VASCULAR MECHANICS, MECHANOBIOLOGY, AND REMODELING

Glaucoma and biomechanics

PURPOSE OF REVIEW

Biomechanics is an important aspect of the complex family of diseases known as the glaucomas. Here, we review recent studies of biomechanics in glaucoma.

RECENT FINDINGS

Several tissues have direct and/or indirect biomechanical roles in various forms of glaucoma, including the trabecular meshwork, cornea, peripapillary sclera, optic nerve head/sheath, and iris. Multiple mechanosensory mechanisms and signaling pathways continue to be identified in both the trabecular meshwork and optic nerve head. Further, the recent literature describes a variety of approaches for investigating the role of tissue biomechanics as a risk factor for glaucoma, including pathological stiffening of the trabecular meshwork, peripapillary scleral structural changes, and remodeling of the optic nerve head. Finally, there have been advances in incorporating biomechanical information in glaucoma prognoses, including corneal biomechanical parameters and iridial mechanical properties in angle-closure glaucoma.

SUMMARY

Biomechanics remains an active aspect of glaucoma research, with activity in both basic science and clinical translation. However, the role of biomechanics in glaucoma remains incompletely understood. Therefore, further studies are indicated to identify novel therapeutic approaches that leverage biomechanics. Importantly, clinical translation of appropriate assays of tissue biomechanical properties in glaucoma is also needed.

Mechano-chemo-biological Computational Models for Arteries in Health, Disease and Healing: From Tissue Remodelling to Drug-eluting Devices

This review aims to highlight urgent priorities for the computational biomechanics community in the framework of mechano-chemo-biological models. Recent approaches, promising directions and open challenges on the computational modelling of arterial tissues in health and disease are introduced and investigated, together with in silico approaches for the analysis of drug-eluting stents that promote pharmacological-induced healing. The paper addresses a number of chemo-biological phenomena that are generally neglected in biomechanical engineering models but are most likely instrumental for the onset and the progression of arterial diseases. An interdisciplinary effort is thus encouraged for providing the tools for an effective in silico insight into medical problems. An integrated mechano-chemo-biological perspective is believed to be a fundamental missing piece for crossing the bridge between computational engineering and life sciences, and for bringing computational biomechanics into medical research and clinical practice.

Coupling hemodynamics with mechanobiology in patient-specific computational models of ascending thoracic aortic aneurysms

BACKGROUND AND OBJECTIVE

The prevention of ascending thoracic aortic aneurysms (ATAAs), which affect thousands of persons every year worldwide, remains a major issue. ATAAs may be caused by anything that weakens the aortic wall. Altered hemodynamics, which concerns a majority of patients with bicuspid aortic valves, has been shown to be related to such weakening and to contribute to ATAA development and progression. However the underlying mechanisms remain unclear and computational modeling in this field could help significantly to elucidate how hemodynamics and mechanobiology interact in ATAAs.

METHODS

Accordingly, we propose a numerical framework combining computational fluid dynamics and 4D flow magnetic resonance imaging (MRI) coupled with finite element (FE) analyses to simulate growth and remodeling (G&R) occurring in patient-specific aortas in relation with altered hemodynamics. The geometries and the blood velocities obtained from 4D flow MRI are used as boundary conditions for CFD simulations. CFD simulations provide an estimation of the wall shear stress (WSS) and relative residence time (RRT) distribution across the luminal surface of the wall. An initial insult is then applied to the FE model of the aortic wall, assuming that the magnitude of the insult correlates spatially with the normalized RRT distribution obtained from CFD simulations. G&R simulations are then performed. The material behavior of each Gauss point in these FE models is evolved continuously to compensate for the deviation of the actual wall stress distribution from the homeostatic state after the initial insult. The whole approach is illustrated on two healthy and two diseased subjects. The G&R parameters are calibrated against previously established statistical models of ATAA growth rates.

RESULTS

Among the variety of results provided by G&R simulations, the analysis focused especially on the evolution of the wall stiffness, which was shown to be a major risk factor for ATAAs. It was shown that the G&R parameters, such as for instance the rate of collagen production or cell mechanosensitivity, play a critical role in ATAA progression and remodeling.

