Computational modeling of volumetric soft tissue growth: application to the cardiac left ventricle

As an initial step to investigate stimulus–response relations in growth and remodeling (G&R) of cardiac tissue, this study aims to develop a method to simulate 3D-inhomogeneous volumetric growth. Growth is regarded as a deformation that is decomposed into a plastic component which describes unconstrained growth and an elastic component to satisfy continuity of the tissue after growth. In current growth models, a single reference configuration is used that remains fixed throughout the entire growth process. However, considering continuous turnover to occur together with growth, such a fixed reference is unlikely to exist in reality. Therefore, we investigated the effect of tissue turnover on growth by incrementally updating the reference configuration. With both a fixed reference and an updated reference, strain-induced cardiac growth in magnitude of 30% could be simulated. However, with an updated reference, the amplitude of the stimulus for growth decreased over time, whereas with a fixed reference this amplitude increased. We conclude that, when modeling volumetric growth, the choice of the reference configuration is of great importance for the computed growth.     

The brain's interstitial clefts and their glial walls

The heterogeneous contents of the CNS interstitial clefts and the configuration of their astrocytic walls may be regionally variable. Astrocytic processes of the glia limitans, in normal midbrain and in astroglial scars, form thin, parallel, concentric sheets comprising the walls of narrow interstitial clefts. There is a critical thickness of about 20 to 30 nm, below which astrocytic cell process or those of the fibroblast-like cells in the meninges, do not invaginate to form transcytotic vesicles. Large hydrophilic solutes cannot, therefore, pass across the thin portion of a cell process. Consequently, (a) the diffusion and convection paths of interstitial fluid and solutes are lengthened, (b) a solute will remain within the interstitial cleft between thin lamellae for a relatively long time and (c) if a ligand does bind to its receptor on the thin process's cell membrane, there can be no receptor-mediated transcytosis at that site. Interstitial clefts, themselves, vary in size, shape and content, including extracellular matrix and basal lamina. A common constituent of basal lamina and extracellular matrix, presumably including that at ependymal, astroglial and endothelial interfaces of the CNS, is heparan sulfate proteoglycans. As in other organs, these proteoglycans may store growth factors, growth inhibitors, cytokines and other modulators which can then be released enzymatically during, e.g., regeneration. Exogenous heparan sulfate proteoglycan might serve as a natural, intermittent-release matrix for delivery of trophic factors.     

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.     

Influence of interstitial fluid dynamics on growth and therapy of angiogenic tumor. Analysis by mathematical model

We have developed a spatially distributed mathematical model of angiogenic tumor growth in tissue with account of interstitial fluid dynamics and bevacizumab monotherapy. In this model the process of neovascularization is initiated by tumor cells in a state of metabolic stress, vascular endothelial growth factor (VEGF) being its main mediator. The model takes into consideration the convection flows arising in dense tissue due to active proliferation and migration of tumor cells as well as interstitial fluid inflow from blood vascular system, its outflow through lymphatic system and redistribution in the area of tumor growth. The work considers the diffusive approximation of interstitial fluid dynamics in tumor and normal tissue. Numerical study of the model showed that in absence of therapy a peritumoral edema is formed due to the increase of interstitial fluid inflow from angiogenic capillaries. In the case of rapid interstitial fluid outflow through lymphatic system and its fast transport from necrotic zone to normal tissue the regimes of full growth stop are observed in case of low-invasive tumor. Under bevacizumab monotherapy the peritumoral edema vanishes and low-invasive tumor may not only decelerate its growth, but also start shrinking for a large range of parameters.     

Fluorofenidone attenuates renal interstitial fibrosis in the rat model of obstructive nephropathy

Fluorofenidone (FD) is a novel pyridone agent with significant antifibrotic effects in vitro. The purpose of this study is to investigate the effects of FD on renal interstitial fibrosis in rats with obstructive nephropathy caused by unilateral ureteral obstruction (UUO). With pirfenidone (PD, 500 mg/kg/day) and enalapril (10 mg/kg/day) as the positive treatment controls, the rats in different experimental groups were administered with FD (500 mg/kg/day) from day 4 to day 14 after UUO. The tubulointerstitial injury, interstitial collagen deposition, and expression of type I and type III collagen, transforming growth factor-β(1) (TGF-β(1)), connective tissue growth factor (CTGF), platelet-derived growth factor (PDGF), α-smooth muscle actin (α-SMA), and tissue inhibitor of metalloproteinase-1 (TIMP-1) were assessed. FD treatment significantly attenuated the prominently increased scores of tubulointerstitial injury, interstitial collagen deposition, and protein expression of type I and type III collagen in ureter-obstructed kidneys, respectively. As compared with untreated rats, FD also significantly reduced the expression of α-SMA, TGF-β(1), CTGF, PDGF, and inhibitor of TIMP-1 in the obstructed kidneys. Fluorofenidone attenuates renal interstitial fibrosis in the rat model of obstructive nephropathy through its regulation on fibrogenic growth factors, tubular cell transdifferentiation, and extracellular matrix.     

