamics of the Heart With MRI,” Annu. Rev. Biomed. Eng., 4, pp. 321–347. [CrossRef] [PubMed]
Saber, N. R., Gosman, A. D., Wood, N. B., Kilner, P. J., Charrier, C. L., and Firman, D. N., 2001, “Computational Flow Modeling of the Left Ventricle Based on In Vivo MRI Data: Initial Experience,” Ann. Biomech. Eng., 29(4), pp. 275–283. [CrossRef]
Tang, D., Yang, C., Geva, T., and del Nido, P. J., 2008, “Patient-Specific MRI-Based 3D FSI RV/LV/Patch Models for Pulmonary Valve Replacement Surgery and Patch Optimization,” ASME J. Biomech. Eng., 130(4), p. 041010. [CrossRef]
Tang, D., Yang, C., Geva, T., and del Nido, P. J., 2010, “Image-Based Patient-Specific Ventricle Models With Fluid–Structure Interaction for Cardiac Function Assessment and Surgical Design Optimization,” Prog. Pediatr. Cardiol., 30(1–2), pp. 51–62. [CrossRef] [PubMed]
Tang, D., Yang, C., Geva, T., Gaudette, G., and del Nido, P. J., 2010, “Effect of Patch Mechanical Properties on Right Ventricle Function Using MRI-Based Two-Layer Anisotropic Models of Human Right and Left Ventricles,” Comput. Model. Eng. Sci., 56(2), pp. 113–130. [CrossRef] [PubMed]
Tang, D., Yang, C., Geva, T., Gaudette, G., and del Nido, P. J., 2011, “Multi-Physics MRI-Based Two-Layer Fluid–Structure Interaction Anisotropic Models of Human Right and Left Ventricles With Different Patch Materials: Cardiac Function Assessment and Mechanical Stress Analysis,” Comput. Struct., 89(11–12), pp. 1059–1068. [CrossRef] [PubMed]
Fan, R., Tang, D., Yao, J., Yang, C., and Xu, D., 2014, “3D Echo-Based Patient-Specific Computational Left Ventricle Models to Quantify Material Properties and Stress/Strain Differences Between Ventricles With and Without Infarct,” Comput. Model. Eng. Sci., 99(6), pp. 491–508. [CrossRef] [PubMed]
Sanchez-Quintana, D., Anderson, R., and Ho, S. Y., 1996, “Ventricular Myoarchitecture in Tetralogy of Fallot,” Heart, 76(3), pp. 280–286. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

Echo images from a patient (P5) with infarct, and reconstructed geometry. Infarct locations were marked by thick circles on the echo images: (a) end-systolic echo images, (b) end-diastolic echo images, (c) reconstructed end-systolic LV geometry, and (d) reconstructed end-diastolic LV geometry

Grahic Jump Location
Fig. 2

Echo images of a healthy volunteer (P6), contours and reconstructed geometries: (a) end-systolic echo, healthy volunteer, (b) end-diastolic echo, healthy volunteer, (c) reconstructed end-systolic LV geometry, and (d) reconstructed end-diastolic LV geometry

Grahic Jump Location
Fig. 3

A sample of recorded and imposed LV blood pressure profile: (a) recorded LV blood pressure profile and (b) imposed LV blood pressure profile

Grahic Jump Location
Fig. 5

LV geometries corresponding to no-load, end-systolic, and end-diastolic conditions: (a) no-load geometry, (b) end-systolic geometry, and (c) end-diastolic geometry

Grahic Jump Location
Fig. 4

Modeling fiber orientation: (a) fiber orientation from a pig model; (b) fiber orientation from a human heart; (c) fiber orientation from our two-layer LV model, end-systolic; and (d) end-diastolic condition

Grahic Jump Location
Fig. 6

Material stress–stretch curves (in fiber coordinate) for P5 (infarct group) and P6 (healthy group). Tff: stress in fiber direction and Tcc: stress in circumferential direction of the fiber: (a) P5, end-systole, (b) P5, end-diastole, (c) P6, end-systole, and (d) P6, end-diastole.

Grahic Jump Location
Fig. 7

Stress-P1 (maximum principal stress) and strain-P1 (maximum principal strain) plots from P5 (with infarct) and P6 (healthy) showing stress/strain distribution patterns corresponding to maximum and minimum pressure conditions: (a) P5, stress-P1, BF; (b) P5, strain-P1, BF; (c) P5, stress-P1, BE; (d) P5, strain-P1, BE; (e) P6, stress-P1, BF; (f) P6, strain-P1, BF; (g) P6, stress-P1, BE; and (h) P6, strain-P1, BE



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In