CONCLUSIONS

These preliminary findings show that patient-specific computational modeling coupling hemodynamics with mechanobiology is a promising approach to explore aneurysm progression.

Diet alters age-related remodeling of aortic collagen in mice susceptible to atherosclerosis

Vascular cells restructure extracellular matrix in response to aging or changes in mechanical loading. Here, we characterized collagen architecture during age-related aortic remodeling in atherosclerosis-prone mice. We hypothesized that changes in collagen fiber orientation reflect an altered balance between passive and active forces acting on the arterial wall. We examined two factors that can alter this balance, endothelial dysfunction and reduced smooth muscle cell (SMC) contractility. Collagen fiber organization was visualized by second-harmonic generation microscopy in aortic adventitia of apolipoprotein E (apoE) knockout (KO) mice at 6 wk and 6 mo of age on a chow diet and at 7.5 mo of age on a Western diet (WD), using image analysis to yield mean fiber orientation. Adventitial collagen fibers became significantly more longitudinally oriented with aging in apoE knockout mice on chow diet. Conversely, fibers became more circumferentially oriented with aging in mice on WD. Total collagen content increased significantly with age in mice fed WD. We compared expression of endothelial nitric oxide synthase and acetylcholine-mediated nitric oxide release but found no evidence of endothelial dysfunction in older mice. Time-averaged volumetric blood flow in all groups showed no significant changes. Wire myography of aortic rings revealed decreases in active stress generation with age that were significantly exacerbated in WD mice. We conclude that the aorta displays a distinct remodeling response to atherogenic stimuli, indicated by altered collagen organization. Collagen reorganization can occur in the absence of altered hemodynamics and may represent an adaptive response to reduced active stress generation by vascular SMCs.NEW & NOTEWORTHY The following major observations were made in this study: 1) aortic adventitial collagen fibers become more longitudinally oriented with aging in apolipoprotein E knockout mice fed a chow diet; 2) conversely, adventitial collagen fibers become more circumferentially oriented with aging in apoE knockout mice fed a high-fat diet; 3) adventitial collagen content increases significantly with age in mice on a high-fat diet; 4) these alterations in collagen organization occur largely in the absence of hemodynamic changes; and 5) circumferential reorientation of collagen is associated with decreased active force generation (contractility) in aged mice on a high-fat diet.

Glomerular filtration and podocyte tensional homeostasis: importance of the minor type IV collagen network

The minor type IV collagen chain, which is a significant component of the glomerular basement membrane in healthy individuals, is known to assemble into large structures (supercoils) that may contribute to the mechanical stability of the collagen network and the glomerular basement membrane as a whole. The absence of the minor chain, as in Alport syndrome, leads to glomerular capillary demise and eventually to kidney failure. An important consideration in this problem is that the glomerular capillary wall must be strong enough to withstand the filtration pressure and porous enough to permit filtration at reasonable pressures. In this work, we propose a coupled feedback loop driven by filtration demand and tensional homeostasis of the podocytes forming the outer portion of the glomerular capillary wall. Briefly, the deposition of new collagen increases the stiffness of basement membrane, helping to stress shield the podocytes, but the new collagen also decreases the permeability of the basement membrane, requiring an increase in capillary transmural pressure drop to maintain filtration; the resulting increased pressure outweighs the increased glomerular basement membrane stiffness and puts a net greater stress demand on the podocytes. This idea is explored by developing a multiscale simulation of the capillary wall, in which a macroscopic (µm scale) continuum model is connected to a set of microscopic (nm scale) fiber network models representing the collagen network and the podocyte cytoskeleton. The model considers two cases: healthy remodeling, in which the presence of the minor chain allows the collagen volume fraction to be increased by thickening fibers, and Alport syndrome remodeling, in which the absence of the minor chain allows collagen volume fraction to be increased only by adding new fibers to the network. The permeability of the network is calculated based on previous models of flow through a fiber network, and it is updated for different fiber radii and volume fractions. The analysis shows that the minor chain allows a homeostatic balance to be achieved in terms of both filtration and cell tension. Absent the minor chain, there is a fundamental change in the relation between the two effects, and the system becomes unstable. This result suggests that mechanobiological or mechanoregulatory therapies may be possible for Alport syndrome and other minor chain collagen diseases of the kidney.

