Controlling seepage in discrete particle simulations of biological systems

It is now commonplace to represent materials in a simulation using assemblies of discrete particles. Sometimes, one wishes to maintain the integrity of boundaries between particle types, for example, when modelling multiple tissue layers. However, as the particle assembly evolves during a simulation, particles may pass across interfaces. This behaviour is referred to as ‘seepage’. The aims of this study were (i) to examine the conditions for seepage through a confining particle membrane and (ii) to define some simple rules that can be employed to control seepage. Based on the force-deformation response of spheres with various sizes and stiffness, we develop analytic expressions for the force required to move a ‘probe particle’ between confining ‘membrane particles’. We analyse the influence that particle’s size and stiffness have on the maximum force that can act on the probe particle before the onset of seepage. The theoretical results are applied in the simulation of a biological cell under unconfined compression.     

Development and validation of a kinematically-driven discrete element model of the patellofemoral joint

Quantifying the complex loads at the patellofemoral joint (PFJ) is vital to understanding the development of PFJ pain and osteoarthritis. Discrete element analysis (DEA) is a computationally efficient method to estimate cartilage contact stresses with potential application at the PFJ to better understand PFJ mechanics. The current study validated a DEA modeling framework driven by PFJ kinematics to predict experimentally-measured PFJ contact stress distributions. Two cadaveric knee specimens underwent quadriceps muscle [215 N] and joint compression [350 N] forces at ten discrete knee positions representing PFJ positions during early gait while measured PFJ kinematics were used to drive specimen-specific DEA models. DEA-computed contact stress and area were compared to experimentally-measured data. There was good agreement between computed and measured mean and peak stress across the specimens and positions (r = 0.63–0.85). DEA-computed mean stress was within an average of 12% (range: 1–47%) of the experimentally-measured mean stress while DEA-computed peak stress was within an average of 22% (range: 1–40%). Stress magnitudes were within the ranges measured (0.17–1.26 MPa computationally vs 0.12–1.13 MPa experimentally). DEA-computed areas overestimated measured areas (average error = 60%; range: 4–117%) with magnitudes ranging from 139 to 307 mm² computationally vs 74–194 mm² experimentally. DEA estimates of the ratio of lateral to medial patellofemoral stress distribution predicted the experimental data well (mean error = 15%) with minimal measurement bias. These results indicate that kinematically-driven DEA models can provide good estimates of relative changes in PFJ contact stress.     

A novel training-free method for real-time prediction of femoral strain

Surrogate methods for rapid calculation of femoral strain are limited by the scope of the training data. We compared a newly developed training-free method based on the superposition principle (Superposition Principle Method, SPM) and popular surrogate methods for calculating femoral strain during activity. Finite-element calculations of femoral strain, muscle, and joint forces for five different activity types were obtained previously. Multi-linear regression, multivariate adaptive regression splines, and Gaussian process were trained for 50, 100, 200, and 300 random samples generated using Latin Hypercube (LH) and Design of Experiment (DOE) sampling. The SPM method used weighted linear combinations of 173 activity-independent finite-element analyses accounting for each muscle and hip contact force. Across the surrogate methods, we found that 200 DOE samples consistently provided low error (RMSE < 100 µε), with model construction time ranging from 3.8 to 63.3 h and prediction time ranging from 6 to 1236 s per activity. The SPM method provided the lowest error (RMSE = 40 µε), the fastest model construction time (3.2 h) and the second fastest prediction time per activity (36 s) after Multi-linear Regression (6 s). The SPM method will enable large numerical studies of femoral strain and will narrow the gap between bone strain prediction and real-time clinical applications.     

Viscous flow through slowly expanding or contracting porous walls with low seepage Reynolds number: a model for transport of biological fluids through vessels

In this article, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, is investigated. The governing non-linear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilising the homotopy perturbation method. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate and seepage Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. Since the transport of biological fluids through contracting or expanding vessels is characterised by low seepage Res, the current study focuses on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls.     

