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Tikenoğullar i OZ, Peirlinck M, Chubb H, Dubin AM, Kuhl E, Marsden AL. Effects of cardiac growth on electrical dyssynchrony in the single ventricle patient. Comput Methods Biomech Biomed Engin 2024; 27:1011-1027. [PMID: 37314141 PMCID: PMC10719423 DOI: 10.1080/10255842.2023.2222203] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Revised: 04/27/2023] [Accepted: 05/04/2023] [Indexed: 06/15/2023]
Abstract
Single ventricle patients, including those with hypoplastic left heart syndrome (HLHS), typically undergo three palliative heart surgeries culminating in the Fontan procedure. HLHS is associated with high rates of morbidity and mortality, and many patients develop arrhythmias, electrical dyssynchrony, and eventually ventricular failure. However, the correlation between ventricular enlargement and electrical dysfunction in HLHS physiology remains poorly understood. Here we characterize the relationship between growth and electrophysiology in HLHS using computational modeling. We integrate a personalized finite element model, a volumetric growth model, and a personalized electrophysiology model to perform controlled in silico experiments. We show that right ventricle enlargement negatively affects QRS duration and interventricular dyssynchrony. Conversely, left ventricle enlargement can partially compensate for this dyssynchrony. These findings have potential implications on our understanding of the origins of electrical dyssynchrony and, ultimately, the treatment of HLHS patients.
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Affiliation(s)
- O. Z. Tikenoğullar i
- Department of Mechanical Engineering, Stanford University, Stanford, California, USA
| | - M. Peirlinck
- Department of Biomechanical Engineering, Delft University of Technology, Delft, Netherlands
| | - H. Chubb
- Department of Pediatrics (Cardiology), Stanford University, Stanford, California, USA
| | - A. M. Dubin
- Department of Pediatrics (Cardiology), Stanford University, Stanford, California, USA
| | - E. Kuhl
- Department of Mechanical Engineering, Stanford University, Stanford, California, USA
| | - A. L. Marsden
- Department of Mechanical Engineering, Stanford University, Stanford, California, USA
- Department of Pediatrics (Cardiology), Stanford University, Stanford, California, USA
- Department of Bioengineering, Stanford University, Stanford, California, USA
- Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California, USA
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2
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Gregorovicova M, Lashkarinia SS, Yap CH, Tomek V, Sedmera D. Hemodynamics During Development and Postnatal Life. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2024; 1441:201-226. [PMID: 38884713 DOI: 10.1007/978-3-031-44087-8_11] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2024]
Abstract
A well-developed heart is essential for embryonic survival. There are constant interactions between cardiac tissue motion and blood flow, which determine the heart shape itself. Hemodynamic forces are a powerful stimulus for cardiac growth and differentiation. Therefore, it is particularly interesting to investigate how the blood flows through the heart and how hemodynamics is linked to a particular species and its development, including human. The appropriate patterns and magnitude of hemodynamic stresses are necessary for the proper formation of cardiac structures, and hemodynamic perturbations have been found to cause malformations via identifiable mechanobiological molecular pathways. There are significant differences in cardiac hemodynamics among vertebrate species, which go hand in hand with the presence of specific anatomical structures. However, strong similarities during development suggest a common pattern for cardiac hemodynamics in human adults. In the human fetal heart, hemodynamic abnormalities during gestation are known to progress to congenital heart malformations by birth. In this chapter, we discuss the current state of the knowledge of the prenatal cardiac hemodynamics, as discovered through small and large animal models, as well as from clinical investigations, with parallels gathered from the poikilotherm vertebrates that emulate some hemodynamically significant human congenital heart diseases.
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Affiliation(s)
- Martina Gregorovicova
- Laboratory of Developmental Cardiology, Institute of Physiology, Czech Academy of Sciences, Prague, Czech Republic
- Institute of Anatomy, First Faculty of Medicine, Charles University, Prague, Czech Republic
| | | | - Choon Hwai Yap
- Department of Bioengineering, Imperial College, London, UK
| | - Viktor Tomek
- Pediatric Cardiology, Motol University Hospital, Prague, Czech Republic
| | - David Sedmera
- Laboratory of Developmental Cardiology, Institute of Physiology, Czech Academy of Sciences, Prague, Czech Republic.
- Institute of Anatomy, First Faculty of Medicine, Charles University, Prague, Czech Republic.
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3
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Ahmad F, Soe S, Albon J, Errington R, Theobald P. Quantifying the microstructural and biomechanical changes in the porcine ventricles during growth and remodelling. Acta Biomater 2023; 171:166-192. [PMID: 37797709 DOI: 10.1016/j.actbio.2023.09.044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2023] [Revised: 09/19/2023] [Accepted: 09/26/2023] [Indexed: 10/07/2023]
Abstract
Cardiac tissue growth and remodelling (G & R) occur in response to the changing physiological demands of the heart after birth. The early shift to pulmonary circulation produces an immediate increase in ventricular workload, causing microstructural and biomechanical changes that serve to maintain overall physiological homoeostasis. Such cardiac G & R continues throughout life. Quantifying the tissue's mechanical and microstructural changes because of G & R is of increasing interest, dovetailing with the emerging fields of personalised and precision solutions. This study aimed to determine equibiaxial, and non-equibiaxial extension, stress-relaxation, and the underlying microstructure of the passive porcine ventricles tissue at four time points spanning from neonatal to adulthood. The three-dimensional microstructure was investigated via two-photon excited fluorescence and second-harmonic generation microscopy on optically cleared tissues, describing the 3D orientation, rotation and dispersion of the cardiomyocytes and collagen fibrils. The results revealed that during biomechanical testing, myocardial ventricular tissue possessed non-linear, anisotropic, and viscoelastic behaviour. An increase in stiffness and viscoelasticity was noted for the left and right ventricular free walls from neonatal to adulthood. Microstructural analyses revealed concomitant increases in cardiomyocyte rotation and dispersion. This study provides baseline data, describing the biomechanical and microstructural changes in the left and right ventricular myocardial tissue during G & R, which should prove valuable to researchers in developing age-specific, constitutive models for more accurate computational simulations. STATEMENT OF SIGNIFICANCE: There is a dearth of experimental data describing the growth and remodelling of left and right ventricular tissue. The published literature is fragmented, with data reported via different experimental techniques using tissues harvested from a variety of animals, with different gender and ages. This prevents developing a continuum of data spanning birth to death, so limiting the potential that can be leveraged to aid computational modelling and simulations. In this study, equibiaxial, non-equibiaxial, and stress-relaxation data are presented, describing directional-dependent material responses. The biomechanical data is consolidated with equivalent microstructural data, an important element for the development of future material models. Combined, these data describe microstructural and biomechanical changes in the ventricles, spanning G &R from neonatal to adulthood.
