Diffusion model to describe osteogenesis within a porous titanium scaffold

In this study, we develop a two-dimensional finite element model, which is derived from an animal experiment and allows simulating osteogenesis within a porous titanium scaffold implanted in ewe's hemi-mandible during 12 weeks. The cell activity is described through diffusion equations and regulated by the stress state of the structure. We compare our model to (i) histological observations and (ii) experimental data obtained from a mechanical test done on sacrificed animal. We show that our mechano-biological approach provides consistent numerical results and constitutes a useful tool to predict osteogenesis pattern.     

An immersed boundary method for simulating a single axisymmetric cell growth and division

For an animal cell, cytokinesis is the process by which a cell divides its cytoplasm to produce two daughter cells. We propose a new mathematical model for simulating cytokinesis. The proposed model is robust and realistic in deciding the position of the cleavage furrow and in defining the contractile force leading to cell division. We use an immersed boundary method to track the morphology of cell membrane during cytokinesis. For accurate calculation, we adaptively add and delete the immersed boundary points. We perform numerical simulations on the axisymmetric domain to have sufficient resolution and to incorporate three-dimensional effects such as anisotropic surface tension. Finally, we investigate the effects of each model parameter and compare a numerical result with the experimental data to demonstrate the efficiency and accuracy of our proposed method.     

Estimation of the rate and effect of new beneficial mutations in asexual populations

The rate and effect of available beneficial mutations are key parameters in determining how a population adapts to a new environment. However, these parameters are poorly known, in large part because of the difficulty of designing and interpreting experiments to examine the rare and intrinsically stochastic process of mutation occurrence. We present a new approach to estimate the rate and selective advantage of beneficial mutations that underlie the adaptation of asexual populations. We base our approach on the analysis of experiments that track the effect of newly arising beneficial mutations on the dynamics of a neutral marker in evolving bacterial populations and develop efficient estimators of mutation rate and selective advantage. Using extensive simulations, we evaluate the accuracy of our estimators and conclude that they are quite robust to the use of relatively low experimental replication. To validate the predictions of our model, we compare theoretical and experimentally determined estimates of the selective advantage of the first beneficial mutation to fix in a series of ten replicate populations. We find that our theoretical predictions are not significantly different from experimentally determined selection coefficients. Application of our method to suitably designed experiments will allow estimation of how population evolvability depends on demographic and initial fitness parameters.     

Tracking collective cell motion by topological data analysis

By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments in the literature, the spreading test exhibits formation of fingers in the moving interfaces, there appear swirls in the velocity field, and the polar order parameter and the correlation and swirl lengths increase with time. Numerical simulations show that cells inside the tissue have smaller area than those at the interface, which has been observed in recent experiments. In the antagonistic migration assay, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce the experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to results of our numerical simulations. We use time series of data generated by numerical simulations to automatically group, track and classify the advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These techniques of topological data analysis are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.     

Modeling DNA shuffling.

In vitro evolution is a new, important laboratory method to evolve molecules with desired properties. It has been used in a variety of biological studies and drug development. In this paper, we study one important mutagenesis method used in in vitro evolution experiments called DNA shuffling. We construct a mathematical model for DNA shuffling and study the properties of molecules after DNA shuffling experiments based on this model. The model for DNA shuffling consists of two parts. First we apply the Lander-Waterman model for physical mapping by fingerprinting random clones to model the distribution of regions that can be reassembled through DNA shuffling. Then we present a model for recombination between different DNA species with different mutations. We compare our theoretical results with experimental data. Finally we propose novel applications of the theoretical results to the optimal design of DNA shuffling experiments and to physical mapping using DNA shuffling.     

Achieving elongated lesions employing cardiac cryoablation: a preclinical evaluation study

Cardiac cryoablation applied for treating cardiac arrhythmias has shown promising results after intervention, particularly for the creation of elongated lesions. A model for simulating and assessing cryoablation interventions was developed, evaluated and validated with animal experiments. We employed two simulations of different freezing outlet settings for a loop shaped cryocatheter, applying Pennes heat equation for cardiac tissue. Our experiments demonstrated that an equidistantly spaced freezing outlet distribution of 5mm led to an improved formation of lesions, i.e., elongated lesions were observed throughout the transmural cardiac volume and on the epicardial structure. A complete transmural frozen lesion was not achieved with a freezing outlet distance of 10mm. These simulation results could be experimentally verified by morphological and histological examinations. Using our simulation model we were able to optimize the intervention procedure by predicting and assessing the freezing process. This should further increase the success rate of cardiac cryoablation in clinical interventions.     

