Hermitian splines for modeling biological soft tissue systems that exhibit nonlinear force-elongation curves

Numerical simulation of soft tissue mechanical properties is a critical step in developing valuable biomechanical models of live organisms. A cubic Hermitian spline optimization routine is proposed in this paper to model nonlinear experimental force-elongation curves of soft tissues, in particular when modeled as lumped elements. Boundary conditions are introduced to account for the positive definiteness and the particular curvature of the experimental curve to be fitted. The constrained least-square routine minimizes user intervention and optimizes fitting of the experimental data across the whole fitting range. The routine provides coefficients of a Hermitian spline or corresponding knots that are compatible with a number of constraints that are suitable for modeling soft tissue tensile curves. These coefficients or knots may become inputs to user-defined component properties of various modeling software. Splines are particularly advantageous over the well-known exponential model to account for the traction curve flatness at low elongations and to allow for more flexibility in the fitting process. This is desirable as soft tissue models begin to include more complex physical phenomena.     

Critical tissue concentrations of potentially toxic elements

Summary Tissue concentrations of young plants, or of young leaves, of crop plants or species used as test plants offer some promise as simple and approximate indicators of toxic levels of elemental pollution of the soil environment.Theupper critical level of an element is the lowest tissue concentration at which it has toxic effects. The results of an extensive survey to extract critical levels from published work are presented for 29 elements.     

Mechanical characteristics of biological soft tissue]

In a detailed study mechanical properties of tendons, muscles, nerves, blood-vessels and skin of just slaughtered pigs have been investigated in nearly stationary stress tests. Tensile tests have produced tensile strength, ultimate stress and their appropriate strains, Young's modulus and the work up to fatigue of samples. In hysteresis tests the deformation work has been determined as a function of numbers of stress cycles. The hysteresis decrease with the number of stress cycles and approaches asymptotically to cero. By preconditioning of tendons, nerves and blood-vessels to steady state significant differences of strain at tensile strength and of Young's modulus have been established. Moreover for nerves the tests have revealed significant deviations of tensile strength. Bruise tests have been carried out with muscle tissue. For the described setup the limit force can be specified, at which pathological changes appear. Subsequently conducted histological investigations have demonstrated this. In dynamical bruise tests there appeared no pathological changes in muscle tissue in spite of higher transmitted energy.     

Finite element analysis of biological soft tissue surrounded by a deformable membrane that controls transmembrane flow

Background

Many biological soft tissues are hydrated porous hyperelastic materials, which consist of a complex solid skeleton with fine voids and fluid filling these voids. Mechanical interactions between the solid and the fluid in hydrated porous tissues have been analyzed by finite element methods (FEMs) in which the mixture theory was introduced in various ways. Although most of the tissues are surrounded by deformable membranes that control transmembrane flows, the boundaries of the tissues have been treated as rigid and/or freely permeable in these studies. The purpose of this study was to develop a method for the analysis of hydrated porous hyperelastic tissues surrounded by deformable membranes that control transmembrane flows.

Results

For this, we developed a new nonlinear finite element formulation of the mixture theory, where the nodal unknowns were the pore water pressure and solid displacement. This method allows the control of the fluid flow rate across the membrane using Neumann boundary condition. Using the method, we conducted a compression test of the hydrated porous hyperelastic tissue, which was surrounded by a flaccid impermeable membrane, and a part of the top surface of this tissue was pushed by a platen. The simulation results showed a stress relaxation phenomenon, resulting from the interaction between the elastic deformation of the tissue, pore water pressure gradient, and the movement of fluid. The results also showed that the fluid trapped by the impermeable membrane led to the swelling of the tissue around the platen.

Conclusions

These facts suggest that our new method can be effectively used for the analysis of a large deformation of hydrated porous hyperelastic material surrounded by a deformable membrane that controls transmembrane flow, and further investigations may allow more realistic analyses of the biological soft tissues, such as brain edema, brain trauma, the flow of blood and lymph in capillaries and pitting edema.

     

Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review

Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.     