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Affiliation(s)
- Faizan Ahmad
- School of Engineering, Cardiff University, UK; School of Health Sciences, Birmingham City University, UK.
| | - Shwe Soe
- FET - Engineering, Design and Mathematics, University of West of England, UK
| | - Julie Albon
- School of Optometry and Vision Sciences, Cardiff University, UK; Viva Scientia Bioimaging Laboratories, Cardiff University, UK
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Siddiqui HB, Dogru S, Lashkarinia SS, Pekkan K. Soft-Tissue Material Properties and Mechanogenetics during Cardiovascular Development. J Cardiovasc Dev Dis 2022; 9:jcdd9020064. [PMID: 35200717 PMCID: PMC8876703 DOI: 10.3390/jcdd9020064] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2021] [Revised: 01/22/2022] [Accepted: 01/28/2022] [Indexed: 12/17/2022] Open
Abstract
During embryonic development, changes in the cardiovascular microstructure and material properties are essential for an integrated biomechanical understanding. This knowledge also enables realistic predictive computational tools, specifically targeting the formation of congenital heart defects. Material characterization of cardiovascular embryonic tissue at consequent embryonic stages is critical to understand growth, remodeling, and hemodynamic functions. Two biomechanical loading modes, which are wall shear stress and blood pressure, are associated with distinct molecular pathways and govern vascular morphology through microstructural remodeling. Dynamic embryonic tissues have complex signaling networks integrated with mechanical factors such as stress, strain, and stiffness. While the multiscale interplay between the mechanical loading modes and microstructural changes has been studied in animal models, mechanical characterization of early embryonic cardiovascular tissue is challenging due to the miniature sample sizes and active/passive vascular components. Accordingly, this comparative review focuses on the embryonic material characterization of developing cardiovascular systems and attempts to classify it for different species and embryonic timepoints. Key cardiovascular components including the great vessels, ventricles, heart valves, and the umbilical cord arteries are covered. A state-of-the-art review of experimental techniques for embryonic material characterization is provided along with the two novel methods developed to measure the residual and von Mises stress distributions in avian embryonic vessels noninvasively, for the first time in the literature. As attempted in this review, the compilation of embryonic mechanical properties will also contribute to our understanding of the mature cardiovascular system and possibly lead to new microstructural and genetic interventions to correct abnormal development.
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Affiliation(s)
- Hummaira Banu Siddiqui
- Department of Mechanical Engineering, Koc University, Istanbul 34450, Turkey; (H.B.S.); (S.D.); (S.S.L.)
| | - Sedat Dogru
- Department of Mechanical Engineering, Koc University, Istanbul 34450, Turkey; (H.B.S.); (S.D.); (S.S.L.)
- Department of Biomedical Engineering, Boston University, Boston, MA 02215, USA
| | - Seyedeh Samaneh Lashkarinia
- Department of Mechanical Engineering, Koc University, Istanbul 34450, Turkey; (H.B.S.); (S.D.); (S.S.L.)
- Department of Bioengineering, Imperial College London, London SW7 2BX, UK
| | - Kerem Pekkan
- Department of Mechanical Engineering, Koc University, Istanbul 34450, Turkey; (H.B.S.); (S.D.); (S.S.L.)
- Correspondence: ; Tel.: +90-(533)-356-3595
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5
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Volumetric growth of soft tissues evaluated in the current configuration. Biomech Model Mechanobiol 2022; 21:569-588. [PMID: 35044527 PMCID: PMC8940838 DOI: 10.1007/s10237-021-01549-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2021] [Accepted: 12/17/2021] [Indexed: 11/02/2022]
Abstract
AbstractThe growth and remodelling of soft tissues plays a significant role in many physiological applications, particularly in understanding and managing many diseases. A commonly used approach for soft tissue growth and remodelling is volumetric growth theory, introduced in the framework of finite elasticity. In such an approach, the total deformation gradient tensor is decomposed so that the elastic and growth tensors can be studied separately. A critical element in this approach is to determine the growth tensor and its evolution with time. Most existing volumetric growth theories define the growth tensor in the reference (natural) configuration, which does not reflect the continuous adaptation processes of soft tissues under the current configuration. In a few studies where growth from a loaded configuration was considered, simplifying assumptions, such as compatible deformation or geometric symmetries, were introduced. In this work, we propose a new volumetric growth law that depends on fields evaluated in the current configuration, which is residually stressed and loaded, without any geometrical restrictions. We illustrate our idea using a simplified left ventricle model, which admits inhomogeneous growth in the current configuration. We compare the residual stress distribution of our approach with the traditional volumetric growth theory, that assumes growth occurring from the natural reference configuration. We show that the proposed framework leads to qualitative agreements with experimental measurements. Furthermore, using a cylindrical model, we find an incompatibility index that explains the differences between the two approaches in more depth. We also demonstrate that results from both approaches reach the same steady solution published previously at the limit of a saturated growth. Although we used a left ventricle model as an example, our theory is applicable in modelling the volumetric growth of general soft tissues.
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6
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Sharifi H, Mann CK, Rockward AL, Mehri M, Mojumder J, Lee LC, Campbell KS, Wenk JF. Multiscale simulations of left ventricular growth and remodeling. Biophys Rev 2021; 13:729-746. [PMID: 34777616 PMCID: PMC8555068 DOI: 10.1007/s12551-021-00826-5] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 08/05/2021] [Indexed: 02/07/2023] Open
Abstract
Cardiomyocytes can adapt their size, shape, and orientation in response to altered biomechanical or biochemical stimuli. The process by which the heart undergoes structural changes-affecting both geometry and material properties-in response to altered ventricular loading, altered hormonal levels, or mutant sarcomeric proteins is broadly known as cardiac growth and remodeling (G&R). Although it is likely that cardiac G&R initially occurs as an adaptive response of the heart to the underlying stimuli, prolonged pathological changes can lead to increased risk of atrial fibrillation, heart failure, and sudden death. During the past few decades, computational models have been extensively used to investigate the mechanisms of cardiac G&R, as a complement to experimental measurements. These models have provided an opportunity to quantitatively study the relationships between the underlying stimuli (primarily mechanical) and the adverse outcomes of cardiac G&R, i.e., alterations in ventricular size and function. State-of-the-art computational models have shown promise in predicting the progression of cardiac G&R. However, there are still limitations that need to be addressed in future works to advance the field. In this review, we first outline the current state of computational models of cardiac growth and myofiber remodeling. Then, we discuss the potential limitations of current models of cardiac G&R that need to be addressed before they can be utilized in clinical care. Finally, we briefly discuss the next feasible steps and future directions that could advance the field of cardiac G&R.
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Affiliation(s)
- Hossein Sharifi
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
| | - Charles K. Mann
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
| | - Alexus L. Rockward
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
| | - Mohammad Mehri
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
| | - Joy Mojumder
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI USA
| | - Lik-Chuan Lee
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI USA
| | - Kenneth S. Campbell
- Department of Physiology & Division of Cardiovascular Medicine, University of Kentucky, Lexington, KY USA
| | - Jonathan F. Wenk
- Department of Mechanical Engineering, University of Kentucky, 269 Ralph G. Anderson Building, Lexington, KY 40506-0503 USA
- Department of Surgery, University of Kentucky, Lexington, KY USA
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Sharifi A, Gendernalik A, Garrity D, Bark D. Valveless pumping behavior of the simulated embryonic heart tube as a function of contractile patterns and myocardial stiffness. Biomech Model Mechanobiol 2021; 20:2001-2012. [PMID: 34297252 DOI: 10.1007/s10237-021-01489-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2020] [Accepted: 06/29/2021] [Indexed: 10/20/2022]
Abstract
During development, the heart begins pumping as a valveless multilayered tube capable of driving blood flow throughout the embryonic vasculature. The mechanical properties and how they interface with pumping function are not well-defined at this stage. Here, we evaluate pumping patterns using a fluid-structure interaction computational model, combined with experimental data and an energetic analysis to investigate myocardial mechanical properties. Through this work, we propose that a myocardium modeled as a Neo-Hookean material with a material constant on the order of 10 kPa is necessary for the heart tube to function with an optimal pressure and cardiac output.
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Affiliation(s)
- Alireza Sharifi
- Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, USA
| | - Alex Gendernalik
- Department of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA
| | - Deborah Garrity
- Department of Biology, Colorado State University, Fort Collins, CO, USA
| | - David Bark
- Department of Mechanical Engineering, Colorado State University, Fort Collins, CO, USA. .,Department of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA. .,Department of Pediatrics, Washington University in St. Louis, St. Louis, MO, USA.