Effect of Twisted Fiber Anisotropy in Cardiac Tissue on Ablation with Pulsed Electric Fields

BackgroundAblation of cardiac tissue with pulsed electric fields is a promising alternative to current thermal ablation methods, and it critically depends on the electric field distribution in the heart.MethodsWe developed a model that incorporates the twisted anisotropy of cardiac tissue and computed the electric field distribution in the tissue. We also performed experiments in rabbit ventricles to validate our model. We find that the model agrees well with the experimentally determined ablation volume if we assume that all tissue that is exposed to a field greater than 3 kV/cm is ablated. In our numerical analysis, we considered how tissue thickness, degree of anisotropy, and electrode configuration affect the geometry of the ablated volume. We considered two electrode configurations: two parallel needles inserted into the myocardium (“penetrating needles” configuration) and one circular electrode each on epi- and endocardium, opposing each other (“epi-endo” configuration).ResultsFor thick tissues (10 mm) and moderate anisotropy ratio (a = 2), we find that the geometry of the ablated volume is almost unaffected by twisted anisotropy, i.e. it is approximately translationally symmetric from epi- to endocardium, for both electrode configurations. Higher anisotropy ratio (a = 10) leads to substantial variation in ablation width across the wall; these variations were more pronounced for the penetrating needle configuration than for the epi-endo configuration.For thinner tissues (4 mm, typical for human atria) and higher anisotropy ratio (a = 10), the epi-endo configuration yielded approximately translationally symmetric ablation volumes, while the penetrating electrodes configuration was much more sensitive to fiber twist.ConclusionsThese results suggest that the epi-endo configuration will be reliable for ablation of atrial fibrillation, independently of fiber orientation, while the penetrating electrode configuration may experience problems when the fiber orientation is not consistent across the atrial wall.     

An ultrasound elastography method to determine the local stiffness of arteries with guided circumferential waves

Arterial stiffness is highly correlated with the functions of the artery and may serve as an important diagnostic criterion for some cardiovascular diseases. To date, it remains a challenge to quantitatively assess local arterial stiffness in a non-invasive manner. To address this challenge, we investigated the possibility of determining arterial stiffness using the guided circumferential wave (GCW) induced in the arterial wall by a focused acoustic radiation force. The theoretical model for the dispersion analysis of the GCW is presented, and a finite element model has been established to calculate the dispersion curve. Our results show that under described conditions, the dispersion relations of the GCW are basically independent of the curvature of the arterial wall and can be well-described using the Lamb wave (LW) model. Based on this conclusion, an inverse method is proposed to characterize the elastic modulus of artery. Both numerical experiments and phantom experiments had been performed to validate the proposed method. We show that our method can be applied to the cases in which the artery has local stenosis and/or the geometry of the artery cross-section is irregular; therefore, this method holds great potential for clinical use.     

Prediction of the Time Course of Callus Stiffness as a Function of Mechanical Parameters in Experimental Rat Fracture Healing Studies - A Numerical Study

Numerous experimental fracture healing studies are performed on rats, in which different experimental, mechanical parameters are applied, thereby prohibiting direct comparison between each other. Numerical fracture healing simulation models are able to predict courses of fracture healing and offer support for pre-planning animal experiments and for post-hoc comparison between outcomes of different in vivo studies. The aims of this study are to adapt a pre-existing fracture healing simulation algorithm for sheep and humans to the rat, to corroborate it using the data of numerous different rat experiments, and to provide healing predictions for future rat experiments. First, material properties of different tissue types involved were adjusted by comparing experimentally measured callus stiffness to respective simulated values obtained in three finite element (FE) models. This yielded values for Young’s moduli of cortical bone, woven bone, cartilage, and connective tissue of 15,750 MPa, 1,000 MPa, 5 MPa, and 1 MPa, respectively. Next, thresholds in the underlying mechanoregulatory tissue differentiation rules were calibrated by modifying model parameters so that predicted fracture callus stiffness matched experimental data from a study that used rigid and flexible fixators. This resulted in strain thresholds at higher magnitudes than in models for sheep and humans. The resulting numerical model was then used to simulate numerous fracture healing scenarios from literature, showing a considerable mismatch in only 6 of 21 cases. Based on this corroborated model, a fit curve function was derived which predicts the increase of callus stiffness dependent on bodyweight, fixation stiffness, and fracture gap size. By mathematically predicting the time course of the healing process prior to the animal studies, the data presented in this work provides support for planning new fracture healing experiments in rats. Furthermore, it allows one to transfer and compare new in vivo findings to previously performed studies with differing mechanical parameters.     