Modeling biomechanical interaction between soft tissue and soft robotic instruments: importance of constitutive anisotropic hyperelastic formulations

Cardiovascular diseases are the leading cause of death in the western countries. Robotic surgery recently emerged as a confirmed strategy in the cardiovascular field, especially thanks to the improvement of soft robotics. These techniques have demonstrated their potential in terms of speed of execution and precision. In this context, a deeper knowledge of the material properties of the blood vessels is required, especially for computational soft robotics applications. A constitutive model including the contribution of the collagen fibers families is needed to take hyperelasticity and anisotropy into account. For this purpose, four different models are presented: two fiber families with dispersion (2FFD), two fiber families without dispersion (2FF), four fiber families with dispersion (4FFD), and four fiber families without dispersion (4FF). A set of experimental biaxial data obtained from ex-vivo specimens was used to assess the model performances. Two fitting procedures were imposed: a procedure with no weighting of scores and a procedure with a weight set to enhance the model performances in the contact range. A finite element simulation of a contact procedure was developed to evaluate the effect on the contact pressures and forces according to the different model implementations. In particular, a minimally invasive aortic valve positioning process through a previously designed soft robot was simulated. The results confirmed the overall fitting procedure. The adoption of the weighting process for the fitting was successful, as it permitted an accurate prediction in the region of interest through models with less parameters.

A chemo-mechano-biological formulation for the effects of biochemical alterations on arterial mechanics: the role of molecular transport and multiscale tissue remodelling

This paper presents a chemo-mechano-biological framework for arterial physiopathology. The model accounts for the fine remodelling in the multiscale hierarchical arrangement of tissue constituents and for the diffusion of molecular species involved in cell-cell signalling pathways. Effects in terms of alterations in arterial compliance are obtained. A simple instructive example is introduced. Although oversimplified with respect to realistic case studies, the proposed application mimics the biochemical activity of matrix metalloproteinases, transforming growth factors beta and interleukins on tissue remodelling. Effects of macrophage infiltration, of intimal thickening and of a healing phase are investigated, highlighting the corresponding influence on arterial compliance. The obtained results show that the present approach is able to capture changes in arterial mechanics as a consequence of the alterations in tissue biochemical environment and cellular activity, as well as to incorporate the protective role of both autoimmune responses and pharmacological treatments.

A method to quantify mechanobiologic forces during zebrafish cardiac development using 4-D light sheet imaging and computational modeling

Blood flow and mechanical forces in the ventricle are implicated in cardiac development and trabeculation. However, the mechanisms of mechanotransduction remain elusive. This is due in part to the challenges associated with accurately quantifying mechanical forces in the developing heart. We present a novel computational framework to simulate cardiac hemodynamics in developing zebrafish embryos by coupling 4-D light sheet imaging with a stabilized finite element flow solver, and extract time-dependent mechanical stimuli data. We employ deformable image registration methods to segment the motion of the ventricle from high resolution 4-D light sheet image data. This results in a robust and efficient workflow, as segmentation need only be performed at one cardiac phase, while wall position in the other cardiac phases is found by image registration. Ventricular hemodynamics are then quantified by numerically solving the Navier-Stokes equations in the moving wall domain with our validated flow solver. We demonstrate the applicability of the workflow in wild type zebrafish and three treated fish types that disrupt trabeculation: (a) chemical treatment using AG1478, an ErbB2 signaling inhibitor that inhibits proliferation and differentiation of cardiac trabeculation; (b) injection of gata1a morpholino oligomer (gata1aMO) suppressing hematopoiesis and resulting in attenuated trabeculation; (c) weak-atriumm58 mutant (wea) with inhibited atrial contraction leading to a highly undeveloped ventricle and poor cardiac function. Our simulations reveal elevated wall shear stress (WSS) in wild type and AG1478 compared to gata1aMO and wea. High oscillatory shear index (OSI) in the grooves between trabeculae, compared to lower values on the ridges, in the wild type suggest oscillatory forces as a possible regulatory mechanism of cardiac trabeculation development. The framework has broad applicability for future cardiac developmental studies focused on quantitatively investigating the role of hemodynamic forces and mechanotransduction during morphogenesis.