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8
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Hendrickson T, Mancino C, Whitney L, Tsao C, Rahimi M, Taraballi F. Mimicking cardiac tissue complexity through physical cues: A review on cardiac tissue engineering approaches. NANOMEDICINE-NANOTECHNOLOGY BIOLOGY AND MEDICINE 2021; 33:102367. [PMID: 33549819 DOI: 10.1016/j.nano.2021.102367] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2020] [Revised: 01/06/2021] [Accepted: 01/15/2021] [Indexed: 02/08/2023]
Abstract
Cardiovascular diseases are the number one killer in the world.1,2 Currently, there are no clinical treatments to regenerate damaged cardiac tissue, leaving patients to develop further life-threatening cardiac complications. Cardiac tissue has multiple functional demands including vascularization, contraction, and conduction that require many synergic components to properly work. Most of these functions are a direct result of the cardiac tissue structure and composition, and, for this reason, tissue engineering strongly proposed to develop substitute engineered heart tissues (EHTs). EHTs usually have combined pluripotent stem cells and supporting scaffolds with the final aim to repair or replace the damaged native tissue. However, as simple as this idea is, indeed, it resulted, after many attempts in the field, to be very challenging. Without design complexity, EHTs remain unable to mature fully and integrate into surrounding heart tissue resulting in minimal in vivo effects.3 Lately, there has been a growing body of evidence that a complex, multifunctional approach through implementing scaffold designs, cellularization, and molecular release appears to be essential in the development of a functional cardiac EHTs.4-6 This review covers the advancements in EHTs developments focusing on how to integrate contraction, conduction, and vascularization mimics and how combinations have resulted in improved designs thus warranting further investigation to develop a clinically applicable treatment.
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Affiliation(s)
- Troy Hendrickson
- Center for Musculoskeletal Regeneration, Houston Methodist Research Institute, Houston Methodist, Houston, TX, USA; Orthopedics and Sports Medicine, Houston Methodist Hospital, Houston, TX, USA; Texas A&M MD/PhD Program, Texas A&M Health Science Center, College Station, TX, USA
| | - Chiara Mancino
- Center for Musculoskeletal Regeneration, Houston Methodist Research Institute, Houston Methodist, Houston, TX, USA; Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milano, (MI), Italy
| | - Lauren Whitney
- Texas A&M Biomedical Engineering, Texas A&M University, College Station, TX, USA
| | - Chris Tsao
- Center for Musculoskeletal Regeneration, Houston Methodist Research Institute, Houston Methodist, Houston, TX, USA
| | - Maham Rahimi
- Department of Cardiovascular Surgery, Houston Methodist, Houston, TX, USA
| | - Francesca Taraballi
- Center for Musculoskeletal Regeneration, Houston Methodist Research Institute, Houston Methodist, Houston, TX, USA; Orthopedics and Sports Medicine, Houston Methodist Hospital, Houston, TX, USA.
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9
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Yoshida K, Holmes JW. Computational models of cardiac hypertrophy. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2021; 159:75-85. [PMID: 32702352 PMCID: PMC7855157 DOI: 10.1016/j.pbiomolbio.2020.07.001] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2020] [Revised: 06/05/2020] [Accepted: 07/02/2020] [Indexed: 02/07/2023]
Abstract
Cardiac hypertrophy, defined as an increase in mass of the heart, is a complex process driven by simultaneous changes in hemodynamics, mechanical stimuli, and hormonal inputs. It occurs not only during pre- and post-natal development but also in adults in response to exercise, pregnancy, and a range of cardiovascular diseases. One of the most exciting recent developments in the field of cardiac biomechanics is the advent of computational models that are able to accurately predict patterns of heart growth in many of these settings, particularly in cases where changes in mechanical loading of the heart play an import role. These emerging models may soon be capable of making patient-specific growth predictions that can be used to guide clinical interventions. Here, we review the history and current state of cardiac growth models and highlight three main limitations of current approaches with regard to future clinical application: their inability to predict the regression of heart growth after removal of a mechanical overload, inability to account for evolving hemodynamics, and inability to incorporate known growth effects of drugs and hormones on heart growth. Next, we outline growth mechanics approaches used in other fields of biomechanics and highlight some potential lessons for cardiac growth modeling. Finally, we propose a multiscale modeling approach for future studies that blends tissue-level growth models with cell-level signaling models to incorporate the effects of hormones in the context of pregnancy-induced heart growth.
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Affiliation(s)
- Kyoko Yoshida
- Department of Biomedical Engineering, University of Virginia, Box 800759, Health System, Charlottesville, VA, 22908, USA.
| | - Jeffrey W Holmes
- Department of Biomedical Engineering, Robert M. Berne Cardiovascular Research Center, University of Virginia, Box 800759, Health System, Charlottesville, VA, 22908, USA.
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10
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Grobbel MR, Lee LC, Watts SW, Fink GD, Roccabianca S. Left ventricular geometry, tissue composition, and residual stress in High Fat Diet Dahl-Salt sensitive rats. EXPERIMENTAL MECHANICS 2021; 61:191-201. [PMID: 33776071 PMCID: PMC7990029 DOI: 10.1007/s11340-020-00664-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Accepted: 09/02/2020] [Indexed: 06/12/2023]
Abstract
BACKGROUND Hypertension drives myocardial remodeling, leading to changes in structure, composition and mechanical behavior, including residual stress, which are linked to heart disease progression in a gender-specific manner. Emerging therapies are also targeting constituent-specific pathological features. All previous studies, however, have characterized remodeling in the intact tissue, rather than isolated tissue constituents, and did not include sex as a biological variable. OBJECTIVE In this study we first identified the contribution of collagen fiber network and myocytes to the myocardial residual stress/strain in Dahl-Salt sensitive rats fed with high fat diet. Then, we quantified the effect of hypertension on the remodeling of the left ventricle (LV), as well as the existence of sex-specific remodeling features. METHODS We performed mechanical tests (opening angle, ring-test) and histological analysis on isolated constituents and intact tissue of the LV. Based on the measurements from the tests, we performed a stress analysis to evaluate the residual stress distribution. Statistical analysis was performed to identify the effects of constituent isolation, elevated blood pressure, and sex of the animal on the output of both experimental measures and modeling results. RESULTS Hypertension leads to reduced residual stress/strain intact tissue, isolated collagen fibers, and isolated myocytes in male and female rats. Collagen remains the largest contributor to myocardial residual stress in both normotensive and hypertensive animals. We identified sex-differences in both hypertensive and normotensive animals. CONCLUSIONS We observed both constituent- and sex-specific remodeling features in the LV of an animal model of hypertension.
