Cardiac tissue engineering using perfusion bioreactor systems

This protocol describes tissue engineering of synchronously contractile cardiac constructs by culturing cardiac cell populations on porous scaffolds (in some cases with an array of channels) and bioreactors with perfusion of culture medium (in some cases supplemented with an oxygen carrier). The overall approach is 'biomimetic' in nature as it tends to provide in vivo-like oxygen supply to cultured cells and thereby overcome inherent limitations of diffusional transport in conventional culture systems. In order to mimic the capillary network, cells are cultured on channeled elastomer scaffolds that are perfused with culture medium that can contain oxygen carriers. The overall protocol takes 2-4 weeks, including assembly of the perfusion systems, preparation of scaffolds, cell seeding and cultivation, and on-line and end-point assessment methods. This model is well suited for a wide range of cardiac tissue engineering applications, including the use of human stem cells, and high-fidelity models for biological research.     

On facilitated oxygen diffusion in muscle tissues.

The role of myoglobin in facilitated diffusion of oxygen in muscle in examined in a tissue model that utilizes a central supplying capillary and a tissue cylinder concentric with the central capillary, and that includes the nonlinear characteristics of the oxygen-hemoglobin dissociation reaction. In contrast to previous work, this model exhibits the effect of blood flow and a realistic, though ideal, tissue-capillary geometry. Solutions of the model equations are obtained by a singular-perturbation technique, and numerical results are discussed for model parameters of physiologic interest. In contrast to the findings of Murray, Rubinow, Taylor, and others, fractional order perturbation terms obtained for the "boundary-layer" regions near the supplying capillaries are quite significant in the overall interpretation of the modeling results. Some closed solutions are found for special cases, and these are contrasted with the full singular-perturbation solution. Interpretations are given for parameters of physiologic interest.     

Oxygen delivery to skeletal muscle fibers: effects of microvascular unit structure and control mechanisms

The number of perfused capillaries in skeletal muscle varies with muscle activation. With increasing activation, muscle fibers are recruited as motor units consisting of widely dispersed fibers, whereas capillaries are recruited as groups called microvascular units (MVUs) that supply several adjacent fibers. In this study, a theoretical model was used to examine the consequences of this spatial mismatch between the functional units of muscle activation and capillary perfusion. Diffusive oxygen transport was simulated in cross sections of skeletal muscle, including several MVUs and fibers from several motor units. Four alternative hypothetical mechanisms controlling capillary perfusion were considered. First, all capillaries adjacent to active fibers are perfused. Second, all MVUs containing capillaries adjacent to active fibers are perfused. Third, each MVU is perfused whenever oxygen levels at its feed arteriole fall below a threshold value. Fourth, each MVU is perfused whenever the average oxygen level at its capillaries falls below a threshold value. For each mechanism, the dependence of the fraction of perfused capillaries on the level of muscle activation was predicted. Comparison of the results led to the following conclusions. Control of perfusion by MVUs increases the fraction of perfused capillaries relative to control by individual capillaries. Control by arteriolar oxygen sensing leads to poor control of tissue oxygenation at high levels of muscle activation. Control of MVU perfusion by capillary oxygen sensing permits adequate tissue oxygenation over the full range of activation without resulting in perfusion of all MVUs containing capillaries adjacent to active fibers.     

Effect of intracapillary resistance to oxygen transport on the diffusional shunting between capillaries

The effect of intracapillary resistance to oxygen transport on distribution of oxygen tension in the tissue and along the capillary was investigated by means of a mathematical model. In some cases resistance significantly affects the diffusive interaction between neighbouring capillaries thus aggravating the dificiency of oxygen supply around capillaries with low oxygen tension.     

Long-term liver cell cultures in bioreactors and possible application for liver support

Hybrid artificial liver systems are being developed as a temporary extracorporeal liver support therapy. A short overview is given which emphasizes the development of hepatocyte culture models for bioreactors, subsequent in vitro studies, animal studies and the clinical application of hybrid liver support systems.An own bioreactor construction has been designed for the utilization of hepatocytes and sinusoidal endothelial cells. The reactor is based on capillaries for hepatocyte aggregate immobilization, coated with biomatrix. Four separate capillary membrane systems, each permitting a different function, are woven in order to create a three-dimensional network. Cells are perfused via independent capillary membrane compartments. Decentralized oxygen supply and carbon dioxide removal with low gradients is possible. There is a decentralized co-culture compartment for nonparenchymal liver cells. The use of identical parallel units to supply a few hepatocytes facilitates scale-up.     