Comparison of models for flow induced deformation of soft biological tissue

The behaviour of a deformable porous medium during the flow of fluid under a pressure difference is examined for both infinitesimal and finite deformations. Models for both cases are solved for the problem of steady one-dimensional compression and compared with experimental data from Parker et al. (J. appl. Mech. 54, 794-800, 1987) for a polyurethane sponge. The purpose of this study is to identify a simple model which agrees qualitatively with these published results. To relate the stress relations for biological tissues to the data for polymer sponges (Parker et al., 1987) a translation of 1.1 kPa was introduced. This allows for some structural differences between the two media. It was found that the infinitesimal models were adequate up to 20% strain, but significant divergence occurred for higher strains. A finite deformation model with the permeability depending exponentially on the strain gave the most consistent results and required the fitting of only two parameters.     

Biorheological features of some soft tissues under a surgical tissue expansion procedure

The aim of this study was to investigate the effects of a surgical tissue expansion procedure on the biomechanical features of the expanded soft tissues. In this procedure a silicone balloon “expander” is surgically inserted into a tissue and inflated. The tissue mass increases under the stretch of the expander. The increased tissue can then be used as an autologous source for the surgical reconstruction of organs. In this article, dog saphenous neurovascular bundle was used. Expanded saphenous nerves, arteries and veins were harvested and their biomechanical features and ultrastructural, histological changes were studied. The stress relaxation features, the continuous spectrum of relaxation time, and the stress-strain relationship of expanded and control specimens were measured. Results show that within two or three weeks after placement of the expanders, the biomechanical properties of expanded saphenous nerves, arteries and veins began to deviate from those of their controls, and the differences between them were proportional to the volume of inflation; but when the expanding period was 15 weeks or longer, the properties of expanded specimens and their controls became close again. Histological study showed that the content of collagenous fibers in blood vessel walls decreased after expansion. The content of elastic fibers in blood vessel walls first increased, then returned to normal, and finally decreased. Ultrastructural studies showed that when elongated by 25–40%, the expanded nerves had well preserved axons and showed fewer smooth myelin sheaths only in the middle and distal part of the expansion.     

Novel mass spectrometry imaging software assisting labeled normalization and quantitation of drugs and neuropeptides directly in tissue sections

MALDI MS imaging has been extensively used to produce qualitative distribution maps of proteins, peptides, lipids, small molecule pharmaceuticals and their metabolites directly in biological tissue sections. There is growing demand to quantify the amount of target compounds in the tissue sections of different organs. We present a novel MS imaging software including protocol for the quantitation of drugs, and for the first time, an endogenous neuropeptide directly in tissue sections. After selecting regions of interest on the tissue section, data is read and processed by the software using several available methods for baseline corrections, subtractions, denoising, smoothing, recalibration and normalization. The concentrations of in vivo administered drugs or endogenous compounds are then determined semi-automatically using either external standard curves, or by using labeled compounds, i.e., isotope labeled analogs as standards. As model systems, we have quantified the distribution of imipramine and tiotropium in the brain and lung of dosed rats. Substance P was quantified in different mouse brain structures, which correlated well with previously reported peptide levels. Our approach facilitates quantitative data processing and labeled standards provide better reproducibility and may be considered as an efficient tool to quantify drugs and endogenous compounds in tissue regions of interest.     

Designing polyHEMA substrates that mimic the viscoelastic response of soft tissue

Matching the mechanical properties of a biomaterial to soft tissue is often overlooked despite the fact that it is well known that cells respond to and are capable of changing their mechanical environment. In this paper, we used NaCl and alginate beads as porogens to make a series of micro- and macro-porous pHEMA substrates (poly(2-hydroxyethly methacrylate)) and quantified their mechanical behavior under low-magnitude shear loads over physiologically relevant frequencies. Using a stress-controlled rheometer, we performed isothermal (37°C) frequency response experiments between 0.628 and 75.4rad/s (0.01-12Hz) at 0.1% strain. Both micro- and macro-porous pHEMA substrates were predominately elastic in nature with a narrow range of G' and G″ values that mimicked the response of human skin. The magnitude of the G' and G″ values of the macro-porous substrates were designed to closely match human skin. To determine how cell growth might alter their mechanical properties, pHEMA substrates were functionalized and human skin fibroblasts grown on them for fourteen days. As a result of cell growth, the magnitude of G' and G″ increased at low frequencies while also altering the degree of high frequency dependence, indicating that cellular interactions with the micro-pore infrastructure has a profound effect on the viscoelastic behavior of the substrates. These data could be fit to a mathematical model describing a soft-solid. A quantitative understanding of the mechanical behavior of biomaterials in regimes that are physiologically relevant and how these mechanics may change after implantation may aid in the design of new materials.     

