Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction–diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterise and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace–Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns.     

Stereoscopically observed deformations of a compliant abdominal aortic aneurysm model

A new experimental setup has been implemented to precisely measure the deformations of an entire model abdominal aortic aneurysm (AAA). This setup addresses a gap between the computational and experimental models of AAA that have aimed at improving the limited understanding of aneurysm development and rupture. The experimental validation of the deformations from computational approaches has been limited by a lack of consideration of the large and varied deformations that AAAs undergo in response to physiologic flow and pressure. To address the issue of experimentally validating these calculated deformations, a stereoscopic imaging system utilizing two cameras was constructed to measure model aneurysm displacement in response to pressurization. The three model shapes, consisting of a healthy aorta, an AAA with bifurcation, and an AAA without bifurcation, were also evaluated with computational solid mechanical modeling using finite elements to assess the impact of differences between material properties and for comparison against the experimental inflations. The device demonstrated adequate accuracy (surface points were located to within 0.07?mm) for capturing local variation while allowing the full length of the aneurysm sac to be observed at once. The experimental model AAA demonstrated realistic aneurysm behavior by having cyclic strains consistent with reported clinical observations between pressures 80 and 120?mm Hg. These strains are 1-2%, and the local spatial variations in experimental strain were less than predicted by the computational models. The three different models demonstrated that the asymmetric bifurcation creates displacement differences but not cyclic strain differences within the aneurysm sac. The technique and device captured regional variations of strain that are unobservable with diameter measures alone. It also allowed the calculation of local strain and removed rigid body motion effects on the strain calculation. The results of the computations show that an asymmetric aortic bifurcation created displacement differences but not cyclic strain differences within the aneurysm sac.     

Graded meshes in bio-thermal problems with transmission-line modeling method

In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems.     

Numerical simulation for heat transfer in prostate cancer cryosurgery

A comprehensive computational framework to simulate heat transfer during the freezing process in prostate cancer cryosurgery is presented. Tissues are treated as nonideal materials wherein phase transition occurs over a temperature range, thermophysical properties are temperature dependent and heating due to blood flow and metabolism are included. Boundary conditions were determined at the surfaces of the commercially available cryoprobes and urethral warmer by experimental study of temperature combined with a mathematical optimization process. For simulations, a suitable computational geometry was designed based on MRI imaging data of a real prostate. An enthalpy formulation-based numerical solution was performed for a prescribed surgical protocol to mimic a clinical freezing process. This computational framework allows for the individual planning of cryosurgical procedures and objective assessment of the effectiveness of prostate cryosurgery.     

Simulation of transcatheter aortic valve implantation: a patient-specific finite element approach

Until recently, heart valve failure has been treated adopting open-heart surgical techniques and cardiopulmonary bypass. However, over the last decade, minimally invasive procedures have been developed to avoid high risks associated with conventional open-chest valve replacement techniques. Such a recent and innovative procedure represents an optimal field for conducting investigations through virtual computer-based simulations: in fact, nowadays, computational engineering is widely used to unravel many problems in the biomedical field of cardiovascular mechanics and specifically, minimally invasive procedures. In this study, we investigate a balloon-expandable valve and we propose a novel simulation strategy to reproduce its implantation using computational tools. Focusing on the Edwards SAPIEN valve in particular, we simulate both stent crimping and deployment through balloon inflation. The developed procedure enabled us to obtain the entire prosthetic device virtually implanted in a patient-specific aortic root created by processing medical images; hence, it allows evaluation of postoperative prosthesis performance depending on different factors (e.g. device size and prosthesis placement site). Notably, prosthesis positioning in two different cases (distal and proximal) has been examined in terms of coaptation area, average stress on valve leaflets as well as impact on the aortic root wall. The coaptation area is significantly affected by the positioning strategy ( ? 24%, moving from the proximal to distal) as well as the stress distribution on both the leaflets (+13.5%, from proximal to distal) and the aortic wall ( ? 22%, from proximal to distal). No remarkable variations of the stress state on the stent struts have been obtained in the two investigated cases.     