Metabolic models of microcirculatory regulation.

The functions and integrity of body tissues are critically dependent on an adequate oxygen supply. Because the transport of oxygen to the cells is intimately linked to the microcirculation, the concept of microcirculation-metabolism coupling has received much attention. In essence, the metabolic theory of intrinsic control of the microcirculation states that microvascular tone is locally modulated to maintain adequate oxygen levels in the parenchymal cells. We propose a two-component control system for the regulation of tissue O2 delivery in accordance with metabolic needs. A precapillary sphincter control mechanism maintains tissue PO2 by governing the number of perfused capillaries. Functional capillary density in turn determines surface area available for diffusion and capillary-to-cell diffusion distance. On the other hand, the arteriolar control system modulates local blood flow in accordance with parenchymal O2 utilization and thereby minimizes changes in capillary PO2 when the O2 availability/demand ratio is decreased. We propose that the precapillary sphincters are more sensitive to changes in tissue PO2 than are the flow-regulating arterioles. Consequently, for mild stresses, adequate tissue oxygenation is maintained mainly by precapillary sphincter control of diffusion parameters without the need for changes in blood flow. However, as metabolic stresses become greater, blood flow regulation becomes the dominant factor in the control of tissue O2 delivery. Thus, by working in concert, the local mechanisms regulating microvascular resistance and effective capillary density provide a wide margin of safety against the development of cellular hypoxia.     

Mathematical modeling of oxygen transport in skeletal muscle

Inhomogeneous perfusion of capillary beds can result in large-scale diffusion of oxygen between distant portions of an organ. The conceptual model of a single capillary supplying oxygen to a surrounding concentric cylinder of tissue is not applicable to a consideration of such processes. An entirely different approach to the modeling of oxygen transport to tissue, with specific reference to the capillary beds of skeletal muscle, is presented here. This approach is intended to replace the theoretical Krogh cylinder model of capillary-tissue oxygen transport with a much more realistic model that takes into account inhomogeneities of capillary density, blood flow velocity, and oxygen concentration inherent in the micro-vasculature. The oxygen distribution in inhomogeneously perfused skeletal muscle is analyzed mathematically by defining an averaged concentration profile that neglects the fine-scale variation from capillary to capillary.     

The development of anoxia following occlusion

Following arteriolar occlusion, tissue oxygen concentration decreases and anoxic tissue eventually develops. Although anoxia first appears in the region most distal to the capillary at the venous end, it eventually spreads throughout the entire region of supply. In this paper the changing oxygen concentration, from the time of occlusion until the tissue is entirely anoxic, is examined mathematically. The equations governing oxygen transport to tissue are solved by iterating a nonlinear integral equation. This solution is valid until anoxia first appears. After anoxia develops it is necessary to solve a moving boundary problem. This is done using the method of matched asymptotic expansions, and accurate solutions are obtained for a wide range of physiological conditions.     

Der O2-Austausch zwischen Capillaren und Gewebe

Summary The distribution of oxygen concentration or oxygen partial pressure (=po₂) in models with different capillary arrangements is calculated. The capillaries form homogeneously perfused concurrent and countercurrent systems or inhomogeneously perfused capillary mesh systems with different velocities of blood flow on the inside of the capillaries. The question arises as to what extent the distribution of the po₂ in the tissue and the capillaries depends on the differences in streaming velocities and directions of the blood. The results show, that the greatest gradients in the po₂ distribution are to be found in the capillary mesh system. A typical example with a set of constants after Thews (1960) shows that the differences between the venous po₂ and the lowest po₂ in the tissue is 32 mm Hg in the case of the capillary network, 9 mm Hg in the case of the concurrent and 3 mm Hg in that of the countercurrent system.     