Discrete element analysis is a valid method for computing joint contact stress in the hip before and after acetabular fracture

Evaluation of abnormalities in joint contact stress that develop after inaccurate reduction of an acetabular fracture may provide a potential means for predicting the risk of developing post-traumatic osteoarthritis. Discrete element analysis (DEA) is a computational technique for calculating intra-articular contact stress distributions in a fraction of the time required to obtain the same information using the more commonly employed finite element analysis technique. The goal of this work was to validate the accuracy of DEA-computed contact stress against physical measurements of contact stress made in cadaveric hips using Tekscan sensors. Four static loading tests in a variety of poses from heel-strike to toe-off were performed in two different cadaveric hip specimens with the acetabulum intact and again with an intentionally malreduced posterior wall acetabular fracture. DEA-computed contact stress was compared on a point-by-point basis to stress measured from the physical experiments. There was good agreement between computed and measured contact stress over the entire contact area (correlation coefficients ranged from 0.88 to 0.99). DEA-computed peak contact stress was within an average of 0.5 MPa (range 0.2–0.8 MPa) of the Tekscan peak stress for intact hips, and within an average of 0.6 MPa (range 0–1.6 MPa) for fractured cases. DEA-computed contact areas were within an average of 33% of the Tekscan-measured areas (range: 1.4–60%). These results indicate that the DEA methodology is a valid method for accurately estimating contact stress in both intact and fractured hips.     

An efficient method for stochastic simulation of biological populations in continuous time

We present an efficient algorithm for individual-based, stochastic simulation of biological populations in continuous time. A simple method for its implementation is given and it is compared to Gillespie's commonly used Direct Method. These two methods are proven to be exactly equivalent and, using a basic evolutionary model, it is demonstrated that the new algorithm can run thousands of times faster. Furthermore, while computational cost per event increases linearly with population size under the Direct Method, this cost is independent of population size under the new algorithm. We argue that this gain in efficiency opens up the possibility to explore a new class of models in population biology.     

Development of a transient large strain contact method for biological heart valve simulations

A new 2D method to implement transient contact using Comsol Multiphysics (finite element analysis software that enables multiphysics simulations) is described, which is based on Hertzian contact. This method is compared to the existing (default) contact method that does not enable real transient simulations, but instead performs steady-state solutions where time is a constant. The two types of contact modelling have been applied to simple 2D biological heart valve models, undergoing strains in the region of 10% under 20 kPa pressure (applied over 0.3 s). Both the methods predicted comparable stress patterns, locations of peak stresses, deformations and directions of principal stress. The default contact method predicted slightly greater contact stresses, but spreads over a shorter surface length than the new contact method. The default contact method is useful for contact systems with little transient dependency, due to ease of use. However, where transient conditions are important the new contact method is preferred.     

Experiments and finite element modelling for the study of prolapse in the pelvic floor system

Pelvic prolapse affects one woman in three of all ages combined and is quite common for more than 60% of patients over 60 years of age. The treatment of this pathological problem is one of the biggest challenges to the gynaecologist today. The rate of surgical intervention failure is quite significant. The recurrence of prolapse could be related to inadequate surgical technique or the pathology or/and biomechanical deficiency of the soft tissues. The modelling and simulation of the behaviour of the pelvic cavity could be a major tool for specific evaluation of pelvic status. A first stage of this model is being developed and reported. The computer-aided design model of the organs of the pelvic floor is created using magnetic resonance image data and the ligament boundary conditions are defined. A multi-organ geometric model is thus created and studied.     

Process parameters for the high-scale production of alginate-encapsulated stem cells for storage and distribution throughout the cell therapy supply chain

With the ever-increasing clinical application of cell-based therapies, it is considered critical to develop systems that facilitate the storage and distribution of cell therapy products (CTPs) between sites of manufacture and the clinic. For such systems to be realized, it is essential that downstream bioprocessing strategies be established that are scalable, reproducible and do not influence the viability or function of the living biologic. To this end, we examined alginate-encapsulation as a method to heighten the preservation of human adipose-derived stem cells (hASCs) during hypothermic storage, and establish a scalable process for high-volume production. A drop-wise method for scalable alginate bead generation, using calcium as the cross-linker, was modified to enable the yield of up to 3500 gelled beads per minute. The effect of alginate concentration on the viscosity of non-gelled sodium alginate and the mechanical properties and internal structure of calcium-crosslinked alginate in response to different alginate and calcium concentrations were investigated. Mechanical strength was chiefly dependent on alginate concentration and 1.2% alginate cross-linked with 100 mM calcium chloride could withstand stress in the order of 35 kPa. Upon selection of appropriate parameters, we demonstrated the suitability of using this method for immobilizing human stem cells. Encapsulated hASCs demonstrated no loss in cell viability, and had a uniform distribution after high-volume production. Following storage, released cells were able to attach and recover a normal morphology upon return to culture conditions. Thus we present a scalable method for stem cell encapsulation and storage for application within the cell therapy supply chain.     