In Vivo Analysis of Heterogeneous Brain Deformation Computations for Model-Updated Image Guidance

Abstract

Neurosurgical image-guidance has historically relied on the registration of the patient and preoperative imaging series with surgical instruments in the operating room (OR) coordinate space. Recent studies measuring intraoperative tissue motion have suggested that deformation-induced misregistration from surgical loading is a serious concern with such systems. In an effort to improve registration fidelity during surgery, we are pursuing an approach which uses a predictive computational model in conjunction with data available in the OR to update the high resolution preoperative image series. In previous work. we have developed an in vivo experimental system in the porcine brain which has been used to investigate a homogeneous finite element rendering of consolidation theory as a tissue deformation model. In this paper, our computational approach has been extended to include heterogeneous tissue property distributions determined from an image-to-grid segmentation scheme. Results produced under two different loading conditions show that heterogeneity in the stiffness properties and interstitial pressure gradients varied over a range of physiologically reasonable values account for 1-3% and 5-8% of the predicted tissue motion, respectively, while homogeneous linear elasticity is responsible for 60-70% of the surgically-induced motion that has been recoverable with our model-based @approach.     

Mechanics of the urethral duct: tissue constitutive formulation and structural modeling for the investigation of lumen occlusion

Urinary incontinence, often related to sphincter damage, is found in male patients, leading to a miserable quality of life and to huge costs for the healthcare system. The most effective surgical solution currently considered for men is the artificial urinary sphincter that exerts a pressure field on the urethra, occluding the duct. The evaluation of this device is currently based on clinical and surgical competences. The artificial sphincter design and mechanical action can be investigated by a biomechanical model of the urethra under occlusion, evaluating the interaction between tissues and prosthesis. A specific computational approach to urethral mechanics is here proposed, recalling the results of previous biomechanical experimental investigation. In this preliminary analysis, the horse urethra is considered, in the light of a significant correlation with human and in consideration of the relevant difficulty to get to human samples, which anyway represents the future advance. Histological data processing allow for the definition of a virtual and a subsequent finite element model of a urethral section. A specific hyperelastic formulation is developed to characterize the nonlinear mechanical behavior. The inverse analysis of tensile tests on urethra samples leads to the definition of preliminary constitutive parameters. The parameters are further refined by the computational analysis of inflation tests carried out on the entire urethral structure. The results obtained represent, in the light of the correlation reported, a valid preliminary support for the information to be assumed for prosthesis design, integrating surgical and biomechanical competences.     

Intelligent testing strategies for chemicals testing -- a case of more haste, less speed?

The prospects for using (Q)SAR modelling, read-across (chemical) and other non-animal approaches as part of integrated testing strategies for chemical risk assessment, within the framework of the EU REACH legislation, are considered. The potential advantages and limitations of (Q)SAR modelling and read-across methods for chemical regulatory risk assessment are reviewed. It is concluded that it would be premature to base a testing strategy on chemical-based computational modelling approaches, until such time as criteria to validate them for their reliability and relevance by using independent and transparent procedures, have been agreed. This is mainly because of inherent problems in validating and accepting (Q)SARs for regulatory use in ways that are analogous to those that have been developed and applied for in vitro tests. Until this issue has been resolved, it is recommended that testing strategies should be developed which comprise the integrated use of computational and read-across approaches. These should be applied in a cautious and judicious way, in association with available tissue culture methods, and in conjunction with metabolism and biokinetic studies. Such strategies should be intelligently applied by being driven by exposure information (based on bioavailability, not merely on production volume) and hazard information needs, in preference to a tick-box approach. In the meantime, there should be increased efforts to develop improved (Q)SARs, expert systems and new in vitro methods, and, in particular, ways to expedite their validation and acceptance must be found and prospectively agreed with all major stakeholders.     

Model checking for ROC regression analysis

Summary .   The receiver operating characteristic (ROC) curve is a prominent tool for characterizing the accuracy of a continuous diagnostic test. To account for factors that might influence the test accuracy, various ROC regression methods have been proposed. However, as in any regression analysis, when the assumed models do not fit the data well, these methods may render invalid and misleading results. To date, practical model-checking techniques suitable for validating existing ROC regression models are not yet available. In this article, we develop cumulative residual-based procedures to graphically and numerically assess the goodness of fit for some commonly used ROC regression models, and show how specific components of these models can be examined within this framework. We derive asymptotic null distributions for the residual processes and discuss resampling procedures to approximate these distributions in practice. We illustrate our methods with a dataset from the cystic fibrosis registry.     

Long-term follow-up of nasomaxillary epithelial inlay skin graft for the saddle nose

The nasomaxillary epithelial inlay skin graft described by H. D. Gillies in 1923 is one of the historical procedures of the twentieth century. Nowadays, this method has been thoroughly abandoned, and no long-term follow-up has been reported. In the Tokyo Metropolitan Police Hospital, between 1962 and 1983, 51 patients with saddle nose were treated using this procedure and a specially devised outer prosthesis. A follow-up study of these cases was attempted and that of nine cases was carried out. Six of nine patients have been using the outer prosthesis without any serious complications and are satisfied to varying extent. Three patients underwent further surgical treatment using autografts because of serious complications, which included full-thickness skin necrosis, refractory ulcer of the dorsum of nose, and anxiety about the unphysiological communication between the nasal and oral cavities.     