Biophysical regulation during cardiac development and application to tissue engineering

Tissue engineering combines the principles of biology, engineering and medicine to create biological substitutes of native tissues, with an overall objective to restore normal tissue function. It is thought that the factors regulating tissue development in vivo (genetic, molecular and physical) can also direct cell fate and tissue assembly in vitro. In light of this paradigm, tissue engineering can be viewed as an effort of "imitating nature". We first discuss biophysical regulation during cardiac development and the factors of interest for application in tissue engineering of the myocardium. Then we focus on the biomimetic approach to cardiac tissue engineering which involves the use of culture systems designed to recapitulate some aspects of the actual in vivo environment. To mimic cell signaling in native myocardium, subpopulations of neonatal rat heart cells were cultured at a physiologically high cell density in three-dimensional polymer scaffolds. To mimic the capillary network, highly porous elastomer scaffolds with arrays of parallel channels were perfused with culture medium. To mimic oxygen supply by hemoglobin, culture medium was supplemented with an oxygen carrier. To enhance electromechanical coupling, tissue constructs were induced to contract by applying electrical signals mimicking those in native heart. Over only eight days of cultivation, the biomimetic approach resulted in tissue constructs which contained electromechanically coupled cells expressing cardiac differentiation markers and cardiac-like ultrastructure and contracting synchronously in response to electrical stimulation. Ongoing studies are aimed at extending this approach to tissue engineering of functional cardiac grafts based on human cells.     

Re-evaluating the Use of Voronoi Tessellations in the Assessment of Oxygen Supply from Capillaries in Muscle

The ability to characterise capillary supply plays a key role in developing effective therapeutic interventions for numerous pathological conditions, such as capillary loss in skeletal or cardiac muscle. However, quantifying capillary supply is fraught with difficulties. Averaged measures such as capillary density or mean inter-capillary distance cannot account for the local geometry of the underlying capillary distribution, and thus can only highlight a tissue wide, global hypoxia. Detailed tissue geometry, such as muscle fibre size, has been incorporated into indices of capillary supply by considering the distribution of Voronoi tessellations generated from capillary locations in a plane perpendicular to muscle fibre orientation, implicitly assuming that each Voronoi polygon represents the area of supply of its enclosed capillary. Using a modelling framework to assess the capillary supply capacity under maximal sustainable conditions in muscle, we theoretically demonstrate that Voronoi tessellations often provide an accurate representation of the regions supplied by each capillary. However, we highlight that this use of Voronoi tessellations is inappropriate and inaccurate in the presence of extensive capillary rarefaction and pathological variations in oxygen tension of different capillaries. In such cases, oxygen flux trapping regions are developed to provide a more general representation of the capillary supply regions, in particular incorporating the additional influences of heterogeneity that are absent in the consideration of Voronoi tessellations.     

Effects of Fiber Type and Size on the Heterogeneity of Oxygen Distribution in Exercising Skeletal Muscle

The process of oxygen delivery from capillary to muscle fiber is essential for a tissue with variable oxygen demand, such as skeletal muscle. Oxygen distribution in exercising skeletal muscle is regulated by convective oxygen transport in the blood vessels, oxygen diffusion and consumption in the tissue. Spatial heterogeneities in oxygen supply, such as microvascular architecture and hemodynamic variables, had been observed experimentally and their marked effects on oxygen exchange had been confirmed using mathematical models. In this study, we investigate the effects of heterogeneities in oxygen demand on tissue oxygenation distribution using a multiscale oxygen transport model. Muscles are composed of different ratios of the various fiber types. Each fiber type has characteristic values of several parameters, including fiber size, oxygen consumption, myoglobin concentration, and oxygen diffusivity. Using experimentally measured parameters for different fiber types and applying them to the rat extensor digitorum longus muscle, we evaluated the effects of heterogeneous fiber size and fiber type properties on the oxygen distribution profile. Our simulation results suggest a marked increase in spatial heterogeneity of oxygen due to fiber size distribution in a mixed muscle. Our simulations also suggest that the combined effects of fiber type properties, except size, do not contribute significantly to the tissue oxygen spatial heterogeneity. However, the incorporation of the difference in oxygen consumption rates of different fiber types alone causes higher oxygen heterogeneity compared to control cases with uniform fiber properties. In contrast, incorporating variation in other fiber type-specific properties, such as myoglobin concentration, causes little change in spatial tissue oxygenation profiles.     