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Affiliation(s)
- M. R. Grobbel
- Michigan State University, Mechanical Engineering Department
| | - L. C. Lee
- Michigan State University, Mechanical Engineering Department
| | - S. W. Watts
- Michigan State University, Pharmacology & Toxicology Department
| | - G. D. Fink
- Michigan State University, Pharmacology & Toxicology Department
| | - S. Roccabianca
- Michigan State University, Mechanical Engineering Department
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11
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Rondanina E, Bovendeerd PHM. Stimulus-effect relations for left ventricular growth obtained with a simple multi-scale model: the influence of hemodynamic feedback. Biomech Model Mechanobiol 2020; 19:2111-2126. [PMID: 32358671 PMCID: PMC7603455 DOI: 10.1007/s10237-020-01327-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2019] [Accepted: 04/10/2020] [Indexed: 01/29/2023]
Abstract
Cardiac growth is an important mechanism for the human body to respond to changes in blood flow demand. Being able to predict the development of chronic growth is clinically relevant, but so far models to predict growth have not reached consensus on the stimulus–effect relation. In a previously published study, we modeled cardiac and hemodynamic function through a lumped parameter approach. We evaluated cardiac growth in response to valve disease using various stimulus–effect relations and observed an unphysiological decline pump function. Here we extend that model with a model of hemodynamic feedback that maintains mean arterial pressure and cardiac output through adaptation of peripheral resistance and circulatory unstressed volume. With the combined model, we obtain stable growth and restoration of pump function for most growth laws. We conclude that a mixed combination of stress and strain stimuli to drive cardiac growth is most promising since it (1) reproduces clinical observations on cardiac growth well, (2) requires only a small, clinically realistic adaptation of the properties of the circulatory system and (3) is robust in the sense that results were fairly insensitive to the exact choice of the chosen mechanics loading measure. This finding may be used to guide the choice of growth laws in more complex finite element models of cardiac growth, suitable for predicting the response to spatially varying changes in tissue load. Eventually, the current model may form a basis for a tool to predict patient-specific growth in response to spatially homogeneous changes in tissue load, since it is computationally inexpensive.
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Affiliation(s)
- Emanuele Rondanina
- Technische Universiteit Eindhoven, PO Box 513, 5600 MB, Eindhoven, The Netherlands.
| | - Peter H M Bovendeerd
- Technische Universiteit Eindhoven, PO Box 513, 5600 MB, Eindhoven, The Netherlands
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12
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Niestrawska JA, Augustin CM, Plank G. Computational modeling of cardiac growth and remodeling in pressure overloaded hearts-Linking microstructure to organ phenotype. Acta Biomater 2020; 106:34-53. [PMID: 32058078 PMCID: PMC7311197 DOI: 10.1016/j.actbio.2020.02.010] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2019] [Revised: 02/06/2020] [Accepted: 02/07/2020] [Indexed: 12/25/2022]
Abstract
Cardiac growth and remodeling (G&R) refers to structural changes in myocardial tissue in response to chronic alterations in loading conditions. One such condition is pressure overload where elevated wall stresses stimulate the growth in cardiomyocyte thickness, associated with a phenotype of concentric hypertrophy at the organ scale, and promote fibrosis. The initial hypertrophic response can be considered adaptive and beneficial by favoring myocyte survival, but over time if pressure overload conditions persist, maladaptive mechanisms favoring cell death and fibrosis start to dominate, ultimately mediating the transition towards an overt heart failure phenotype. The underlying mechanisms linking biological factors at the myocyte level to biomechanical factors at the systemic and organ level remain poorly understood. Computational models of G&R show high promise as a unique framework for providing a quantitative link between myocardial stresses and strains at the organ scale to biological regulatory processes at the cellular level which govern the hypertrophic response. However, microstructurally motivated, rigorously validated computational models of G&R are still in their infancy. This article provides an overview of the current state-of-the-art of computational models to study cardiac G&R. The microstructure and mechanosensing/mechanotransduction within cells of the myocardium is discussed and quantitative data from previous experimental and clinical studies is summarized. We conclude with a discussion of major challenges and possible directions of future research that can advance the current state of cardiac G&R computational modeling. STATEMENT OF SIGNIFICANCE: The mechanistic links between organ-scale biomechanics and biological factors at the cellular size scale remain poorly understood as these are largely elusive to investigations using experimental methodology alone. Computational G&R models show high promise to establish quantitative links which allow more mechanistic insight into adaptation mechanisms and may be used as a tool for stratifying the state and predict the progression of disease in the clinic. This review provides a comprehensive overview of research in this domain including a summary of experimental data. Thus, this study may serve as a basis for the further development of more advanced G&R models which are suitable for making clinical predictions on disease progression or for testing hypotheses on pathogenic mechanisms using in-silico models.
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Affiliation(s)
- Justyna A Niestrawska
- Gottfried Schatz Research Center: Division of Biophysics, Medical University of Graz, Graz 8010, Austria
| | - Christoph M Augustin
- Gottfried Schatz Research Center: Division of Biophysics, Medical University of Graz, Graz 8010, Austria.
| | - Gernot Plank
- Gottfried Schatz Research Center: Division of Biophysics, Medical University of Graz, Graz 8010, Austria; BioTechMed-Graz, Austria
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13
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Lee T, Vaca EE, Ledwon JK, Bae H, Topczewska JM, Turin SY, Kuhl E, Gosain AK, Tepole AB. Improving tissue expansion protocols through computational modeling. J Mech Behav Biomed Mater 2018; 82:224-234. [PMID: 29627733 PMCID: PMC6028355 DOI: 10.1016/j.jmbbm.2018.03.034] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2018] [Revised: 03/23/2018] [Accepted: 03/26/2018] [Indexed: 01/29/2023]
Abstract
Tissue expansion is a common technique in reconstructive surgery used to grow skin in vivo for correction of large defects. Despite its popularity, there is a lack of quantitative understanding of how stretch leads to growth of new skin. This has resulted in several arbitrary expansion protocols that rely on the surgeon's personal training and experience rather than on accurate predictive models. For example, choosing between slow or rapid expansion, or small or large inflation volumes remains controversial. Here we explore four tissue expansion protocols by systematically varying the inflation volume and the protocol duration in a porcine model. The quantitative analysis combines three-dimensional photography, isogeometric kinematics, and finite growth theory. Strikingly, all four protocols generate similar peak stretches, but different growth patterns: Smaller filling volumes of 30 ml per inflation did not result in notable expander-induced growth neither for the short nor for the long protocol; larger filling volumes of 60 ml per inflation trigger skin adaptation, with larger expander-induced growth in regions of larger stretch, and more expander-induced growth for the 14-day compared to the 10-day expansion protocol. Our results suggest that expander-induced growth is not triggered by the local stretch alone. While stretch is clearly a driver for growth, the local stretch at a given point is not enough to predict the expander-induced growth at that location. From a clinical perspective, our study suggests that longer expansion protocols are needed to ensure sufficient growth of sizable skin patches.
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Affiliation(s)
- Taeksang Lee
- School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA
| | - Elbert E Vaca
- Ann and Robert H. Lurie Children's Hospital of Chicago, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611, USA
| | - Joanna K Ledwon
- Ann and Robert H. Lurie Children's Hospital of Chicago, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611, USA
| | - Hanah Bae
- Ann and Robert H. Lurie Children's Hospital of Chicago, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611, USA
| | - Jolanta M Topczewska
- Ann and Robert H. Lurie Children's Hospital of Chicago, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611, USA
| | - Sergey Y Turin
- Ann and Robert H. Lurie Children's Hospital of Chicago, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611, USA
| | - Ellen Kuhl
- Departments of Mechanical Engineering, Bioengineering, and Cardiothoracic Surgery, Stanford University, CA 94305, USA
| | - Arun K Gosain
- Ann and Robert H. Lurie Children's Hospital of Chicago, Feinberg School of Medicine, Northwestern University, Chicago, IL 60611, USA
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Sizarov A, Boudjemline Y. Valve Interventions in Utero: Understanding the Timing, Indications, and Approaches. Can J Cardiol 2017; 33:1150-1158. [DOI: 10.1016/j.cjca.2017.06.009] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2016] [Revised: 06/16/2017] [Accepted: 06/16/2017] [Indexed: 12/25/2022] Open
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15
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Carruth ED, McCulloch AD, Omens JH. Transmural gradients of myocardial structure and mechanics: Implications for fiber stress and strain in pressure overload. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2016; 122:215-226. [PMID: 27845176 DOI: 10.1016/j.pbiomolbio.2016.11.004] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Although a truly complete understanding of whole heart activation, contraction, and deformation is well beyond our current reach, a significant amount of effort has been devoted to discovering and understanding the mechanisms by which myocardial structure determines cardiac function to better treat patients with cardiac disease. Several experimental studies have shown that transmural fiber strain is relatively uniform in both diastole and systole, in contrast to predictions from traditional mechanical theory. Similarly, mathematical models have largely predicted uniform fiber stress across the wall. The development of this uniform pattern of fiber stress and strain during filling and ejection is due to heterogeneous transmural distributions of several myocardial structures. This review summarizes these transmural gradients, their contributions to fiber mechanics, and the potential functional effects of their remodeling during pressure overload hypertrophy.