TGF-β in progression of liver disease

Transforming growth factor-β (TGF-β) is a central regulator in chronic liver disease contributing to all stages of disease progression from initial liver injury through inflammation and fibrosis to cirrhosis and hepatocellular carcinoma. Liver-damage-induced levels of active TGF-β enhance hepatocyte destruction and mediate hepatic stellate cell and fibroblast activation resulting in a wound-healing response, including myofibroblast generation and extracellular matrix deposition. Being recognised as a major profibrogenic cytokine, the targeting of the TGF-β signalling pathway has been explored with respect to the inhibition of liver disease progression. Whereas interference with TGF-β signalling in various short-term animal models has provided promising results, liver disease progression in humans is a process of decades with different phases in which TGF-β or its targeting might have both beneficial and adverse outcomes. Based on recent literature, we summarise the cell-type-directed double-edged role of TGF-β in various liver disease stages. We emphasise that, in order to achieve therapeutic effects, we need to target TGF-β signalling in the right cell type at the right time.     

Regulation of proliferation of embryonic heart mesenchyme: role of transforming growth factor-beta 1 and the interstitial matrix

Proliferation of atrioventricular cushion mesenchyme of the embryonic avian heart maintained in three-dimensional aggregate culture is stimulated by interaction with the interstitial matrix. Chicken serum or transforming growth factor-beta 1, which stimulates proliferation, induces matrix deposition in regions of the aggregate showing high labeling indices with tritiated thymidine. Dispersed heart mesenchyme interstitial matrix introduced into serum-free culture is incorporated into the aggregate and stimulates cellular proliferation similar to serum or transforming growth factor-beta 1. Proliferation is reversibly inhibited by the peptide Gly-Arg-Gly-Asp-Ser-Pro. It is suggested that transforming growth factor-beta 1 stimulates the production of interstitial matrix and that a sufficient stimulus for proliferation in this system is the presence of the matrix, which acts as the adhesive support for cellular anchorage.     

Recombinant expression, purification, and functional characterisation of connective tissue growth factor and nephroblastoma-overexpressed protein

The CCN family of proteins, especially its prominent member, the Connective tissue growth factor (CTGF/CCN2) has been identified as a possible biomarker for the diagnosis of fibrotic diseases. As a downstream mediator of TGF-β1 signalling, it is involved in tissue scarring, stimulates interstitial deposition of extracellular matrix proteins, and promotes proliferation of several cell types. Another member of this family, the Nephroblastoma-Overexpressed protein (NOV/CCN3), has growth-inhibiting properties. First reports further suggest that these two CCN family members act opposite to each other in regulating extracellular matrix protein expression and reciprocally influence their own expression when over-expressed. We have established stable HEK and Flp-In-293 clones as productive sources for recombinant human CCN2/CTGF. In addition, we generated an adenoviral vector for recombinant expression of rat NOV and established protocols to purify large quantities of these CCN proteins. The identity of purified human CCN2/CTGF and rat CCN3/NOV was proven by In-gel digest followed by ESI-TOF/MS mass spectrometry. The biological activity of purified proteins was demonstrated using a Smad3-sensitive reporter gene and BrdU proliferation assay in permanent cell line EA•hy 926 cells. We further demonstrate for the first time that both recombinant CCN proteins are N-glycosylated.     