Microprobe analysis and fine structure of mitochondrial granules in ultrathin frozen sections of rat pancreas

High resolution electron microscopy and microprobe analysis studies on untreated frozen sections of normal pancreas reveal a distinct appearance of mitochondrial granules. These granules have been shown to contain a significant amount of calcium and potassium. Based upon these findings, it is proposed that normal mitochondrial granules represent special sites for cation storage and release since these structures are quite labile in contrast to the abnormal accumulation of divalent cations in loading experiments.     

Fluorescence microscopy procedure for quantitation of yeasts in beverages

Existing methods for quantitating yeasts in beverages include time-consuming plate counts that detect only living cells and hemacytometer counts that are reliable only at very high concentrations (e.g., 10(6) to 20 X 10(6) cells per ml). The new method described here involves the use of fluorescence microscopy with the fluorescent stain aniline blue to differentiate yeasts (and other fungi) from backgrounds for easy counting and also may be used in conjunction with membrane filtration to concentrate yeasts from liquids before cell enumeration. Recoveries averaged 91.5% for beverages spiked with levels of 500 to 600,000 organisms per ml. The correlation coefficient of count to spike level was 0.996.     

Segmentation of scenes in tissue sections

The segmentation of scenes of fixed tissue sections for quantitative histopathology is the crucial step for further image processing. Different segmentation methods for the separation of nuclei, nucleoli and whole cells in methacrylate-embedded sections of rat liver were investigated. Reasonable segmentation results were obtained using a contrast-enhanced polar-coordinate transformation to distinguish nuclei, a compactness algorithm to distinguish nucleoli and a skeletonization algorithm to delineate cells when a priori information on the morphometric and photometric properties of the liver tissue was included.     

Masking of epitopes in tissue sections

Summary Antisera to chicken brain antigen (CBA) isolated by hydroxyapatite chromatography from 8 M urea extracts following repeated extractions with phosphate buffer selectively decorate neurofilaments (NF) in neuronal perikarya, dendrites and axons. The antisera also reacted with GFA protein, the astrocyte-specific intermediate filament protein, as indicated by the adsorption of NF immunoreactivity following passage of the antisera through columns prepared with purified GFA protein. Moreover, the antisera stained the polypeptides of the NF triplet (70 kd, 150 kd, 200 kd) and GFA protein by the immunoblotting procedure. Monoclonal antibodies selectively decorating NF in tissue sections were isolated from a fusion of mouse myeloma cells with spleen cells of mice immunized with CBA. By the immunoblotting procedure the antibodies decorated the 150 kd NF polypeptide and GFA protein. No staining of glial filaments or any other structure on tissue sections was also observed with antibodies derived from another fusion strongly reacting with GFA protein on immunoblots. All antibodies (monoclonal and polyclonal) appeared to react with the same region of the GFA polypeptide as indicated by immunoblots of cleavage products.     

Taurine and zoo felids: considerations of dietary and biological tissue concentrations

Taurine (TAU) is an essential amino acid required in the diets of Felidae at concentrations ranging between 0.04 and 0.2% on a dry matter (DM) basis (in purified, highly digestible diets, and canned diets, respectively). Although the domestic cat seems to be an appropriate physiologic model for zoo felids, it is sometimes difficult to assess TAU status in zoo feeding programs owing to scattered information on feed ingredient TAU content as well as a lack of normal ranges for assessment of TAU in biological tissues. Knowing that TAU is required in the formulation of hand‐rearing diets for exotic felids, the TAU content of 38 ingredients or products used in zoo carnivore feeding or hand‐rearing programs was summarized, including 21 new feedstuffs for which TAU data were previously lacking. The kitten milk replacer contained a lower than expected value for TAU. Commercially prepared frozen or canned meat products, seafood products, whole rodent prey, and most strained meat jarred baby foods contained adequate TAU; chunk meats, and some specific types of jarred baby food meats were considerably lower in TAU content (≤0.10% DM) than other foodstuffs. TAU concentrations in plasma and whole blood of eight spp. of zoo felids sampled opportunistically fell within reference ranges for domestic cats (80–120 and 300–600 nmol/ml in plasma and whole blood, respectively). Plasma concentrations are a useful measure of dietary impact, whereas whole blood concentrations seem to reflect tissue storage of this nutrient. Zoo Biol 26:517–531, 2007. © 2007 Wiley‐Liss, Inc.