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Affiliation(s)
- Eric D Carruth
- Department of Bioengineering, University of California San Diego, La Jolla, CA, USA.
| | - Andrew D McCulloch
- Department of Bioengineering, University of California San Diego, La Jolla, CA, USA.
| | - Jeffrey H Omens
- Department of Bioengineering, University of California San Diego, La Jolla, CA, USA; Department of Medicine, University of California San Diego, La Jolla, CA, USA.
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16
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Lee LC, Kassab GS, Guccione JM. Mathematical modeling of cardiac growth and remodeling. WILEY INTERDISCIPLINARY REVIEWS. SYSTEMS BIOLOGY AND MEDICINE 2016; 8:211-26. [PMID: 26952285 PMCID: PMC4841715 DOI: 10.1002/wsbm.1330] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2015] [Revised: 01/06/2016] [Accepted: 01/07/2016] [Indexed: 11/05/2022]
Abstract
This review provides an overview of the current state of mathematical models of cardiac growth and remodeling (G&R). We concisely describe the experimental observations associated with cardiac G&R and discuss existing mathematical models that describe this process. To facilitate the discussion, we have organized the G&R models in terms of (1) the physical focus (biochemical vs mechanical) and (2) the process that they describe (myocyte hypertrophy vs extracellular matrix remodeling). The review concludes with a discussion of some possible directions that can advance the existing state of cardiac G&R mathematical modeling. WIREs Syst Biol Med 2016, 8:211-226. doi: 10.1002/wsbm.1330 For further resources related to this article, please visit the WIREs website.
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Affiliation(s)
- L C Lee
- Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA
| | - G S Kassab
- California Medical Innovations Institute, San Diego, CA, USA
| | - J M Guccione
- Department of Surgery, University of California at San Francisco, San Francisco, CA, USA
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17
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Maas SA, Erdemir A, Halloran JP, Weiss JA. A general framework for application of prestrain to computational models of biological materials. J Mech Behav Biomed Mater 2016; 61:499-510. [PMID: 27131609 DOI: 10.1016/j.jmbbm.2016.04.012] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2015] [Revised: 03/28/2016] [Accepted: 04/06/2016] [Indexed: 11/15/2022]
Abstract
It is often important to include prestress in computational models of biological tissues. The prestress can represent residual stresses (stresses that exist after the tissue is excised from the body) or in situ stresses (stresses that exist in vivo, in the absence of loading). A prestressed reference configuration may also be needed when modeling the reference geometry of biological tissues in vivo. This research developed a general framework for representing prestress in finite element models of biological materials. It is assumed that the material is elastic, allowing the prestress to be represented via a prestrain. For prestrain fields that are not compatible with the reference geometry, the computational framework provides an iterative algorithm for updating the prestrain until equilibrium is satisfied. The iterative framework allows for enforcement of two different constraints: elimination of distortion in order to address the incompatibility issue, and enforcing a specified in situ fiber strain field while allowing for distortion. The framework was implemented as a plugin in FEBio (www.febio.org), making it easy to maintain the software and to extend the framework if needed. Several examples illustrate the application and effectiveness of the approach, including the application of in situ strains to ligaments in the Open Knee model (simtk.org/home/openknee). A novel method for recovering the stress-free configuration from the prestrain deformation gradient is also presented. This general purpose theoretical and computational framework for applying prestrain will allow analysts to overcome the challenges in modeling this important aspect of biological tissue mechanics.
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Affiliation(s)
- Steve A Maas
- Department of Bioengineering, and Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA
| | - Ahmet Erdemir
- Computational Biomodeling (CoBi) Core and Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, USA
| | - Jason P Halloran
- Mechanical Department Cleveland State University, Cleveland, Ohio, USA
| | - Jeffrey A Weiss
- Department of Bioengineering, and Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT, USA.
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Abstract
The heart pumps blood to maintain circulation and ensure the delivery of oxygenated blood to all the organs of the body. Mechanics play a critical role in governing and regulating heart function under both normal and pathological conditions. Biological processes and mechanical stress are coupled together in regulating myocyte function and extracellular matrix structure thus controlling heart function. Here, we offer a brief introduction to the biomechanics of left ventricular function and then summarize recent progress in the study of the effects of mechanical stress on ventricular wall remodeling and cardiac function as well as the effects of wall mechanical properties on cardiac function in normal and dysfunctional hearts. Various mechanical models to determine wall stress and cardiac function in normal and diseased hearts with both systolic and diastolic dysfunction are discussed. The results of these studies have enhanced our understanding of the biomechanical mechanism in the development and remodeling of normal and dysfunctional hearts. Biomechanics provide a tool to understand the mechanism of left ventricular remodeling in diastolic and systolic dysfunction and guidance in designing and developing new treatments.
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Affiliation(s)
- Andrew P. Voorhees
- Department of Mechanical Engineering, The University of Texas at San Antonio, Biomedical Engineering Program, UTSA-UTHSCSA
| | - Hai-Chao Han
- Department of Mechanical Engineering, The University of Texas at San Antonio, Biomedical Engineering Program, UTSA-UTHSCSA
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19
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Nordbø Ø, Gjuvsland AB, Nermoen A, Land S, Niederer S, Lamata P, Lee J, Smith NP, Omholt SW, Vik JO. Towards causally cohesive genotype-phenotype modelling for characterization of the soft-tissue mechanics of the heart in normal and pathological geometries. J R Soc Interface 2015; 12:rsif.2014.1166. [PMID: 25833237 DOI: 10.1098/rsif.2014.1166] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
A scientific understanding of individual variation is key to personalized medicine, integrating genotypic and phenotypic information via computational physiology. Genetic effects are often context-dependent, differing between genetic backgrounds or physiological states such as disease. Here, we analyse in silico genotype-phenotype maps (GP map) for a soft-tissue mechanics model of the passive inflation phase of the heartbeat, contrasting the effects of microstructural and other low-level parameters assumed to be genetically influenced, under normal, concentrically hypertrophic and eccentrically hypertrophic geometries. For a large number of parameter scenarios, representing mock genetic variation in low-level parameters, we computed phenotypes describing the deformation of the heart during inflation. The GP map was characterized by variance decompositions for each phenotype with respect to each parameter. As hypothesized, the concentric geometry allowed more low-level parameters to contribute to variation in shape phenotypes. In addition, the relative importance of overall stiffness and fibre stiffness differed between geometries. Otherwise, the GP map was largely similar for the different heart geometries, with little genetic interaction between the parameters included in this study. We argue that personalized medicine can benefit from a combination of causally cohesive genotype-phenotype modelling, and strategic phenotyping that captures effect modifiers not explicitly included in the mechanistic model.