Mechanics of Vascular Smooth Muscle

Vascular smooth muscle (VSM; see Table 1 for a list of abbreviations) is a heterogeneous biomaterial comprised of cells and extracellular matrix. By surrounding tubes of endothelial cells, VSM forms a regulated network, the vasculature, through which oxygenated blood supplies specialized organs, permitting the development of large multicellular organisms. VSM cells, the engine of the vasculature, house a set of regulated nanomotors that permit rapid stress-development, sustained stress-maintenance and vessel constriction. Viscoelastic materials within, surrounding and attached to VSM cells, comprised largely of polymeric proteins with complex mechanical characteristics, assist the engine with countering loads imposed by the heart pump, and with control of relengthening after constriction. The complexity of this smart material can be reduced by classical mechanical studies combined with circuit modeling using spring and dashpot elements. Evaluation of the mechanical characteristics of VSM requires a more complete understanding of the mechanics and regulation of its biochemical parts, and ultimately, an understanding of how these parts work together to form the machinery of the vascular tree. Current molecular studies provide detailed mechanical data about single polymeric molecules, revealing viscoelasticity and plasticity at the protein domain level, the unique biological slip-catch bond, and a regulated two-step actomyosin power stroke. At the tissue level, new insight into acutely dynamic stress-strain behavior reveals smooth muscle to exhibit adaptive plasticity. At its core, physiology aims to describe the complex interactions of molecular systems, clarifying structure-function relationships and regulation of biological machines. The intent of this review is to provide a comprehensive presentation of one biomachine, VSM.

Insights into regional adaptations in the growing pulmonary artery using a meso-scale structural model: effects of ascending aorta impingement

As the next step in our investigations into the structural adaptations of the main pulmonary artery (PA) during postnatal growth, we utilized the extensive experimental measurements of the growing ovine PA from our previous study (Fata et al., 2013, "Estimated in vivo Postnatal Surface Growth Patterns of the Ovine Main Pulmonary Artery and Ascending Aorta," J. Biomech. Eng., 135(7), pp. 71010-71012). to develop a structural constitutive model for the PA wall tissue. Novel to the present approach was the treatment of the elastin network as a distributed fiber network rather than a continuum phase. We then utilized this model to delineate structure-function differences in the PA wall at the juvenile and adult stages. Overall, the predicted elastin moduli exhibited minor differences remained largely unchanged with age and region (in the range of 150 to 200 kPa). Similarly, the predicted collagen moduli ranged from ∼1,600 to 2700 kPa in the four regions studied in the juvenile state. Interestingly, we found for the medial region that the elastin and collagen fiber splay underwent opposite changes (collagen standard deviation juvenile = 17 deg to adult = 28 deg, elastin standard deviation juvenile = 35 deg to adult = 27 deg), along with a trend towards more rapid collagen fiber strain recruitment with age, along with a drop in collagen fiber moduli, which went from 2700 kPa for the juvenile stage to 746 kPa in the adult. These changes were likely due to the previously observed impingement of the relatively stiff ascending aorta on the growing PA medial region. Intuitively, the effects of the local impingement would be to lower the local wall stress, consistent with the observed parallel decrease in collagen modulus. These results suggest that during the postnatal somatic growth period local stresses can substantially modulate regional tissue microstructure and mechanical behaviors in the PA. We further underscore that our previous studies indicated an increase in effective PA wall stress with postnatal maturation. When taken together with the fact that the observed changes in mechanical behavior and structure in the growing PA wall were modest in the other three regions studied, our collective results suggest that the majority of the growing PA wall is subjected to increasing stress levels with age without undergoing major structural adaptations. This observation is contrary to the accepted theory of maintenance of homeostatic stress levels in the regulation of vascular function, and suggests alternative mechanisms might regulate postnatal somatic growth. Understanding the underlying mechanisms will help to improve our understanding of congenital defects of the PA and lay the basis for functional duplication in their repair and replacement.