Mathematical modelling of oxygen transport to tissue

 The equations governing oxygen transport from blood to tissue are presented for a cylindrical tissue compartment, with blood flowing along a co–axial cylindrical capillary inside the tissue. These governing equations take account of: (i) the non–linear reactions between oxygen and haemoglobin in blood and between oxygen and myoglobin in tissue; (ii) diffusion of oxygen in both the axial and radial directions; and (iii) convection of haemoglobin and plasma in the capillary. A non–dimensional analysis is carried out to assess some assumptions made in previous studies. It is predicted that: (i) there is a boundary layer for oxygen partial pressure but not for haemoglobin or myoglobin oxygen saturation close to the inflow boundary in the capillary; (ii) axial diffusion may not be neglected everywhere in the model; (iii) the reaction between oxygen and both haemoglobin and myoglobin may be assumed to be instantaneous in nearly all cases; and (iv) the effect of myoglobin is only significant for tissue with a low oxygen partial pressure. These predictions are validated by solving the full equations numerically and are then interpreted physically. Received: 13 October 2000 / Revised version: 12 June 2001 / Published online: 17 May 2002     

Causal Structure of Brain Physiology after Brain Injury from Subarachnoid Hemorrhage

High frequency physiologic data are routinely generated for intensive care patients. While massive amounts of data make it difficult for clinicians to extract meaningful signals, these data could provide insight into the state of critically ill patients and guide interventions. We develop uniquely customized computational methods to uncover the causal structure within systemic and brain physiologic measures recorded in a neurological intensive care unit after subarachnoid hemorrhage. While the data have many missing values, poor signal-to-noise ratio, and are composed from a heterogeneous patient population, our advanced imputation and causal inference techniques enable physiologic models to be learned for individuals. Our analyses confirm that complex physiologic relationships including demand and supply of oxygen underlie brain oxygen measurements and that mechanisms for brain swelling early after injury may differ from those that develop in a delayed fashion. These inference methods will enable wider use of ICU data to understand patient physiology.     

Computational modelling of wounded tissue subject to negative pressure wound therapy following trans-femoral amputation

Proof-of-concept computational models were developed and applied as tools to gain insights into biomechanical interactions and variations of oxygen gradients of wounded tissue subject to negative pressure wound therapy (NPWT), following trans-femoral amputation. A macro-scale finite-element model of a lower limb was first developed based on computed tomography data, and distributions of maximum and minimum principal stress values we calculated for a region of interest (ROI). Then, the obtained results were applied iteratively as new sets of boundary conditions for a specific spatial position in a capillary sub-model. Data from coupled capillary stress and mass- diffusion sub-models were transferred to the macro-scale model to map the spatial changes of tissue oxygen gradients in the ROI. The ?70 mmHg NPWT resulted in a dramatic change of a wound surface area and the greatest relative contraction was observed at ?150 mmHg. Tissue lateral to the depth of the wound cavity revealed homogenous patterns of decrease in oxygenation area and the extent of such decrease was dependent on the distance from the wound surface. However, tissue lateral to the width of the wound demonstrated heterogeneous patterns of change, as evidenced by both gradual increase and decrease in the oxygenation area. The multiscale models developed in the current study showed a significant influence of NPWT on both macro-deformations and changes of tissue oxygenation. The patterns of changes depended on the depth of the tissue, the geometry of the wound, and also the location of tissue plane.     

Homogenization modeling for the mechanics of perfused myocardium

Altered coronary perfusion can change the apparent diastolic stiffness of ventricular myocardium--the ‘garden hose’ effect. Our recent findings showed that myocardial strains are reduced during ventricular filling, primarily along the directions transverse to the coronary microvessels. In this article, we review hypotheses and theoretical models regarding the role that regional wall stress plays in the mechanical interaction between myocardium and coronary circulation. Various mechanisms have been used to explain the effects of the tissue stress on coronary flow, as well as the effect of coronary dynamics on myocardial mechanics. Many models of coronary pressure-flow relations using lumped parameter circuit analogs. Poroelasticity and swelling theories have been used to model the mechanics of perfused muscle. Here, we describe a new mathematical model of the mechanics of perfused myocardium derived using homogenization theory. In this model, perfused myocardium is treated as a nonlinear anisotropic elastic solid embedded with cylindrical vessels of known distensibility. The solid compartment is incompressible but the vascular compartment may change volume according to a simple relation between vessel diameter and perfusion pressure. The work done by the perfusion pressure in changing vascular volume contributes to the macroscopic strain energy and hence affects the stress and stiffness of the composite. Conversely, the stress in the tissue affects microvessel diameter and volume, since tractions transverse to the vessel axis oppose the internal blood pressure. Finite element simulations of passive filling show good agreement of model with experimental results.     