Phellogen Regeneration in Injured Peach Tree Bark

Injury to peach bark phellogen leads to the generation of newtissues and the re-establishment of meristematic continuity.Two types of tissue changes after wounding were identified andquantified in bark of seven peach clones: (1) cell wall modifications(lignification and suberization) of tissues present at the timeof wounding, and (2) generation of the new phellogen and itsderivatives. Tissue responses were quantified with a microscopephotometer using selective histochemistry and autofluorescenceto detect lignin and suberin deposition over time. Suberin continuitywas re-established via suberin deposition in a layer of cells,present at the time of wounding, approximately 800 µminternal to the wound surface. Phellogen continuity was re-establishedimmediately internal to and abutting the suberized tissue. Thenew phellogen gave rise to suberized phellem which, in its outwardexpansion, crushed the suberized boundary zone tissue formedearlier. All injured peach clones produced the same sequenceof tissue changes, although timing and degree of response variedwith clone and time of year. Differentiation, impervious tissue, lignin, Prunus persica (L.) Batsch, suberin, wounding     

Genetic control theory of developmental events

An earlier theory of cell differentiation and morphogenesis (Wassermann, 1972, 1973, 1978) is combined with the genetic control model of Davidson and Britten (e.g. 1979). The resulting new theory suggests how, bysystematic process algorithms, specifically enumerated combinations of batteries of structural genes can become switched on in particularly enumerated cells, via battery-specific enumerable regulator genes. The systematization is idealized. Up to a certain stage of development in each mitotically arising cell a unique cell-specific combination of structural genes called ‘marker genes’ is active. Marker genes are assumed to code for cell-specifying marker proteins (CSMPs) which permit cells carrying related markers to recognize each other, thus permitting specific cell sorting.Batteries of marker genes could ensure great developmental precision and can safeguard—via redundancies of CSMP types—against accidental loss or detrimental mutational modification of CSMPs or marker genes, respectively. This paper is much concerned with cell lineage in relation to ‘microdifferentiation’, where ‘microdifferentiation’ of a cell refers to a cell's active marker genes and its syntheses of CSMPs. A drastic distinction is made between ‘microdifferentiation’ and ‘gross’ differentiation of a cell, where the same ‘gross’ differentiation may be shared by a large number of cells that could each be uniquely ‘microdifferentiated’. Typical ‘gross’ differentiation could manifest itself in tissue specificity, whereas, up to certain stages of development, all cells of the same gross differentiation type (say tissue specificity) could each be uniquely ‘microdifferentiated’. The theory also assumes that at certain stages of the developmental process some (or in some organisms all) of the previously uniquely specified cells could give rise to small (or occasionally large) clones of equispecified cells, some of which might form clusters that represent complete ‘morphogenetic fields’ Tentative implementation mechanisms are proposed which suggest how the theory could operate in molecular biological terms. In particular, CSMPs could endow cell surface membranes with a highly specific protein network, and an associated equally specific cell surface coat. It is suggested how these highly specified cell surface coats and other systems could provide an ‘extracellular guidance network’ which could help to direct cells to attain energetically optimal locations relative to each other based on the matching of their surface specificities. In numerous experimental situations, where normally present optimal matching of cells is excluded, ‘alternative matching’ based on experiment-specific suboptimal matching could explain many data, notably in experimental development neurobiology (Wassermann, 1978).     

Immunohistochemical localization of estrogen receptors ERα and ERβ in the spiny mouse (<Emphasis Type="Italic">Acomys cahirinus</Emphasis>) ovary during postnatal development

This study was designed to determine the expression pattern of estrogen receptor (ER) subtypes in the Acomys cahirinus ovarian cells during its postnatal development. Immunohistochemical studies revealed the presence of ERα and ERβ in germinal epithelium cells and interstitial tissue. Both these ER subtypes were also seen in granulosa cells and oocytes of growing follicles, however, the level of ERβ expression was higher in comparison with ERα. In contrast to ERβ, ERα protein was also present in theca cells. The expression of ERs increased with animals’ age, but it decreased during follicular maturation. Moreover, the immunolocalization of ER subtypes in luteal cells showed that not ERβ, but ERα expression is up-regulated throughout corpus luteum development. These immunohistochemical studies demonstrate, for the first time, that ERα is also expressed in the mouse granulosa cells and it may be a mediator of estrogen action in granulosa cells proliferation and differentiation.     