A finite element study on variations in mass transport in stented porcine coronary arteries based on location in the coronary arterial tree

Drug-eluting stents have a significant clinical advantage in late-stage restenosis due to the antiproliferative drug release. Understanding how drug transport occurs between coronary arterial locations can better help guide localized drug treatment options. Finite element models with properties from specific porcine coronary artery sections (left anterior descending (LAD), right (RCA); proximal, middle, distal regions) were created for stent deployment and drug delivery simulations. Stress, strain, pore fluid velocity, and drug concentrations were exported at different time points of simulation (0-180 days). Tests indicated that the highest stresses occurred in LAD sections. Higher-than-resting homeostatic levels of stress and strain existed at upwards of 3.0 mm away from the stented region, whereas concentration of species only reached 2.7 mm away from the stented region. Region-specific concentration showed 2.2 times higher concentrations in RCA artery sections at times corresponding to vascular remodeling (peak in the middle segment) compared to all other segments. These results suggest that wall transport can occur differently based on coronary artery location. Awareness of peak growth stimulators and where drug accumulation occurs in the vasculature can better help guide local drug delivery therapies.

Interstitial growth and remodeling of biological tissues: tissue composition as state variables

Growth and remodeling of biological tissues involves mass exchanges between soluble building blocks in the tissue's interstitial fluid and the various constituents of cells and the extracellular matrix. As the content of these various constituents evolves with growth, associated material properties, such as the elastic modulus of the extracellular matrix, may similarly evolve. Therefore, growth theories may be formulated by accounting for the evolution of tissue composition over time in response to various biological and mechanical triggers. This approach has been the foundation of classical bone remodeling theories that successfully describe Wolff's law by establishing a dependence between Young's modulus and bone apparent density and by formulating a constitutive relation between bone mass supply and the state of strain. The goal of this study is to demonstrate that adding tissue composition as state variables in the constitutive relations governing the stress-strain response and the mass supply represents a very general and straightforward method to model interstitial growth and remodeling in a wide variety of biological tissues. The foundation for this approach is rooted in the framework of mixture theory, which models the tissue as a mixture of multiple solid and fluid constituents. A further generalization is to allow each solid constituent in a constrained solid mixture to have its own reference (stress-free) configuration. Several illustrations are provided, ranging from bone remodeling to cartilage tissue engineering and cervical remodeling during pregnancy.

AN IMPROVED MODEL FOR REDUCED-ORDER PHYSIOLOGICAL FLUID FLOWS

An improved one-dimensional mathematical model based on the Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation whose coefficients are smoothly varying functions of the spatial variable. The resulting momentum equation along with the continuity equation and pressure-area relation form our reduced-order model for physiological fluid flows in one dimension and are aimed at providing accurate and fast-to-compute global models for physiological systems represented as networks of quasi one-dimensional fluid flows. The consequent nonlinear coupled system of equations is solved by the Lax-Wendroff scheme and is then applied to an open model arterial network of the human vascular system containing the largest 55 arteries. The proposed model with functional coefficients is compared with current classical one-dimensional theories which assume steady state Hagen-Poiseuille velocity profiles, either parabolic or plug-like, throughout the whole arterial tree. The effects of the nonlinear term in the momentum equation and different strategies for bifurcation points in the network, as well as the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results show that the proposed model can be used as an efficient tool for investigating the dynamics of reduced-order models of flows in physiological systems and would, in particular, be a good candidate for the one-dimensional, system-level component of geometric multiscale models of physiological systems.