A Fourier transform infrared microspectroscopic imaging investigation into an animal model exhibiting glioblastoma multiforme

Glioblastoma multiforme (GBM) is a highly malignant human brain tumour for which no cure is available at present. Numerous clinical studies as well as animal experiments are under way with the goal being to understand tumour biology and develop potential therapeutic approaches. C6 cell glioma in the adult rat is a frequently used and well accepted animal model for the malignant human glial tumour. By combining standard analytical methods such as histology and immunohistochemistry with Fourier Transform Infrared (FTIR) microspectroscopic imaging and multivariate statistical approaches, we are developing a novel approach to tumour diagnosis which allows us to obtain information about the structure and composition of tumour tissues that could not be obtained easily with either method alone. We have used a "Stingray" FTIR imaging spectrometer to analyse and compare the compositions of coronal brain tissue sections of a tumour-bearing animal and those from a healthy animal. We have found that the tumour tissue has a characteristic chemical signature, which distinguishes it from tumour-free brain tissue. The physical-chemical differences, determined by image and spectral comparison are consistent with changes in total protein absorbance, phosphodiester absorbance and physical dispersive artefacts. The results indicate that FTIR imaging analysis could become a valuable analytic method in brain tumour research and possibly in the diagnosis of human brain tumours.     

A Fourier transform infrared microspectroscopic imaging investigation into an animal model exhibiting glioblastoma multiforme

Glioblastoma multiforme (GBM) is a highly malignant human brain tumour for which no cure is available at present. Numerous clinical studies as well as animal experiments are under way with the goal being to understand tumour biology and develop potential therapeutic approaches. C6 cell glioma in the adult rat is a frequently used and well accepted animal model for the malignant human glial tumour. By combining standard analytical methods such as histology and immunohistochemistry with Fourier Transform Infrared (FTIR) microspectroscopic imaging and multivariate statistical approaches, we are developing a novel approach to tumour diagnosis which allows us to obtain information about the structure and composition of tumour tissues that could not be obtained easily with either method alone. We have used a “Stingray” FTIR imaging spectrometer to analyse and compare the compositions of coronal brain tissue sections of a tumour-bearing animal and those from a healthy animal. We have found that the tumour tissue has a characteristic chemical signature, which distinguishes it from tumour-free brain tissue. The physical-chemical differences, determined by image and spectral comparison are consistent with changes in total protein absorbance, phosphodiester absorbance and physical dispersive artefacts. The results indicate that FTIR imaging analysis could become a valuable analytic method in brain tumour research and possibly in the diagnosis of human brain tumours.     

The chick embryo: hatching a model for contemporary biomedical research

Animal models play a crucial role in fundamental and medical research. Progress in the fields of drug discovery, regenerative medicine and cancer research among others are heavily dependent on in vivo models to validate in vitro observations, and develop new therapeutic approaches. However, conventional rodent and large animal experiments face ethical, practical and technical issues that limit their usage. The chick embryo represents an accessible and economical in vivo model, which has long been used in developmental biology, gene expression analysis and loss/gain of function experiments. It is also an established model for tissue/cell transplantation, and because of its lack of immune system in early development, the chick embryo is increasingly recognised as a model of choice for mammalian biology with new applications for stem cell and cancer research. Here, we review novel applications of the chick embryo model, and discuss future developments of this in vivo model for biomedical research.     

An improved numerical method for strong coupling of excitation and contraction models in the heart

Quantifying the interactions between excitation and contraction is fundamental to furthering our understanding of cardiac physiology. To date simulating these effects in strongly coupled excitation and contraction tissue models has proved computationally challenging. This is in part due to the numerical methods implemented to maintain numerical stability in previous simulations, which produced computationally intensive problems. In this study, we analytically identify and quantify the velocity and length dependent sources of instability in the current established coupling method and propose a new method which addresses these issues. Specifically, we account for the length and velocity dependence of active tension within the finite deformation equations, such that the active tension is updated at each intermediate Newton iteration, within the mechanics solution step. We then demonstrate that the model is stable and converges in a three-dimensional rod under isometric contraction. Subsequently, we show that the coupling method can produce stable solutions in a cube with many of the attributes present in the heart, including asymmetrical activation, an inhomogeneous fibre field and a nonlinear constitutive law. The results show no instabilities and quantify the error introduced by discrete length updates. This validates our proposed coupling framework, demonstrating significant improvement in the stability of excitation and contraction simulations.     

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.     

Biological and artificial cognition: what can we learn about mechanisms by modelling physical cognition problems using artificial intelligence planning techniques?