The role of polyp-stolon junctions in the redox signaling of colonial hydroids

An encrusting colonial hydroid can be regarded as a network of polyps or ‘mouths’ connected by tube-like stolons. The success of the colony crucially depends on putting these mouths where the available food is. Feeding-related perturbations may provide important signals in this regard. After feeding, polyps contract regularly, dispersing food throughout the colony via the gastrovascular fluid. Mitochondrion-rich epitheliomuscular cells concentrated near polyp-stolon junctions likely drive these contractions. Putatively, the redox state of these cells may influence colony-level form. For instance, the metabolic demand associated with feeding-related contractions results in mitochondria that have relatively oxidized electron carriers and produce lesser amounts of reactive oxygen species (ROS). ROS or other redox-sensitive molecules emitted from polyp-stolon junctions into the gastrovascular fluid may provide stolons with signals influencing elongation, branching, and regression. Treatments of colonies with anti-oxidants cause peripheral stolon tips to rapidly regress. This regression appears to be an active process involving a flux of locally produced peroxides and cell and tissue death. At the same time, polyps and stolon tips in the center of treated colonies remain healthy. ‘Sheet-like’ growth of short, branched stolons ensues. Signals that inhibit the outward growth of stolons may lead by default to the concentrated growth of stolons and polyps in food-rich areas. ROS may mediate signaling mechanisms involving nitric oxide, programmed cell death, a variety of redox-regulated proteins, or all of these.     

Deep cerebellar neurons mirror the spinal cord’s gain to implement an inverse controller

Smooth and coordinated motion requires precisely timed muscle activation patterns, which due to biophysical limitations, must be predictive and executed in a feed-forward manner. In a previous study, we tested Kawato’s original proposition, that the cerebellum implements an inverse controller, by mapping a multizonal microcomplex’s (MZMC) biophysics to a joint’s inverse transfer function and showing that inferior olivary neuron may use their intrinsic oscillations to mirror a joint’s oscillatory dynamics. Here, to continue to validate our mapping, we propose that climbing fiber input into the deep cerebellar nucleus (DCN) triggers rebounds, primed by Purkinje cell inhibition, implementing gain on IO’s signal to mirror the spinal cord reflex’s gain thereby achieving inverse control. We used biophysical modeling to show that Purkinje cell inhibition and climbing fiber excitation interact in a multiplicative fashion to set DCN’s rebound strength; where the former primes the cell for rebound by deinactivating its T-type Ca2⁺ channels and the latter triggers the channels by rapidly depolarizing the cell. We combined this result with our control theory mapping to predict how experimentally injecting current into DCN will affect overall motor output performance, and found that injecting current will proportionally scale the output and unmask the joint’s natural response as observed by motor output ringing at the joint’s natural frequency. Experimental verification of this prediction will lend support to a MZMC as a joint’s inverse controller and the role we assigned underlying biophysical principles that enable it.     

Binocular fusion in Panum’s limiting case of stereopsis obeys the uniqueness constraint

In the information processing procedure of stereo vision, the uniqueness constraint has been used as one of the constraints to solve the “correspondence problem”. While the uniqueness constraint is valid in most cases, whether it is still valid in some particular stimulus configuration (such as Panum’s limiting case) has been a problem of widespread debate for a long time. To investigate the problem, we adopted the Panum’s limiting case as its basic stimulus configuration, and delved into the phenomenon of binocular fusion from two distinct aspects: visual direction and orientation disparity. The results show that in Panum’s limiting case binocular fusion does not comply with the rules governing regular binocular fusion as far as visual direction and orientation disparity are concerned. This indicates that double fusion does not happen in Panum’s limiting case and that the uniqueness constraint is still valid.     

Binocular fusion in Panum’s limiting case of stereopsis obeys the uniqueness constraint

In the information processing procedure of stereo vision, the uniqueness constraint has been used as one of the constraints to solve the “correspondence problem”. While the uniqueness constraint is valid in most cases, whether it is still valid in some particular stimulus configuration (such as Panum’s limiting case) has been a problem of widespread debate for a long time. To investigate the problem, we adopted the Panum’s limiting case as its basic stimulus configuration, and delved into the phenomenon of binocular fusion from two distinct aspects: visual direction and orientation disparity. The results show that in Panum’s limiting case binocular fusion does not comply with the rules governing regular binocular fusion as far as visual direction and orientation disparity are concerned. This indicates that double fusion does not happen in Panum’s limiting case and that the uniqueness constraint is still valid.     