A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes

A generalized finite difference (GFD) method is presented that can be used to solve the bi-domain equations modeling cardiac electrical activity. Classical finite difference methods have been applied by many researchers to the bi-domain equations. However, these methods suffer from the limitation of requiring computational meshes that are structured and orthogonal. Finite element or finite volume methods enable the bi-domain equations to be solved on unstructured meshes, although implementations of such methods do not always cater for meshes with varying element topology. The GFD method solves the bi-domain equations on arbitrary and irregular computational meshes without any need to specify element basis functions. The method is useful as it can be easily applied to activation problems using existing meshes that have originally been created for use by finite element or finite difference methods. In addition, the GFD method employs an innovative approach to enforcing nodal and non-nodal boundary conditions. The GFD method performs effectively for a range of two and three-dimensional test problems and when computing bi-domain electrical activation moving through a fully anisotropic three-dimensional model of canine ventricles.     

Spike-timing-dependent plasticity: common themes and divergent vistas

Recent experimental observations of spike-timing-dependent synaptic plasticity (STDP) have revitalized the study of synaptic learning rules. The most surprising aspect of these experiments lies in the observation that synapses activated shortly after the occurrence of a postsynaptic spike are weakened. Thus, synaptic plasticity is sensitive to the temporal ordering of pre- and postsynaptic activation. This temporal asymmetry has been suggested to underlie a range of learning tasks. In the first part of this review we highlight some of the common themes from a range of findings in the framework of predictive coding. As an example of how this principle can be used in a learning task, we discuss a recent model of cortical map formation. In the second part of the review, we point out some of the differences in STDP models and their functional consequences. We discuss how differences in the weight-dependence, the time-constants and the non-linear properties of learning rules give rise to distinct computational functions. In light of these computational issues raised, we review current experimental findings and suggest further experiments to resolve some controversies.     

Assignment of polar states for protein amino acid residues using an interaction cluster decomposition algorithm and its application to high resolution protein structure modeling

We have developed a new method (Independent Cluster Decomposition Algorithm, ICDA) for creating all-atom models of proteins given the heavy-atom coordinates, provided by X-ray crystallography, and the pH. In our method the ionization states of titratable residues, the crystallographic mis-assignment of amide orientations in Asn/Gln, and the orientations of OH/SH groups are addressed under the unified framework of polar states assignment. To address the large number of combinatorial possibilities for the polar hydrogen states of the protein, we have devised a novel algorithm to decompose the system into independent interacting clusters, based on the observation of the crucial interdependence between the short range hydrogen bonding network and polar residue states, thus significantly reducing the computational complexity of the problem and making our algorithm tractable using relatively modest computational resources. We utilize an all atom protein force field (OPLS) and a Generalized Born continuum solvation model, in contrast to the various empirical force fields adopted in most previous studies. We have compared our prediction results with a few well-documented methods in the literature (WHATIF, REDUCE). In addition, as a preliminary attempt to couple our polar state assignment method with real structure predictions, we further validate our method using single side chain prediction, which has been demonstrated to be an effective way of validating structure prediction methods without incurring sampling problems. Comparisons of single side chain prediction results after the application of our polar state prediction method with previous results with default polar state assignments indicate a significant improvement in the single side chain predictions for polar residues.     

The Phenix software for automated determination of macromolecular structures

X-ray crystallography is a critical tool in the study of biological systems. It is able to provide information that has been a prerequisite to understanding the fundamentals of life. It is also a method that is central to the development of new therapeutics for human disease. Significant time and effort are required to determine and optimize many macromolecular structures because of the need for manual interpretation of complex numerical data, often using many different software packages, and the repeated use of interactive three-dimensional graphics. The Phenix software package has been developed to provide a comprehensive system for macromolecular crystallographic structure solution with an emphasis on automation. This has required the development of new algorithms that minimize or eliminate subjective input in favor of built-in expert-systems knowledge, the automation of procedures that are traditionally performed by hand, and the development of a computational framework that allows a tight integration between the algorithms. The application of automated methods is particularly appropriate in the field of structural proteomics, where high throughput is desired. Features in Phenix for the automation of experimental phasing with subsequent model building, molecular replacement, structure refinement and validation are described and examples given of running Phenix from both the command line and graphical user interface.     

