Modeling capsule tissue growth around disk-shaped implants: a numerical and in vivo study

We propose a new mathematical model that describes the growth of fibrous tissue around rigid, disk-shaped implants. A solution methodology based on an efficient regularized iterative method is presented to calibrate the model from some measurements of the capsule tissue concentration. Numerical results obtained with synthetic data are presented to demonstrate the ability of the proposed solution methodology to determine the model parameters corresponding to a given implant. In addition, numerical results obtained with experimental data are presented to illustrate the validity of the proposed model.     

Long-term biocompatibility of NanoGATE drug delivery implant

The fouling of components and the formation of a fibrotic tissue capsule around subcutaneously implanted medical devices are two major obstacles in developing viable, long-term implantable drug delivery systems. NanoGATE is a subcutaneous implant designed for constant-output passive diffusion of a drug of interest through a silicon nanopore membrane. To this end, we have investigated the long-term in vivo biocompatibility of the NanoGATE implant in terms of the fouling of the nanopore membrane and the formation of a fibrotic tissue capsule around the implant. We have also evaluated how these effects influence diffusion of a lysozyme surrogate from the device once implanted within the vascular compartment of a Sprague-Dawley rat model. Using several model biomolecules such as glucose, lysozyme, and albumin, our studies suggest that silicon nanopore membranes do not foul when implanted subcutaneously for 6 mo. This study also reveals the tissue capsule that naturally forms around the implant does not limit diffusion of molecules with molecular weights on the order of 14.4 kDa at therapeutic delivery rates of tens of micrograms per day. This indicates that our NanoGATE implant should be completely functional in vivo, providing constant release levels of a drug over an extended time period. Thus, by adjusting the release rate to fit the pharmacokinetic clearance profile of the Sprague-Dawley rat, long-term steady-state blood plasma concentrations can be achieved.     

Study of encapsulation of silicone rubber implants in animals. A foreign-body reaction.

It has long been known that the formation of a fibrous capsule around an implant is a general phenomenon in nature, an inevitable result of the tissue defense mechanism called the foreign body reaction. We have investigated this reaction in animals and find it consists of a series of interrelated processes in which the final result may vary, depending on the susceptibility of the foreign material to phagocytosis, incorporation by giant cells, or isolation by fibrosis. This susceptibility depends, in turn, on the physical and chemical properties of the implant. The process of capsule formation, as well as the structure of the final capsule, is similar in animal models and in humans--so that investigations of human encapsulation may be done in animals. The cause of abnormal induration around human breast implants is still unknown, and the question of whether normal induration in the animal model can be used to elucidate abnormal clinical induration depends on further investigation of both phenomena.     

Histological Evaluation of the Biocompatibility of Polyurea Crosslinked Silica Aerogel Implants in a Rat Model: A Pilot Study

Background

Aerogels are a versatile group of nanostructured/nanoporous materials with physical and chemical properties that can be adjusted to suit the application of interest. In terms of biomedical applications, aerogels are particularly suitable for implants such as membranes, tissue growth scaffolds, and nerve regeneration and guidance inserts. The mesoporous nature of aerogels can also be used for diffusion based release of drugs that are loaded during the drying stage of the material. From the variety of aerogels polyurea crosslinked silica aerogels have the most potential for future biomedical applications and are explored here.

Methodology

This study assessed the short and long term biocompatibility of polyurea crosslinked silica aerogel implants in a Sprague-Dawley rat model. Implants were inserted at two different locations a) subcutaneously (SC), at the dorsum and b) intramuscularly (IM), between the gluteus maximus and biceps femoris of the left hind extremity. Nearby muscle and other internal organs were evaluated histologically for inflammation, tissue damage, fibrosis and movement (travel) of implant.