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Affiliation(s)
- Øyvind Nordbø
- Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, PO Box 5003, 1432 Ås, Norway
| | - Arne B Gjuvsland
- Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, PO Box 5003, 1432 Ås, Norway
| | - Anders Nermoen
- International Research Institute of Stavanger, PO Box 8046, 4068 Stavanger, Norway
| | - Sander Land
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Steven Niederer
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Pablo Lamata
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Jack Lee
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Nicolas P Smith
- Biomedical Engineering Department, King's College London, London SE1 7EH, UK
| | - Stig W Omholt
- Department of Circulation and Medical Imaging, Cardiac Exercise Research Group, NTNU Norwegian University of Science and Technology, PO Box 8905, 7491 Trondheim, Norway
| | - Jon Olav Vik
- Department of Animal and Aquacultural Sciences, Norwegian University of Life Sciences, PO Box 5003, 1432 Ås, Norway
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20
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Kowalski WJ, Pekkan K, Tinney JP, Keller BB. Investigating developmental cardiovascular biomechanics and the origins of congenital heart defects. Front Physiol 2014; 5:408. [PMID: 25374544 PMCID: PMC4204442 DOI: 10.3389/fphys.2014.00408] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2014] [Accepted: 10/02/2014] [Indexed: 11/24/2022] Open
Abstract
Innovative research on the interactions between biomechanical load and cardiovascular (CV) morphogenesis by multiple investigators over the past 3 decades, including the application of bioengineering approaches, has shown that the embryonic heart adapts both structure and function in order to maintain cardiac output to the rapidly growing embryo. Acute adaptive hemodynamic mechanisms in the embryo include the redistribution of blood flow within the heart, dynamic adjustments in heart rate and developed pressure, and beat to beat variations in blood flow and vascular resistance. These biomechanically relevant events occur coincident with adaptive changes in gene expression and trigger adaptive mechanisms that include alterations in myocardial cell growth and death, regional and global changes in myocardial architecture, and alterations in central vascular morphogenesis and remodeling. These adaptive mechanisms allow the embryo to survive these biomechanical stresses (environmental, maternal) and to compensate for developmental errors (genetic). Recent work from numerous laboratories shows that a subset of these adaptive mechanisms is present in every developing multicellular organism with a “heart” equivalent structure. This chapter will provide the reader with an overview of some of the approaches used to quantify embryonic CV functional maturation and performance, provide several illustrations of experimental interventions that explore the role of biomechanics in the regulation of CV morphogenesis including the role of computational modeling, and identify several critical areas for future investigation as available experimental models and methods expand.
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Affiliation(s)
- William J Kowalski
- Cardiovascular Innovation Institute, University of Louisville Louisville, KY, USA ; Department of Pediatrics, University of Louisville Louisville, KY, USA
| | - Kerem Pekkan
- Department of Biomedical Engineering, Carnegie Mellon University Pittsburgh, PA, USA
| | - Joseph P Tinney
- Cardiovascular Innovation Institute, University of Louisville Louisville, KY, USA ; Department of Pediatrics, University of Louisville Louisville, KY, USA
| | - Bradley B Keller
- Cardiovascular Innovation Institute, University of Louisville Louisville, KY, USA ; Department of Pediatrics, University of Louisville Louisville, KY, USA ; Department of Biomedical Engineering, Carnegie Mellon University Pittsburgh, PA, USA
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21
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Vostarek F, Sankova B, Sedmera D. Studying dynamic events in the developing myocardium. PROGRESS IN BIOPHYSICS AND MOLECULAR BIOLOGY 2014; 115:261-9. [PMID: 24954141 DOI: 10.1016/j.pbiomolbio.2014.06.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2014] [Accepted: 06/10/2014] [Indexed: 01/25/2023]
Abstract
Differentiation and conduction properties of the cardiomyocytes are critically dependent on physical conditioning both in vitro and in vivo. Historically, various techniques were introduced to study dynamic events such as electrical currents and changes in ionic concentrations in live cells, multicellular preparations, or entire hearts. Here we review this technological progress demonstrating how each improvement in spatial or temporal resolution provided answers to old and provoked new questions. We further demonstrate how high-speed optical mapping of voltage and calcium can uncover pacemaking potential within the outflow tract myocardium, providing a developmental explanation of ectopic beats originating from this region in the clinical settings.
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Affiliation(s)
- Frantisek Vostarek
- Institute of Physiology, Academy of Sciences of the Czech Republic, Czech Republic; Faculty of Science, Charles University, Prague, Czech Republic
| | - Barbora Sankova
- Institute of Physiology, Academy of Sciences of the Czech Republic, Czech Republic; Institute of Anatomy, First Medical Faculty, Charles University, Prague, Czech Republic
| | - David Sedmera
- Institute of Physiology, Academy of Sciences of the Czech Republic, Czech Republic; Institute of Anatomy, First Medical Faculty, Charles University, Prague, Czech Republic.
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22
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Lee LC, Genet M, Acevedo-Bolton G, Ordovas K, Guccione JM, Kuhl E. A computational model that predicts reverse growth in response to mechanical unloading. Biomech Model Mechanobiol 2014; 14:217-29. [PMID: 24888270 DOI: 10.1007/s10237-014-0598-0] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2014] [Accepted: 05/21/2014] [Indexed: 01/15/2023]
Abstract
Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure-volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry.
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Affiliation(s)
- L C Lee
- Department of Surgery, School of Medicine, University of California at San Francisco, San Francisco, CA, 94143, USA,
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23
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Bayly PV, Taber LA, Kroenke CD. Mechanical forces in cerebral cortical folding: a review of measurements and models. J Mech Behav Biomed Mater 2013; 29:568-81. [PMID: 23566768 DOI: 10.1016/j.jmbbm.2013.02.018] [Citation(s) in RCA: 113] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Revised: 02/17/2013] [Accepted: 02/19/2013] [Indexed: 12/22/2022]
Abstract
Folding of the cerebral cortical surface is a critical process in human brain development, yet despite decades of indirect study and speculation the mechanics of the process remain incompletely understood. Leading hypotheses have focused on the roles of circumferential expansion of the cortex, radial growth, and internal tension in neuronal fibers (axons). In this article, we review advances in the mathematical modeling of growth and morphogenesis and new experimental data, which together promise to clarify the mechanical basis of cortical folding. Recent experimental studies have illuminated not only the fundamental cellular and molecular processes underlying cortical development, but also the stress state and mechanical behavior of the developing brain. The combination of mathematical modeling and biomechanical data provides a means to evaluate hypothesized mechanisms objectively and quantitatively, and to ensure that they are consistent with physical law, given plausible assumptions and reasonable parameter values.
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Affiliation(s)
- P V Bayly
- Department of Mechanical Engineering and Materials Science, 1 Brookings Drive, Saint Louis, MO 63130, United States.
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24
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Bayly PV, Okamoto RJ, Xu G, Shi Y, Taber LA. A cortical folding model incorporating stress-dependent growth explains gyral wavelengths and stress patterns in the developing brain. Phys Biol 2013; 10:016005. [PMID: 23357794 DOI: 10.1088/1478-3975/10/1/016005] [Citation(s) in RCA: 109] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
In humans and many other mammals, the cortex (the outer layer of the brain) folds during development. The mechanics of folding are not well understood; leading explanations are either incomplete or at odds with physical measurements. We propose a mathematical model in which (i) folding is driven by tangential expansion of the cortex and (ii) deeper layers grow in response to the resulting stress. In this model the wavelength of cortical folds depends predictably on the rate of cortical growth relative to the rate of stress-induced growth. We show analytically and in simulations that faster cortical expansion leads to shorter gyral wavelengths; slower cortical expansion leads to long wavelengths or even smooth (lissencephalic) surfaces. No inner or outer (skull) constraint is needed to produce folding, but initial shape and mechanical heterogeneity influence the final shape. The proposed model predicts patterns of stress in the tissue that are consistent with experimental observations.