Do we fully understand the structure of the problems we present to our subjects in experiments on animal cognition, and the information required to solve them? While we currently have a good understanding of the behavioural and neurobiological mechanisms underlying associative learning processes, we understand much less about the mechanisms underlying more complex forms of cognition in animals. In this study, we present a proposal for a new way of thinking about animal cognition experiments. We describe a process in which a physical cognition task domain can be decomposed into its component parts, and models constructed to represent both the causal events of the domain and the information available to the agent. We then implement a simple set of models, using the planning language MAPL within the MAPSIM simulation environment, and applying it to a puzzle tube task previously presented to orangutans. We discuss the results of the models and compare them with the results from the experiments with orangutans, describing the advantages of this approach, and the ways in which it could be extended.     

Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order

In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically.     

Development and estimation of a novel cryoprobe utilizing the Peltier effect for precise and safe cryosurgery

We have developed a novel cryoprobe for skin cryosurgery utilizing the Peltier effect. The four most important parameters for necrotizing tissue efficiently are the cooling rate, end temperature, hold time and thawing rate. In cryosurgery for small skin diseases such as flecks or early carcinoma, it is also important to control the thickness of the frozen region precisely to prevent necrotizing healthy tissue. To satisfy these exacting conditions, we have developed a novel cryoprobe to which a Peltier module was attached. The cryoprobe makes it possible to control heat transfer to skin surface precisely using a proportional-integral-derivative (PID) controller, and because it uses the Peltier effect, the cryoprobe does not need to move during the operation. We also developed a numerical simulation method that allows us to predict the frozen region and the temperature profile during cryosurgery.We tested the performance of our Peltier cryoprobe by cooling agar, and the results show that the cryoprobe has sufficient cooling performance for cryosurgery, because it can apply a cooling rate of more than 250 °C/min until the temperature reaches −40 °C. We also used a numerical simulation to reconstruct the supercooling phenomenon and examine the immediate progress of the frozen region with ice nucleation. The calculated frozen region was compared with the experimentally measured frozen region observed by an interferometer, and the calculation results showed good agreement. The results of numerical simulation confirmed that the frozen region could be predicted accurately with a margin of error as small as 150 μm during use of the cryoprobe in cryosurgery. The numerical simulation also showed that the cryoprobe can control freezing to a depth as shallow as 300 μm.     

Predicting the formation of different tissue types during Achilles tendon healing using mechanoregulated and oxygen-regulated frameworks

During Achilles tendon healing in rodents, besides the expected tendon tissue, also cartilage-, bone- and fat-like tissue features have been observed during the first twenty weeks of healing. Several studies have hypothesized that mechanical loading may play a key role in the formation of different tissue types during healing. We recently developed a computational mechanobiological framework to predict tendon tissue production, organization and mechanical properties during tendon healing. In the current study, we aimed to explore possible mechanobiological related mechanisms underlying formation of other tissue types than tendon tissue during tendon healing. To achieve this, we further developed our recent framework to predict formation of different tissue types, based on mechanobiological models established in other fields, which have earlier not been applied to study tendon healing. We explored a wide range of biophysical stimuli, i.e., principal strain, hydrostatic stress, pore pressure, octahedral shear strain, fluid flow, angiogenesis and oxygen concentration, that may promote the formation of different tissue types. The numerical framework predicted spatiotemporal formation of tendon-, cartilage-, bone- and to a lesser degree fat-like tissue throughout the first twenty weeks of healing, similar to recent experimental reports. Specific features of experimental data were captured by different biophysical stimuli. Our modeling approach showed that mechanobiology may play a role in governing the formation of different tissue types that have been experimentally observed during tendon healing. This study provides a numerical tool that can contribute to a better understanding of tendon mechanobiology during healing. Developing these tools can ultimately lead to development of better rehabilitation regimens that stimulate tendon healing and prevent unwanted formation of cartilage-, fat- and bone-like tissues.

     

Virtualisation of stress distribution in heart valve tissue

This study presents an image-based finite element analysis incorporating histological photomicrographs of heart valve tissues. We report stress fields inside heart valve tissues, where heterogeneously distributed collagen fibres are responsible for transmitting forces into cells. Linear isotropic and anisotropic tissue material property models are incorporated to quantify the overall stress distributions in heart valve tissues. By establishing an effective predictive method with new computational tools and by performing virtual experiments on the heart valve tissue photomicrographs, we clarify how stresses are transferred from matrix to cell. The results clearly reveal the roles of heterogeneously distributed collagen fibres in mitigating stress developments inside heart valve tissues. Moreover, most local peak stresses occur around cell nuclei, suggesting that higher stress may be mediated by cells for biomechanical regulations.