Conclusion/Significance

In general polyurea crosslinked silica aerogel (PCSA) was well tolerated as a subcutaneous and an intramuscular implant in the Sprague-Dawley rat with a maximum incubation time of twenty months. In some cases a thin fibrous capsule surrounded the aerogel implant and was interpreted as a normal response to foreign material. No noticeable toxicity was found in the tissues surrounding the implants nor in distant organs. Comparison was made with control rats without any implants inserted, and animals with suture material present. No obvious or noticeable changes were sustained by the implants at either location. Careful necropsy and tissue histology showed age-related changes only. An effective sterilization technique for PCSA implants as well as staining and sectioning protocol has been established. These studies further support the notion that silica-based aerogels could be useful as biomaterials.     

TGF-β1 Expression in Chromophobe Renal Cell Carcinoma and Renal Oncocytoma

Distinguishing renal oncocytoma (RO) from the eosinophilic variant of chromophobe renal cell carcinoma (ChRCC) under the light microscope is a common diagnostic problem. Our recent research has shown significant difference between the presence of tumor fibrous capsule in ChRCCs and ROs. Transforming growth factor beta 1 (TGF-β1) is a potent cytokine involved in regulating a number of cellular processes. Two main purposes of this research were to investigate whether the TGF-β1 staining could be related to the presence of tumor fibrous capsule and if it could be used in the differential diagnosis between ChRCC and RO. We investigated 34 cases: 16 ChRCCs (8 eosinophilic and 8 classic) and 18 ROs. All available slides of each tumor, routinely stained with hematoxylin and eosin (H&E) were first analyzed to note the presence of tumor fibrous capsule. One paraffin embedded tissue block matching the representative H&E slide was selected for the immunohistochemical analysis. TGF-β1 expression was analyzed semiquantitatively in the tumor tissue, the tumor fibrous capsule, if present and the peritumoral renal parenchyma. Intensity of TGF-β1 expression was weaker in ChRCCs than the one observed in ROs (P<0.05). The type of reaction in ChRCCs was predominantly membranous unlike in ROs, which exhibited a predominantly cytoplasmic reaction (P<0.05). Moreover, none of the ROs showed membranous type of reaction for TGF-β1. In the group of ChRCCs, tumors with capsule had statistically significant higher quantity of TGF-β1 expression in tumor tissue and in peritumoral renal parenchyma compared to the tumors without capsule (P<0.05). Our results showed different types of TGF-β1 expression in ChRCCs and ROs: ChRCCs had predominantly membranous type of reaction, and ROs predominantly cytoplasmic. Furthermore, ChRCCs with capsule had statistically significant higher quantity of TGF-β1 expression in tumor tissue and in peritumoral renal parenchyma compared to the tumors without capsule. Based on these findings we can speculate that it could be possible that TGF-β1 plays a role in the formation of fibrous capsule in ChRCCs.Key words: capsule, chromophobe renal cell carcinoma, renal oncocytoma, TGF-β1     

An introduction to the mathematical structure of the Wright–Fisher model of population genetics

In this paper, we develop the mathematical structure of the Wright–Fisher model for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size in its simplest form, that is, without mutation or selection. We establish a new concept of a global solution for the diffusion approximation (Fokker–Planck equation), prove its existence and uniqueness and then show how one can easily derive all the essential properties of this random genetic drift process from our solution. Thus, our solution turns out to be superior to the local solution constructed by Kimura.     

Game Dynamic Model for Yeast Development

Game theoretic models, along with replicator equations, have been applied successfully to the study of evolution of populations of competing species, including the growth of a population, the reaching of the population to an equilibrium state, and the evolutionary stability of the state. In this paper, we analyze a game model proposed by Gore et al. (Nature 456:253-256, 2009) in their recent study on the co-development of two mixed yeast strains. We examine the mathematical properties of this model with varying experimental parameters. We simulate the growths of the yeast strains and compare them with the experimental results. We also compute and analyze the equilibrium state of the system and prove that it is asymptotically and evolutionarily stable.     