SENSITIVITY ANALYSIS OF COMPUTATIONAL STRUCTURAL DYNAMICS IN A CEREBRAL ANEURYSM MODEL TO WALL THICKNESS AND MODEL

Intracranial saccular aneurysms tend to be thin walled and stiffer compared with a normal artery. The current work describes computational structural dynamics (CSD) in an anatomically realistic model of a cerebral aneurysm located in the ophthalmic region, using different wall thickness, model data for the artery and aneurysm, and geometry size. The model was obtained from three-dimensional rotational angiography image data. The wall was assumed three-dimensional hyperelastic solid with different thickness in the artery and in the aneurysm regions. The effects of carotid siphon length are reported. The CSD was solved with the finite elements package ADINA. The predictions of stress and strain on the aneurysm wall were compared.

NONINVASIVE POWER SPECTRUM ANALYSIS OF RADIAL PRESSURE WAVEFORM FOR ASSESSMENT OF VASCULAR SYSTEM

Wrist pulse diagnosis has been used in traditional Chinese medicine (TCM) for thousands of years, because pulse pressure signal contains a large number of physiological and pathological information of people. In this research, a systematic approach was proposed to analyze the computerized radial pressure waveform, with the focus placed on the power spectrum. We gained the power spectrum by using a modified fast Fourier transform, and the power-spectral characteristics were analyzed and compared. The analyzing program calculated the first peak frequency (F1) and the second peak (F2) automatically, and gained the time of phase shift between two frequencies. They could provide a simple noninvasive means for studying changes in the elastic properties of the vascular system depending on the age and the disease. Namely, the frequency analysis of radial pressure waveform gives new insight into the dynamics of cardiovascular system.

RADIAL DIASTOLIC AUGMENTATION INDEX IS A USEFUL PREDICTOR OF ARTERIAL STIFFNESS

Diastolic augmentation index (DAI), calculated from radial artery pressure waveform, has been associated with the risk of cardiovascular disease. In the present study, we aimed to evaluate whether DAI could be used as a predictor of arterial stiffness and the effect of heart rate (HR) on it. Measurements of anthropometric parameters, blood pressure (BP), Augmentation index (AI) and DAI were taken in 242 healthy subjects (130 men and 112 women; age 16–78 years). DAI and AI were measured in a subgroup of 16 subjects (10 men and 6 women; age 19–69 years) in a two-month follow-up study, which aimed to investigate the effect of HR changes. Statistically, DAI was higher in women compared to men (44.8% ± 7.7% compared with 43.6% ± 6.9%, P < 0.05). DAI was decreased with age (men: r = -0.755, P < 0.05; women: r = -0.708, P < 0.05) and negatively correlated to AI (men: r = -0.704, P < 0.05; women: r = -0.756, P < 0.05). There was no significant change in DAI when HR ranged from 60 to 80 bpm. Multiple regression analysis demonstrated fewer determinants affect DAI compared with AI. These findings indicate that the simple radial DAI might be used as an index to assess vascular aging.

WALL SHEAR AND CIRCUMFERENTIAL STRESS CHANGES IN A PORCINE DOUBLE-LAYER VEIN GRAFT

This study aimed to evaluate short-term changes of wall shear stress and circumferential stress in a self-designed double-layer vein graft in a porcine vein graft model. In this study, left and right hind femoral arteries of 40 white pigs were randomly divided into an experimental group (double-layer vein graft) and a control group (single-layer vein graft). At one hour and then at one, two and four weeks after venous bypass grafting, sets of ten animals underwent Doppler-ultrasonic and electromagnetic flowmeter examinations to calculate wall shear stress in middle sections of the vein grafts. Then, the vein grafts were excised and subjected to mechanical tests to assess the circumferential stress. As a result, the double-layer vein grafts showed an increase in wall shear stress by 43.5% compared with the control group at one hour after venous bypass grafting. With time wall shear stress gradually increased, the intimal circumferential stress gradually decreased in the two groups. Intimal circumferential stress in the experimental group was significantly lower than that in the control group at each observational time-point. Hence, the double-layer support of the vein graft may have contributed towards a rise in wall shear stress and reduction in circumferential stress in the true vein graft over the four-week period after venous bypass grafting, and thus conferring some protection to the true vein graft.