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Affiliation(s)
- P V Bayly
- Department of Mechanical Engineering and Materials Science, Washington University in Saint Louis, 1 Brookings Drive, Saint Louis, MO 63105, USA.
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25
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Buffinton CM, Faas D, Sedmera D. Stress and strain adaptation in load-dependent remodeling of the embryonic left ventricle. Biomech Model Mechanobiol 2012; 12:1037-51. [PMID: 23254562 DOI: 10.1007/s10237-012-0461-0] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2011] [Accepted: 12/03/2012] [Indexed: 01/01/2023]
Abstract
Altered pressure in the developing left ventricle (LV) results in altered morphology and tissue material properties. Mechanical stress and strain may play a role in the regulating process. This study showed that confocal microscopy, three-dimensional reconstruction, and finite element analysis can provide a detailed model of stress and strain in the trabeculated embryonic heart. The method was used to test the hypothesis that end-diastolic strains are normalized after altered loading of the LV during the stages of trabecular compaction and chamber formation. Stage-29 chick LVs subjected to pressure overload and underload at stage 21 were reconstructed with full trabecular morphology from confocal images and analyzed with finite element techniques. Measured material properties and intraventricular pressures were specified in the models. The results show volume-weighted end-diastolic von Mises stress and strain averaging 50-82 % higher in the trabecular tissue than in the compact wall. The volume-weighted-average stresses for the entire LV were 115, 64, and 147 Pa in control, underloaded, and overloaded models, while strains were 11, 7, and 4 %; thus, neither was normalized in a volume-weighted sense. Localized epicardial strains at mid-longitudinal level were similar among the three groups and to strains measured from high-resolution ultrasound images. Sensitivity analysis showed changes in material properties are more significant than changes in geometry in the overloaded strain adaptation, although resulting stress was similar in both types of adaptation. These results emphasize the importance of appropriate metrics and the role of trabecular tissue in evaluating the evolution of stress and strain in relation to pressure-induced adaptation.
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Affiliation(s)
- Christine M Buffinton
- Department of Mechanical Engineering, Bucknell University, One Dent Drive, Lewisburg, PA, 17837, USA,
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Kuijpers NHL, Hermeling E, Bovendeerd PHM, Delhaas T, Prinzen FW. Modeling cardiac electromechanics and mechanoelectrical coupling in dyssynchronous and failing hearts: insight from adaptive computer models. J Cardiovasc Transl Res 2012; 5:159-69. [PMID: 22271009 PMCID: PMC3294221 DOI: 10.1007/s12265-012-9346-y] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/13/2011] [Accepted: 01/04/2012] [Indexed: 12/13/2022]
Abstract
Computer models have become more and more a research tool to obtain mechanistic insight in the effects of dyssynchrony and heart failure. Increasing computational power in combination with increasing amounts of experimental and clinical data enables the development of mathematical models that describe electrical and mechanical behavior of the heart. By combining models based on data at the molecular and cellular level with models that describe organ function, so-called multi-scale models are created that describe heart function at different length and time scales. In this review, we describe basic modules that can be identified in multi-scale models of cardiac electromechanics. These modules simulate ionic membrane currents, calcium handling, excitation-contraction coupling, action potential propagation, and cardiac mechanics and hemodynamics. In addition, we discuss adaptive modeling approaches that aim to address long-term effects of diseases and therapy on growth, changes in fiber orientation, ionic membrane currents, and calcium handling. Finally, we discuss the first developments in patient-specific modeling. While current models still have shortcomings, well-chosen applications show promising results on some ultimate goals: understanding mechanisms of dyssynchronous heart failure and tuning pacing strategy to a particular patient, even before starting the therapy.
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Affiliation(s)
- Nico H. L. Kuijpers
- Department of Biomedical Engineering, Maastricht University, Maastricht, The Netherlands
| | - Evelien Hermeling
- Department of Biomedical Engineering, Maastricht University, Maastricht, The Netherlands
| | - Peter H. M. Bovendeerd
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Tammo Delhaas
- Department of Biomedical Engineering, Maastricht University, Maastricht, The Netherlands
| | - Frits W. Prinzen
- Department of Physiology, Maastricht University, Maastricht, The Netherlands
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27
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Kerckhoffs RCP. Computational modeling of cardiac growth in the post-natal rat with a strain-based growth law. J Biomech 2011; 45:865-71. [PMID: 22169150 DOI: 10.1016/j.jbiomech.2011.11.028] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/30/2011] [Indexed: 01/17/2023]
Abstract
INTRODUCTION The postnatal heart grows mostly in response to increased hemodynamic load. However, the specific biomechanical stimuli that stimulate cardiac growth as a reaction to increased hemodynamic load are still poorly understood. It has been shown that isolated neonatal rat cardiac myocytes normalize resting sarcomere length by adding sarcomeres in series when subjected to uniaxial static strain. Because there is experimental evidence that myocytes can distinguish the direction of stretch, it was postulated that myocytes also may normalize interfilament lattice spacing as a response to cross-fiber stretch. METHODS A growth law was proposed in which fiber axial growth was stimulated by fiber strain deviating from zero and fiber radial growth by cross-fiber strain (parallel to the wall surface) deviating from zero. Fiber radial growth rate constant was 1/3 of the fiber axial growth rate constant. The growth law was implemented in a finite element model of the newborn Sprague-Dawley rat residually stressed left ventricle (LV). The LV was subjected to an end-diastolic pressure of 1 kPa and about 25 weeks of normal growth was simulated. RESULTS Most cellular and chamber dimension changes in the model matched experimentally measured ones: LV cavity and wall volume increased from 2.3 and 54 μl, respectively, in the newborn to 276 μl and 1.1 ml, respectively, in the adult rat; LV shape became more spherical; internal LV radius increased faster than wall thickness; and unloaded sarcomere lengths exhibited a transmural gradient. The major discrepancy with experiments included a reversed transmural gradient of cell length in the older rat. CONCLUSION A novel strain-based growth law has been presented that reproduced physiological postnatal growth in the rat LV.
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Affiliation(s)
- Roy C P Kerckhoffs
- University of California San Diego, Department of Bioengineering, La Jolla, CA 92093-0412, USA.
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28
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Bovendeerd PHM. Modeling of cardiac growth and remodeling of myofiber orientation. J Biomech 2011; 45:872-81. [PMID: 22169149 DOI: 10.1016/j.jbiomech.2011.11.029] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/01/2011] [Indexed: 11/26/2022]
Abstract
The heart has the ability to respond to long-term changes in its environment through changes in mass (growth), shape (morphogenesis) and tissue properties (remodeling). For improved quantitative understanding of cardiac growth and remodeling (G&R) experimental studies need to be complemented by mathematical models. This paper reviews models for cardiac growth and remodeling of myofiber orientation, as induced by mechanical stimuli. A distinction is made between optimization models, that focus on the end stage of G&R, and adaptation models, that aim to more closely describe the mechanistic relation between stimulus and effect. While many models demonstrate qualitatively promising results, a lot of questions remain, e.g. with respect to the choice of the stimulus for G&R or the long-term stability of the outcome of the model. A continued effort combining information on mechanotransduction at the cellular level, experimental observations on G&R at organ level, and testing of hypotheses on stimulus-effect relations in mathematical models is needed to answer these questions on cardiac G&R. Ultimately, models of cardiac G&R seem indispensable for patient-specific modeling, both to reconstruct the actual state of the heart and to assess the long-term effect of potential interventions.
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Affiliation(s)
- Peter H M Bovendeerd
- Department of Biomedical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands.