Periodic solutions: a robust numerical method for an S-I-R model of epidemics

 We describe and analyze a numerical method for an S-I-R type epidemic model. We prove that it is unconditionally convergent and that solutions it produces share many qualitative and quantitative properties of the solution of the differential problem being approximated. Finally, we establish explicit sufficient conditions for the unique endemic steady state of the system to be unstable and we use our numerical algorithm to approximate the solution in such cases and discover that it can be periodic, just as suggested by the instability of the endemic steady state. Received: 1 September 1995 / Revised version: 30 April 1997     

Cells,growth factors and bioactive surface properties in a mechanobiological model of implant healing

Interface conditions are of prime importance for implant fixation in the early post-operative period and modelling of specific biochemical interactions at implant surface is still missing. We hypothesized that updating osteoblast adhesion properties and growth factor source in an active zone located at the implant surface was relevant to model biochemical interactions of implant with its environment. We proposed an innovative set of diffusive–convective–reactive equations which relevant parameters were the cell decay factor, the cell motility and the growth factor balance.Initial comparison with histomorphometic results from a stable PMMA canine implant model provided an encouraging base to implement a numerical sensitivity analysis to evaluate the role of three types of bioactive surfaces: acid-etched titanium, coarse grit-blasted acid-etched titanium and coarse grit-blasted acid-etched titanium with RGDS peptide. We found that cell diffusion decrease (acid-etched+RGDS peptide vs. PMMA), and increase of local growth factor fraction (PMMA vs. acid-etched+RGDS peptide), significantly improved the amount of mineralized tissue on the implant surface. When the variation of structural fraction to cell motility and growth factor synthesis was investigated, an envelope pattern with an optimum was obtained but this could be exceeded for strong surface modifications and/or for high growth factor concentrations. The model also confirmed that implant bioactive properties should play a limited role to reduce heterogeneity of new-formed tissue. In conclusion, we suggested that our innovative theoretical approach was relevant to investigate implant fixation and could potentially help in reduction of implant revision.     

Preparation and biocompatibility of novel UV-curable chitosan derivatives

UV-curable chitosans (UVCC-7-10) were synthesized using less-toxic agents. The UVCC-7 was completely cured by UV spot irradiation for 4 s. The UVCC-7 was implanted into murine subcutaneous tissues, and the response to the implantation was observed by histological examination at 7 days after implantation. In the histological findings, the implant was surrounded by thin fibrous granulating tissue with no inflammatory cellular infiltration. Fibroblasts infiltrate between the cured implant. The novel synthesized UVCC-7 showed good biocompatibility.     

Inferring spatial variations of microstructural properties from macroscopic mechanical response

Disease alters tissue microstructure, which in turn affects the macroscopic mechanical properties of tissue. In elasticity imaging, the macroscopic response is measured and is used to infer the spatial distribution of the elastic constitutive parameters. When an empirical constitutive model is used, these parameters cannot be linked to the microstructure. However, when the constitutive model is derived from a microstructural representation of the material, it allows for the possibility of inferring the local averages of the spatial distribution of the microstructural parameters. This idea forms the basis of this study. In particular, we first derive a constitutive model by homogenizing the mechanical response of a network of elastic, tortuous fibers. Thereafter, we use this model in an inverse problem to determine the spatial distribution of the microstructural parameters. We solve the inverse problem as a constrained minimization problem and develop efficient methods for solving it. We apply these methods to displacement fields obtained by deforming gelatin–agar co-gels and determine the spatial distribution of agar concentration and fiber tortuosity, thereby demonstrating that it is possible to image local averages of microstructural parameters from macroscopic measurements of deformation.     

Effects of fibrin on the integration hydroxyapatite coating implants: experimental study in a rabbit model

The purpose of this study was to investigate the effects of the addition of fibrin (SAF) to titanium alloy implants coated with hydroxyapatite (HAP) on osteogenesis in rabbits. A titanium (Ti) alloy implant was inserted into the femoral neck of twenty-four adult rabbits. Six rabbits were included on each of the following groups: Ti control, HAP-coated Ti module, HAP-coated Ti module with added fibrin glue and Ti module also with added fibrin glue. After seven weeks, bone growth was examined radiographically and by histo-morphometry. The SAF/HAP mixture did caused to a significant increase in bone growth compared to the other groups. The addition of fibrin did not result in an increase in new-bone growth and increase the formation of fibrous tissue in contact with the implant. We concluded that SAF did not demonstrate osteoinductive properties.     

