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Expert View

Model First and Ask Questions Later: Confessions of a Reformed Experimentalist

[+] Author and Article Information
Jeffrey W. Holmes

Departments of Biomedical
Engineering and Medicine,
Robert M. Berne Cardiovascular
Research Center, and Center for
Engineering in Medicine,
University of Virginia,
P.O. Box 800759,
Charlottesville, VA 22908
e-mail: holmes@virginia.edu

1Corresponding author.

Manuscript received June 14, 2018; final manuscript received March 28, 2019; published online May 23, 2019. Editor: Victor H. Barocas.

J Biomech Eng 141(7), 074701 (May 23, 2019) (6 pages) Paper No: BIO-18-1282; doi: 10.1115/1.4043432 History: Received June 14, 2018; Revised March 28, 2019

This paper is an invited perspective written in association with the awarding of the 2018 American Society of Mechanical Engineers Van C. Mow Medal. Inspired by Professor Mow's collaboration with Professor Michael Lai and the role mathematical modeling played in their work on cartilage biomechanics, this article uses our group's work on myocardial infarct healing as an example of the potential value of models in modern experimental biomechanics. Focusing more on the thought process and lessons learned from our studies on infarct mechanics than on the details of the science, this article argues that the complexity of current research questions and the wealth of information already available about almost any cell, tissue, or organ should change how we approach problems and design experiments. In particular, this paper proposes that constructing a mathematical or computational model is now in many cases a critical prerequisite to designing scientifically useful, informative experiments.