Developmental regulation of interstitial cell density in bullfrog skeletal muscle

Denervation of skeletal muscle results in striking connective tissue remodelling in junctional areas of muscle. Since extracellular matrix molecules mediate axonal growth and synaptic differentiation, it is likely that the interstitial cells and matrix molecules that accumulate near synaptic sites after denervation influence the regrowth and regeneration of synaptic connections. The experiments presented here addressed the question of whether the junctional connective tissue in developing bullfrog skeletal muscle was also specialized in its cellular and molecular composition. Denervation responses of muscle, such as extrajunctional sensitivity to acetylcholine, often reproduce the characteristics of developing muscle during synaptogenesis. In developing muscle, the distribution of interstitial cells was nonuniform during the period of muscle fibre birth and synaptogenesis. Interstitial cells were concentrated near synaptic sites as in denervated adult muscle. Unlike denervated adult muscle, there were no junctional accumulations of fibronectin or tenascin, matrix molecules produced by interstitial cells, in developing muscles. These results demonstrate that the junctional connective tissue in developing muscle is identified by a high density of interstitial cells that may play a role in the identification and formation of synaptic sites. Further, the junctional matrix environment of developing muscle is distinct from the matrix remodelling that occurs in response to denervation, suggesting that the matrix production by interstitial cells during development is regulated differently from that after denervation of the neuromuscular junction.     

Interstitial cells from the atrial and ventricular sides of the bovine mitral valve respond differently to denuding endocardial injury

Summary The mitral valve has atrial and ventricular sides, each lined by endocardial cells. The valve stroma contains α smooth muscle actin positive interstitial cells, collagen, glycosaminoglycans, and elastic tissue. To eliminate the effect of endocardium on wound repair in bovine mitral valve organ culture, the endocardium was removed from both sides of the valve. At 6 days, organ cultures of these preparations revealed surface cells on the ventricular side but not on the atrial side. Ventricular surface cells were negative for Factor VIII-related antigen, and positive for α smooth muscle actin. Immuno-peroxidase staining for proliferating cell nuclear antigen/cyclin, a marker for cell proliferation, revealed a positive labeling index of (mean ± standard deviation) 0.08 ± 0.16% for interstitial cells from the atrial side and 0.14 ± 0.19% for ventricular side interstitial cells in uncultured preparations (not significant), and 0.44 ± 0.69% for atrial side interstitial cells and 2.25 ± 1.64% for ventricular side interstitial cells in the cultured preparations (significant,P<0.0006). The results suggest that in organ culture, interstitial cells from the ventricular side of the mitral valve respond to a denuding endocardial injury by proliferating and migrating onto the adjacent surface whereas interstitial cells from the atrial side do not. This difference in the response to injury of interstitial cells from the atrial and ventricular sides of the valve may reflect differences in phenotype or may be due to effects of extracellular matrix on interstitial cell behavior. The latter is possible because of differences in the extracellular matrix of the atrial and ventricular sides of the valve.     

Computational modeling of chemical reactions and interstitial growth and remodeling involving charged solutes and solid-bound molecules

Mechanobiological processes are rooted in mechanics and chemistry, and such processes may be modeled in a framework that couples their governing equations starting from fundamental principles. In many biological applications, the reactants and products of chemical reactions may be electrically charged, and these charge effects may produce driving forces and constraints that significantly influence outcomes. In this study, a novel formulation and computational implementation are presented for modeling chemical reactions in biological tissues that involve charged solutes and solid-bound molecules within a deformable porous hydrated solid matrix, coupling mechanics with chemistry while accounting for electric charges. The deposition or removal of solid-bound molecules contributes to the growth and remodeling of the solid matrix; in particular, volumetric growth may be driven by Donnan osmotic swelling, resulting from charged molecular species fixed to the solid matrix. This formulation incorporates the state of strain as a state variable in the production rate of chemical reactions, explicitly tying chemistry with mechanics for the purpose of modeling mechanobiology. To achieve these objectives, this treatment identifies the specific theoretical and computational challenges faced in modeling complex systems of interacting neutral and charged constituents while accommodating any number of simultaneous reactions where reactants and products may be modeled explicitly or implicitly. Several finite element verification problems are shown to agree with closed-form analytical solutions. An illustrative tissue engineering analysis demonstrates tissue growth and swelling resulting from the deposition of chondroitin sulfate, a charged solid-bound molecular species. This implementation is released in the open-source program FEBio (www.febio.org). The availability of this framework may be particularly beneficial to optimizing tissue engineering culture systems by examining the influence of nutrient availability on the evolution of inhomogeneous tissue composition and mechanical properties, the evolution of construct dimensions with growth, the influence of solute and solid matrix electric charge on the transport of cytokines, the influence of binding kinetics on transport, the influence of loading on binding kinetics, and the differential growth response to dynamically loaded versus free-swelling culture conditions.