Biocompatibility of a physiological pressure sensor

A newly developed fiber optic micropressure sensor was evaluated for biocompatibility using the International Organization for Standardization (ISO) test standard 10993-6. The test material and an inert control (fused silica glass) were tested in New Zealand white rabbits. Four test specimens were implanted in the paravertebral muscles on one side of the spine about 2-5 cm from the mid-line and parallel to the spinal column. Similarly, four control specimens were implanted on the opposite side. The implantation periods were 1, 4, and 12 weeks to ensure a steady state biological tissue response. Four animals were tested at each time period. Macroscopic and microscopic observations were performed to compare the biological reactions between the test and control materials. There was an inflammatory reaction at 1 week which subsided at 4 weeks. There was fibrous tissue growth near the implant that also decreased over time. Most importantly, there was no significant difference in the biological response between the test and control materials. Therefore, we conclude that the pressure microsensor is biocompatible.     

Stability analysis for a peri-implant osseointegration model

We investigate stability of the solution of a set of partial differential equations, which is used to model a peri-implant osseointegration process. For certain parameter values, the solution has a ‘wave-like’ profile, which appears in the distribution of osteogenic cells, osteoblasts, growth factor and bone matrix. This ‘wave-like’ profile contradicts experimental observations. In our study we investigate the conditions, under which such profile appears in the solution. Those conditions are determined in terms of model parameters, by means of linear stability analysis, carried out at one of the constant solutions of the simplified system. The stability analysis was carried out for the reduced system of PDE’s, of which we prove, that it is equivalent to the original system of equations, with respect to the stability properties of constant solutions. The conclusions, derived from the linear stability analysis, are extended for the case of large perturbations. If the constant solution is unstable, then the solution of the system never converges to this constant solution. The analytical results are validated with finite element simulations. The simulations show, that stability of the constant solution could determine the behavior of the solution of the whole system, if certain initial conditions are considered.     

Action Potential Duration Heterogeneity of Cardiac Tissue Can Be Evaluated from Cell Properties Using Gaussian Green's Function Approach

Action potential duration (APD) heterogeneity of cardiac tissue is one of the most important factors underlying initiation of deadly cardiac arrhythmias. In many cases such heterogeneity can be measured at tissue level only, while it originates from differences between the individual cardiac cells. The extent of heterogeneity at tissue and single cell level can differ substantially and in many cases it is important to know the relation between them. Here we study effects from cell coupling on APD heterogeneity in cardiac tissue in numerical simulations using the ionic TP06 model for human cardiac tissue. We show that the effect of cell coupling on APD heterogeneity can be described mathematically using a Gaussian Green''s function approach. This relates the problem of electrotonic interactions to a wide range of classical problems in physics, chemistry and biology, for which robust methods exist. We show that, both for determining effects of tissue heterogeneity from cell heterogeneity (forward problem) as well as for determining cell properties from tissue level measurements (inverse problem), this approach is promising. We illustrate the solution of the forward and inverse problem on several examples of 1D and 2D systems.     

Ameboid cell motility: a model and inverse problem, with an application to live cell imaging data

In this article a mathematical model for ameboid cell movement is developed using a spring-dashpot system with Newtonian dynamics. The model is based on the facts that the cytoskeleton plays a primary role for cell motility and that the cytoplasm is viscoelastic. Based on the model, the inverse problem can be posed: if a structure like a spring-dashpot system is embedded into the living cell, what kind of characteristic properties must the structure have in order to reproduce a given movement of the cell? This inverse problem is the primary topic of this paper. On one side the model mimics some features of the movement, and on the other side, the solution to the inverse problem provides model parameters that give some insight, principally into the mechanical aspect, but also, through qualitative reasoning, into chemical and biophysical aspects of the cell. Moreover, this analysis can be done locally or globally and in different media by using the simplest possible information: positions of the cell and nuclear membranes. It is shown that the model and solution to the inverse problem for simulated data sets are highly accurate. An application to a set of live cell imaging data obtained from random movements of a human brain tumor cell (U87-MG human glioblastoma cell line) then provides an example of the efficiency of the model, through the solution of its inverse problem, as a way of understanding experimental data.     