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References

Mow, V. C. , Kuei, S. C. , Lai, W. M. , and Armstrong, C. G. , 1980, “ Biphasic Creep and Stress Relaxation of Articular Cartilage in Compression? Theory and Experiments,” ASME J. Biomech. Eng., 102(1), pp. 73–84. [CrossRef]
Armstrong, C. G. , Lai, W. M. , and Mow, V. C. , 1984, “ An Analysis of the Unconfined Compression of Articular Cartilage,” ASME J. Biomech. Eng., 106(2), pp. 165–173. [CrossRef]
Lai, W. M. , Hou, J. S. , and Mow, V. C. , 1991, “ A Triphasic Theory for the Swelling and Deformation Behaviors of Articular Cartilage,” ASME J. Biomech. Eng., 113(3), pp. 245–258. [CrossRef]
Holmes, J. W. , Nuñez, J. A. , and Covell, J. W. , 1997, “ Functional Implications of Myocardial Scar Structure,” Am. J. Physiol., 272(5 Pt 2), pp. H2123–H2130. [PubMed]
Fomovsky, G. M. , and Holmes, J. W. , 2010, “ Evolution of Scar Structure, Mechanics, and Ventricular Function After Myocardial Infarction in the Rat,” Am. J. Physiol. Heart Circ. Physiol., 298(1), pp. H221–H228. [CrossRef] [PubMed]
Fomovsky, G. M. , Rouillard, A. D. , and Holmes, J. W. , 2012, “ Regional Mechanics Determine Collagen Fiber Structure in Healing Myocardial Infarcts,” J. Mol. Cell. Cardiol., 52(5), pp. 1083–1090. [CrossRef] [PubMed]
Fomovsky, G. M. , Macadangdang, J. R. , Ailawadi, G. , and Holmes, J. W. , 2011, “ Model-Based Design of Mechanical Therapies for Myocardial Infarction,” J. Cardiovasc. Transl. Res., 4(1), pp. 82–91. [CrossRef] [PubMed]
Fomovsky, G. M. , Clark, S. A. , Parker, K. M. , Ailawadi, G. , and Holmes, J. W. , 2012, “ Anisotropic Reinforcement of Acute Anteroapical Infarcts Improves Pump Function,” Circ. Heart Fail., 5(4), pp. 515–522. [CrossRef] [PubMed]
Richardson, W. J. , Clarke, S. A. , Quinn, T. A. , and Holmes, J. W. , 2015, “ Physiological Implications of Myocardial Scar Structure,” Compr. Physiol., 5(4), pp. 1877–1909. [CrossRef] [PubMed]
Clarke, S. A. , Richardson, W. J. , and Holmes, J. W. , 2016, “ Modifying the Mechanics of Healing Infarcts: Is Better the Enemy of Good?,” J. Mol. Cell. Cardiol., 93, pp. 115–124. [CrossRef] [PubMed]
Holmes, J. W. , Laksman, Z. , and Gepstein, L. , 2016, “ Making Better Scar: Emerging Approaches for Modifying Mechanical and Electrical Properties Following Infarction and Ablation,” Prog. Biophys. Mol. Biol., 120(1–3), pp. 134–148. [CrossRef] [PubMed]
Holmes, J. W. , Yamashita, H. , Waldman, L. K. , and Covell, J. W. , 1994, “ Scar Remodeling and Transmural Deformation After Infarction in the Pig,” Circulation, 90(1), pp. 411–420. [CrossRef] [PubMed]
Zimmerman, S. D. , Karlon, W. J. , Holmes, J. W. , Omens, J. H. , and Covell, J. W. , 2000, “ Structural and Mechanical Factors Influencing Infarct Scar Collagen Organization,” Am. J. Physiol. Heart Circ. Physiol., 278(1), pp. H194–H200. [CrossRef] [PubMed]
Knezevic, V. , Sim, A. J. , Borg, T. K. , and Holmes, J. W. , 2002, “ Isotonic Biaxial Loading of Fibroblast-Populated Collagen Gels: A Versatile, Low-Cost System for the Study of Mechanobiology,” Biomech. Model. Mechanobiol., 1(1), pp. 59–67. [CrossRef] [PubMed]
Costa, K. D. , Lee, E. J. , and Holmes, J. W. , 2003, “ Creating Alignment and Anisotropy in Engineered Heart Tissue: Role of Boundary Conditions in a Model Three-Dimensional Culture System,” Tissue Eng., 9(4), pp. 567–577. [CrossRef] [PubMed]
Thomopoulos, S. , Fomovsky, G. M. , and Holmes, J. W. , 2005, “ The Development of Structural and Mechanical Anisotropy in Fibroblast Populated Collagen Gels,” ASME J. Biomech. Eng., 127(5), pp. 742–750. [CrossRef]
Thomopoulos, S. , Fomovsky, G. M. , Chandran, P. L. , and Holmes, J. W. , 2007, “ Collagen Fiber Alignment Does Not Explain Mechanical Anisotropy in Fibroblast Populated Collagen Gels,” ASME J. Biomech. Eng., 129(5), pp. 642–650. [CrossRef]
Lee, E. J. , Holmes, J. W. , and Costa, K. D. , 2008, “ Remodeling of Engineered Tissue Anisotropy in Response to Altered Loading Conditions,” Ann. Biomed. Eng., 36(8), pp. 1322–1334. [CrossRef] [PubMed]
Janes, K. A. , Chandran, P. L. , Ford, R. M. , Lazzara, M. J. , Papin, J. A. , Peirce, S. M. , Saucerman, J. J. , and Lauffenburger, D. A. , 2017, “ An Engineering Design Approach to Systems Biology,” Integr. Biol. (Camb)., 9(7), pp. 574–583. [CrossRef] [PubMed]
Rouillard, A. D. , and Holmes, J. W. , 2012, “ Mechanical Regulation of Fibroblast Migration and Collagen Remodelling in Healing Myocardial Infarcts,” J. Physiol., 590(18), pp. 4585–4602. [CrossRef] [PubMed]
Caggiano, L. R. , Lee, J.-J. , and Holmes, J. W. , 2018, “ Surgical Reinforcement Alters Collagen Alignment and Turnover in Healing Myocardial Infarcts,” Am. J. Physiol. Heart Circ. Physiol., 315(4), pp. H1041–H1050. [CrossRef] [PubMed]
Huxley, A. F. , 1957, “ Muscle Structure and Theories of Contraction,” Prog. Biophys. Biophys. Chem., 7, pp. 255–318. [CrossRef] [PubMed]
Noble, D. , 2002, “ Modeling the Heart–From Genes to Cells to the Whole Organ,” Science, 295(5560), pp. 1678–1682. [CrossRef] [PubMed]
Aldridge, B. B. , Burke, J. M. , Lauffenburger, D. A. , and Sorger, P. K. , 2006, “ Physicochemical Modelling of Cell Signalling Pathways,” Nat. Cell Biol., 8(11), pp. 1195–1203. [CrossRef] [PubMed]
Chuang, H.-Y. , Hofree, M. , and Ideker, T. , 2010, “ A Decade of Systems Biology,” Annu. Rev. Cell Dev. Biol., 26, pp. 721–744. [CrossRef] [PubMed]
Ditlev, J. A. , Mayer, B. J. , and Loew, L. M. , 2013, “ There is More Than One Way to Model an Elephant. Experiment-Driven Modeling of the Actin Cytoskeleton,” Biophys. J., 104(3), pp. 520–532. [CrossRef] [PubMed]
Peck, S. L. , 2004, “ Simulation as Experiment: A Philosophical Reassessment for Biological Modeling,” Trends Ecol. Evol., 19(10), pp. 530–534. [CrossRef] [PubMed]
Humphrey, J. D. , 2002, Cardiovascular Solid Mechanics: Cells, Tissues, and Organs, Springer-Verlag, New York.