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Culver JC, Dickinson ME. The effects of hemodynamic force on embryonic development. Microcirculation 2010; 17:164-78. [PMID: 20374481 DOI: 10.1111/j.1549-8719.2010.00025.x] [Citation(s) in RCA: 135] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Blood vessels have long been known to respond to hemodynamic force, and several mechanotransduction pathways have been identified. However, only recently have we begun to understand the effects of hemodynamic force on embryonic development. In this review, we will discuss specific examples illustrating the role of hemodynamic force during the development of the embryo, with particular focus on the development of the vascular system and the morphogenesis of the heart. We will also discuss the important functions served by mechanotransduction and hemodynamic force during placentation, as well as in regulating the maintenance and division of embryonic, hematopoietic, neural, and mesenchymal stem cells. Pathological misregulation of mechanosensitive pathways during pregnancy and embryonic development may contribute to the occurrence of cardiovascular birth defects, as well as to a variety of other diseases, including preeclampsia. Thus, there is a need for future studies focusing on better understanding the physiological effects of hemodynamic force during embryonic development and their role in the pathogenesis of disease.
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Affiliation(s)
- James C Culver
- Department of Molecular Physiology and Biophysics, Baylor College of Medicine, Houston, TX 77030, USA
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Unraveling Changes in Myocardial Contractility During Human Fetal Growth: A Finite Element Analysis Based on In Vivo Ultrasound Measurements. Ann Biomed Eng 2010; 38:2702-15. [DOI: 10.1007/s10439-010-0010-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2009] [Accepted: 03/10/2010] [Indexed: 10/19/2022]
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Hu N, Christensen DA, Agrawal AK, Beaumont C, Clark EB, Hawkins JA. Dependence of Aortic Arch Morphogenesis on Intracardiac Blood Flow in the Left Atrial Ligated Chick Embryo. Anat Rec (Hoboken) 2009; 292:652-60. [DOI: 10.1002/ar.20885] [Citation(s) in RCA: 47] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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Rana OR, Zobel C, Saygili E, Brixius K, Gramley F, Schimpf T, Mischke K, Frechen D, Knackstedt C, Schwinger RHG, Schauerte P, Saygili E. A simple device to apply equibiaxial strain to cells cultured on flexible membranes. Am J Physiol Heart Circ Physiol 2007; 294:H532-40. [PMID: 17965285 DOI: 10.1152/ajpheart.00649.2007] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
The biomechanical environment to which cells are exposed is important to their normal growth, development, interaction, and function. Accordingly, there has been much interest in studying the role of biomechanical forces in cell biology and pathophysiology. This has led to the introduction and even commercialization of many experimental devices. Many of the early devices were limited by the heterogeneity of deformation of cells cultivated in different locations of the culture plate membranes and were also attached with complicated technical/electronic efforts resulting in a restriction of the reproducibility of these devices. The objective of this study was to design and build a simple device to allow the application of dose-dependent homogeneous equibiaxial static stretch to cells cultured on flexible silicone membranes to investigate biological and biomedical questions. In addition, cultured neonatal rat atrial cardiomyocytes were stretched with the proposed device with different strain gradients. For the first time with this study we could demonstrate that stretch up to 21% caused dose-dependent changes in biological markers such as the calcineurin activity, modulatory calcineurin-interacting protein-1, voltage-gated potassium channel isoform 4.2, and voltage-gated K(+) channel-interacting proteins-2 gene expression and transient outward potassium current densities but not the protein-to-DNA ratio and atrial natriuretic peptide mRNA. With both markers mentioned last, dose-dependent stretch alterations could only be achieved with stretch up to 13%. The simple and low-cost device presented here might be applied to a wide range of experimental settings in different fields of research.
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Affiliation(s)
- Obaida R Rana
- Univ. Hospital RWTH Aachen, Dept. I of Internal Medicine, Division of Cardiology, Pulmonary and Vascular Diseases, Pauwelsstrasse 30, Aachen, Germany.
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Rauch C, Loughna PT. Static stretch promotes MEF2A nuclear translocation and expression of neonatal myosin heavy chain in C2C12myocytes in a calcineurin- and p38-dependent manner. Am J Physiol Cell Physiol 2005; 288:C593-605. [PMID: 15483225 DOI: 10.1152/ajpcell.00346.2004] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
Although the effects of mechanical stimuli have been studied extensively in fully differentiated skeletal muscle and have been shown to promote changes in phenotype, including altered myosin heavy chain isoform expression, the effects of a change in mechanical environment have been poorly studied at earlier stages of skeletal muscle differentiation. In particular, the early events elicited by mechanical stimuli upon differentiating myocytes have not been investigated. In the present study, the effect of static stretch on the activation of transcriptional factors MEF2A and NFATc1, which have been shown to be involved in the differentiation and phenotype regulation of skeletal muscle, have been examined. Furthermore, putative second messenger signaling pathways that could be involved in the dephosphorylation and hence activation of these factors were also examined. We have demonstrated that static stretch application produces a robust increase in p38 phosphorylation preceding MEF2A, but not NFATc1, nuclear translocation as well as deactivation of GSK-3β via its phosphorylation. Using SB-203580 and cyclosporine A drugs to inhibit both p38- or/and calcineurin-dependent signals, respectively, we have shown that MEF2A phosphorylation and subsequent nuclear translocation are regulated by p38 and calcineurin in a biphasic, time-dependent manner. Moreover, we also present evidence for another kinase that is involved in the stretch-related signal triggering MEF2A hyperphosphorylation, impairing its nuclear translocation, and that is related to p38. Finally, we have shown that static stretch application overnight promotes neonatal myosin heavy chain expression, which is inhibited by an inactivation of both p38 and calcineurin.
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Affiliation(s)
- Cyril Rauch
- Muscle and Molecular Biology Unit, Department of Veterinary Basic Sciences, Royal Veterinary College, University of London, Royal College St., London NW1 0TU, United Kingdom
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Lappa M. The growth and the fluid dynamics of protein crystals and soft organic tissues: models and simulations, similarities and differences. J Theor Biol 2003; 224:225-40. [PMID: 12927529 DOI: 10.1016/s0022-5193(03)00160-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Abstract
The fluid-dynamic environment within typical growth reactors as well as the interaction of such flow with the intrinsic kinetics of the growth process are investigated in the frame of the new fields of protein crystal and tissue engineering. The paper uses available data to introduce a set of novel growth models. The surface conditions are coupled to the exchange mass flux at the specimen/culture-medium interface and lead to the introduction of a group of differential equations for the nutrient concentration around the sample and for the evolution of the construct mass displacement. These models take into account the sensitivity of the construct/liquid interface to the level of supersaturation in the case of macromolecular crystal growth and to the "direct" effect of the fluid-dynamic shear stress in the case of biological tissue growth. They then are used to show how the proposed surface kinetic laws can predict (through sophisticated numerical simulations) many of the known characteristics of protein crystals and biological tissues produced using well-known and widely used reactors. This procedure provides validation of the models and associated numerical method and at the same time gives insights into the mechanisms of the phenomena. The onset of morphological instabilities is discussed and investigated in detail. The interplay between the increasing size of the sample and the structure of the convective field established inside the reactor is analysed. It is shown that this interaction is essential in determining the time evolution of the specimen shape. Analogies about growing macromolecular crystals and growing biological tissues are pointed out in terms of behaviours and cause-and-effect relationships. These aspects lead to a common source (in terms of original mathematical models, ideas and results) made available for the scientific community under the optimistic idea that the contacts established between the "two fields of engineering" will develop into an ongoing, mutually beneficial dialogue.
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Affiliation(s)
- Marcello Lappa
- MARS (Microgravity Advanced Research and Support Center), Via Gianturco 31, 80146, Napoli, Italy.
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