Simplified Generation of Biomedical 3D Surface Model Data for Embedding into 3D Portable Document Format (PDF) Files for Publication and Education

The usefulness of the 3D Portable Document Format (PDF) for clinical, educational, and research purposes has recently been shown. However, the lack of a simple tool for converting biomedical data into the model data in the necessary Universal 3D (U3D) file format is a drawback for the broad acceptance of this new technology. A new module for the image processing and rapid prototyping framework MeVisLab does not only provide a platform-independent possibility to create surface meshes out of biomedical/DICOM and other data and to export them into U3D – it also lets the user add meta data to these meshes to predefine colors and names that can be processed by a PDF authoring software while generating 3D PDF files. Furthermore, the source code of the respective module is available and well documented so that it can easily be modified for own purposes.     

A three-dimensional finite element model of round window membrane vibration before and after stapedotomy surgery

Piston stapes prostheses are implanted in patients with refractory conductive or mixed hearing loss due to stapes otosclerosis to stimulate the perilymph with varying degrees of success. The overclosure effect described by the majority of researchers affects mainly low and medium frequencies, and a large number of patients report a lack of satisfactory results for frequencies above 2 kHz. The mechanics of perilymph stimulation with the piston have not been studied in a systematic manner. The objective of this study was to assess the influence of stapedotomy surgery on round window membrane vibration and to estimate the postoperative outcomes using the finite element (FE) method. The study hypothesis is that the three-dimensional FE model developed of the human inner ear, which simulates the round window (RW) membrane vibration, can be used to assess the influence of stapedotomy on auditory outcomes achieved after the surgical procedure. An additional objective of the study was to enable the simulation of RW membrane vibration after stapedotomy using a new type of stapes prosthesis currently under investigation at Warsaw University of Technology. A three-dimensional finite element (FE) model of the human inner ear was developed and validated using experimental data. The model was then used to simulate the round window membrane vibration before and after stapedotomy surgery. Functional alterations of the RW membrane vibration were derived from the model and compared with the results of experimental measurements from temporal bones of a human cadaver. Piston stapes prosthesis implantation causes an approximately fivefold (14 dB) lower amplitude of the RW membrane vibrations compared with normal anatomical conditions. A satisfactory agreement between the FE model and the experimental data was found. The new prosthesis caused an increase of 20–30 dB in the RW displacement amplitude compared with the 0.4-mm piston prosthesis. In all frequencies, the FE model predicted a RW displacement curve that was above the experimental curves for the normal ear. The stapedotomy can be well simulated by the FE model to predict the auditory outcomes achieved following this otosurgery procedure. The 3D FE model developed in this study may be used to optimize the geometry of a new type of stapes prosthesis in order to achieve a similar sound transmission through the inner ear as for a normal middle ear. This should provide better auditory outcomes for patients with stapedial otosclerosis.     

A computational model of limb impedance control based on principles of internal model uncertainty

Efficient human motor control is characterized by an extensive use of joint impedance modulation, which is achieved by co-contracting antagonistic muscles in a way that is beneficial to the specific task. While there is much experimental evidence available that the nervous system employs such strategies, no generally-valid computational model of impedance control derived from first principles has been proposed so far. Here we develop a new impedance control model for antagonistic limb systems which is based on a minimization of uncertainties in the internal model predictions. In contrast to previously proposed models, our framework predicts a wide range of impedance control patterns, during stationary and adaptive tasks. This indicates that many well-known impedance control phenomena naturally emerge from the first principles of a stochastic optimization process that minimizes for internal model prediction uncertainties, along with energy and accuracy demands. The insights from this computational model could be used to interpret existing experimental impedance control data from the viewpoint of optimality or could even govern the design of future experiments based on principles of internal model uncertainty.     

A method of reconstructing a pendulous breast utilizing the tissue expander

It is possible to reconstruct a breast mound of almost any size by utilizing tissue expansion. In order to produce a pendulous breast which is also ptotic, the tissue-expansion technique has been combined with two other procedures. A new technique is being introduced. It is that of elevating the lower third of the mature breast capsule surrounding the tissue expander at the time the permanent prosthesis is to be exchanged for the expander. The established techniques of inframammary fold reconstruction of Pennisi and Ryan are used to provide pedicle skin coverage for the undersurface of the breast and the bed of the elevated capsule. Internal and external surgical approaches are described, and two examples of each are illustrated. Breasts reconstructed in this manner have remained pendulous structures. Some loss of the initial degree of ptosis has been noted in some cases.