An inverse method for predicting tissue-level mechanics from cellular mechanical input

Extracellular matrix (ECM) provides a dynamic three-dimensional structure which translates mechanical stimuli to cells. This local mechanical stimulation may direct biological function including tissue development. Theories describing the role of mechanical regulators hypothesize the cellular response to variations in the external mechanical forces on the ECM. The exact ECM mechanical stimulation required to generate a specific pattern of localized cellular displacement is still unknown. The cell to tissue inverse problem offers an alternative approach to clarify this relationship. Developed for structural dynamics, the inverse dynamics problem translates measurements of local state variables (at the cell level) into an unknown or desired forcing function (at the tissue or ECM level). This paper describes the use of eigenvalues (resonant frequencies), eigenvectors (mode shapes), and dynamic programming to reduce the mathematical order of a simplified cell–tissue system and estimate the ECM mechanical stimulation required for a specified cellular mechanical environment. Finite element and inverse numerical analyses were performed on a simple two-dimensional model to ascertain the effects of weighting parameters and a reduction of analytical modes leading toward a solution. Simulation results indicate that the reduced number of mechanical modes (from 30 to 14 to 7) can adequately reproduce an unknown force time history on an ECM boundary. A representative comparison between cell to tissue (inverse) and tissue to cell (boundary value) modeling illustrates the multiscale applicability of the inverse model.     

Stability analysis of a continuum-based constrained mixture model for vascular growth and remodeling

A stabilizing criterion is derived for equations governing vascular growth and remodeling. We start from the integral state equations of the continuum-based constrained mixture theory of vascular growth and remodeling and obtain a system of time-delayed differential equations describing vascular growth. By employing an exponential form of the constituent survival function, the delayed differential equations can be reduced to a nonlinear ODE system. We demonstrate the degeneracy of the linearized system about the homeostatic state, which is a fundamental cause of the neutral stability observations reported in prior studies. Due to this degeneracy, stability conclusions for the original nonlinear system cannot be directly inferred. To resolve this problem, a sub-system is constructed by recognizing a linear relation between two states. Subsequently, Lyapunov’s indirect method is used to connect stability properties between the linearized system and the original nonlinear system, to rigorously establish the neutral stability properties of the original system. In particular, this analysis leads to a stability criterion for vascular expansion in terms of growth and remodeling kinetic parameters, geometric quantities and material properties. Numerical simulations were conducted to evaluate the theoretical stability criterion under broader conditions, as well as study the influence of key parameters and physical factors on growth properties. The theoretical results are also compared with prior numerical and experimental findings in the literature.     

光学成像中兼具光学和力学性质的生物组织仿体

在生物医学光学成像方法的研发、评估和使用中,需要用到在较长时间内具有稳定的光学及力学属性的生物组织仿体,以使光学成像实验可以重复进行。这些仿体一般由混有散射、吸收粒子的基质制成。常用散射粒子包括脂质微粒、聚合物微球、金属氧化物粉末和金纳米粒子等,吸收粒子(及其溶液)包括血液、印度墨水(Indian Ink)和分子染料等。常用来模拟组织特性的基质包括硅胶、纤维蛋白和聚乙烯醇凝胶(Polyvinyl alcohol cryogel,PVA-C)等。讨论和分析常见仿体的光学性质(吸收系数、散射系数、折射率)和力学性质(弹性和粘弹性)。从生物相容性、制备难易程度及耗时情况、稳定性等方面比较了几种常见散射粒子、吸收粒子和基质的优缺点,并据此总结其适用范围。最后对仿体研究的发展进行了展望。