Bridging cell-scale simulations and radiologic images to explain short-time intratumoral oxygen fluctuations

Radiologic images provide a way to monitor tumor development and its response to therapies in a longitudinal and minimally invasive fashion. However, they operate on a macroscopic scale (average value per voxel) and are not able to capture microscopic scale (cell-level) phenomena. Nevertheless, to examine the causes of frequent fast fluctuations in tissue oxygenation, models simulating individual cells’ behavior are needed. Here, we provide a link between the average data values recorded for radiologic images and the cellular and vascular architecture of the corresponding tissues. Using hybrid agent-based modeling, we generate a set of tissue morphologies capable of reproducing oxygenation levels observed in radiologic images. We then use these in silico tissues to investigate whether oxygen fluctuations can be explained by changes in vascular oxygen supply or by modulations in cellular oxygen absorption. Our studies show that intravascular changes in oxygen supply reproduce the observed fluctuations in tissue oxygenation in all considered regions of interest. However, larger-magnitude fluctuations cannot be recreated by modifications in cellular absorption of oxygen in a biologically feasible manner. Additionally, we develop a procedure to identify plausible tissue morphologies for a given temporal series of average data from radiology images. In future applications, this approach can be used to generate a set of tissues comparable with radiology images and to simulate tumor responses to various anti-cancer treatments at the tissue-scale level.     

O2 transport in cerebral microregions (mathematical simulation)

The effects of the circulation rate in capillaries, the intensity of O2 consumption by nerve cells and the capillary network density on the O2 tension distribution in the cerebral cortex have been studied, utilizing a mathematical model simulating actual neuron-capillary relationships. The model has been written as a system of equations in partial derivatives, its solution obtained by the net-point method. Regulatory variations of the capillary circulation rate in certain cerebral microregions have been shown to ensure similar changes in oxygen supply throughout the region. A drop of the pO2 level in a cerebral microregion with a rising O2 consumption by nerve cells is shown to be due, by 75 percent, to the increase of O2 consumption and by 25 percent, to the lower pO2 in the capillaries. Conversely, an increase in pO2 in microregions resulting from a lower O2 consumption by neurons is due by 75 percent, to a pO2 rise in capillaries and by 25 percent, at the expense of an O2 consumption decrease. In cerebral regions differing in capillary network density by 20 percent, changes in the conditions for oxygen supply to tissue are due by 1/3 to pO2 variations in the capillaries and by 2/3 to alterations in the diffusion distances.     

Physiological determinants of the pulmonary filtration coefficient

Current emphasis on translational application of genetic models of lung disease has renewed interest in the measurement of the gravimetric filtration coefficient (K(f)) as a means to assess vascular permeability changes in isolated perfused lungs. The K(f) is the product of the hydraulic conductivity and the filtration surface area, and is a sensitive measure of vascular fluid permeability when the pulmonary vessels are fully recruited and perfused. We have observed a remarkable consistency of the normalized baseline K(f) values between species with widely varying body weights from mice to sheep. Uniformity of K(f) values can be attributed to the thin alveolar capillary barrier required for gas exchange and the conserved matching of lung vascular surface area to the oxygen requirements of the body mass. An allometric correlation between the total lung filtration coefficient (K(f,t)) and body weight in several species (r(2)=1.00) had a slope that was similar to those reported for alveolar and pulmonary capillary surface areas and pulmonary diffusion coefficients determined by morphometric methods in these species. A consistent K(f) is dependent on accurately separating the filtration and vascular volume components of lung weight gain, then K(f) is a consistent and repeatable index of lung vascular permeability.