Figures

Grahic Jump Location
Fig. 1

Muscle and collagen fiber orientation and mechanics in healing pig infarcts: (a) schematic showing the circumferential (0 deg) and longitudinal directions (90 deg) used to define allorientation measurements in this article. Muscle fiber orientation normally varies with depth between the outer surface (epicardium) and inner surface (endocardium). (b) In this experiment, the orientation of undamaged muscle fibers varied from −55 deg to +60 deg (gray bars), while the mean orientation of collagen fibers 3 weeks after infarction ranged from −45 deg to +30 deg (red bars, data re-analyzed and replotted from Ref. [4]; epi = epicardium, endo = endocardium). (c) Tracking midwall strains using implanted radiopaque markers in this same animal model showed that healing infarcts stretched primarily in the circumferential direction (black bars) with little stretch in the longitudinal direction (gray bars), suggesting a role for mechanics in influencing scar collagen structure (based on data reported in Ref. [12], control = immediately prior to infarction, acute = 15 min after coronary ligation).

Grahic Jump Location
Fig. 2

ABM predictions of collagen alignment in multiple animal models. (a) schematic illustrating two rat cryoinfarct locations and shapes for which data and predictions are presented here. (b) Cryoinfarcts at the equator healed with circumferentially aligned collagen, regardless of the infarct shape, as illustrated in this histologic section stained with picrosirius red and imaged under circularly polarized light to highlight collagen fibers. (c) By contrast, cryoinfarcts at the apex healed with randomly oriented collagen. (d) The model predicted preferred alignment in the circumferential direction for rat cryoinfarcts located near the equator (red dotted line) but nearly random orientation for cryoinfarcts located at the apex (blue solid line); both predictions matched experimental measurements 3 weeks following infarction (red circles and blue triangles mean±SD; model results replotted from [6], data replotted from [20]). B: Simulations of multiple transmural layers in healing pig infarcts with the same ABM predicted shifts in the transmural distribution of fiber angles that closely matched our previously reported data (see Fig. 1).

Grahic Jump Location
Fig. 3

Predicted time course of midwall collagen alignment with and without circumferential surgical reinforcement in the rat. ((a) and (b)) The ABM predicted that the mean angle of collagen fibers would remain near 0 deg in the untreated animals (baseline), while surgical reinforcement (patch) will cause collagen accumulation in the direction of the predominant longitudinal strain, causing the mean angle to switch to longitudinal (±90 deg) by 3 weeks. The experimental data showed the predicted reorientation of collagen, but it occurred more quickly than predicted by the model, suggesting a less important role for contact guidance in vivo than assumed in the model. (Note: error bars not shown because mean vector length presented in panels C and D quantifies the variation between subjects.) ((c) and (d)) The ABM predicted that mean vector length (a measure of collagen alignment ranging from 0 to 1) would decrease to near zero (random) in untreated rat infarcts (baseline), while surgical reinforcement (patch) would cause a drop and then rise in alignment strength as longitudinal deposition initially dilutes and then overwhelms the pre-existing collagen. The experimental data showed higher alignment than predicted, again reflecting a more dominant role for mechanics versus other factors than assumed in the model.

Grahic Jump Location
Fig. 4

Proposed explanation for the failure of MMP inhibitors to alter collagen content in healing scar (simulations based on model first reported in Ref. [10]): (a) a simple single-equation model with time-varying MMP concentrations derived from literature (gray bars) provides a good match to measured collagen area fractions in healing rat infarcts (red bars, mean±SD). Simulated 75% inhibition of MMPs (black bars) takes several weeks to produce an effect size that would be detectable given the variability in the measurements. (b) Reported MMP activity (green dashed line) peaks within a few days after infarction in rodents and then falls, while collagen gradually accumulates (blue solid line); the product of these curves (gray dotted line) reflects the expected rate of collagen degradation, which rises much more slowly than would have been expected from the MMP curve alone.

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