The role of cell membrane in the regulation of cell division and malignant transformation

An earlier model in which uptake of essential nutrients for which the cell is auxotrophic, regulates cell division, is discussed in the light of new experimental findings, specifically the purification of a new type of transport-inhibitory protein from rat liver and the properties of the protein. The possible role of such proteins in malignant transformation is also discussed.     

Secretion and binding of HMG1 protein to the external surface of the membrane are required for murine erythroleukemia cell differentiation

We show here that murine erythroleukemia (MEL) cells, following induction with hexamethylene bisacetamide, accumulate high mobility group (HMG)1 protein onto the external surface of the cell in a membrane-associated form detectable by immunostaining with a specific anti-HMG1 protein antibody. This association is maximal at a time corresponding to cell commitment. At longer times, immunostainable cells are progressively reduced and become almost completely undetectable along with the appearance of hemoglobin molecules. Binding to MEL cells does not affect the native molecular structure of HMG1 protein. The type of functional correlation between HMG1 protein and MEL cell differentiation is suggested by the observation that if an anti-HMG1 protein antibody is added at the same time of the inducer almost complete inhibition of cell differentiation is observed, whereas if the antibody is added within the time period in which cells undergo through irreversible commitment, inhibition progressively disappears. A correlation between MEL cell commitment and the biological effect of HMG1 protein can thus be consistently suggested.     

Formulation of a coupled mechanism between solute diffusion,phosphatase-kinase reactions and membrane potentials for the primary active transport of phosphorylated substrates through biological membranes

Coupled interrelations occurring between a phosphatase/kinase reaction sequence acting in unstirred layers and on both sides of a charged biomembrane pore structure are presented as a plausible kinetic model for the primary active transport of phosphorylated molecules. Simulations conducted at the cell level and with credible numerical values demonstrate that the enzymes positions strongly regulate the membrane permeability for the transported substrate. Depending on both the enzymes positions (more or less far from the membrane) and the membrane charges, the membrane may appear either impervious, either permeable or able to actively transport a phosphorylated substrate. Globally all happens as if, in function of the enzymes positions, a permanent pore may be regulated, changing from a more closed to a more open conformation.     

Computational study of cell adhesion and rolling in flow channel by meshfree method

Tethering and rolling of circulating leukocytes on the surface of endothelium are critical steps during an inflammatory response. A soft solid cell model was proposed to study monocytes tethering and rolling behaviors on substrate surface in shear flow. The interactions between monocytes and micro-channel surface were modeled by a coarse-grained molecular adhesive potential. The computational model was implemented in a Lagrange-type meshfree Galerkin formulation to investigate the monocyte tethering and rolling process with different flow rates. From the simulation results, it was found that the flow rate has profound effects on the rolling velocity, contact area and effective stress of monocytes. As the flow rate increased, the rolling velocity would increase linearly, whereas the contact area and average effective stress in monocyte showed nonlinear increase.     

Biomechanical analysis of the Universal 2 implant in total wrist arthroplasty: a finite element study

Little is known about the mechanics of in vivo loading on total wrist prostheses where many studies have looked at the mechanics of other types of arthroplasty such as for the hip and the knee which has contributed to the overall success of these types of procedures. Currently surgeons would prefer to carry out arthrodesis on the wrist rather than consider arthroplasty as clinical data have shown that the outcome of total wrist arthroplasty is poorer than compared to the hip and knee. More research is needed on the loading mechanisms of the implants in order to enhance the design of future generation implants. This study looks at the load transfer characteristics of the Universal 2 implant using a finite element model of a virtually implanted prosthesis during gripping. The results showed that the loading on the implant is higher on the dorsal and ulnar aspect than on the volar and radial aspect of the implant. The whole load is transmitted through the radius and none through the ulna.     

Numerical investigations of the mechanical properties of a braided non-vascular stent design using finite element method

This paper discusses various issues relating to the mechanical properties of a braided non-vascular stent made of a Ni–Ti alloy. The design of the stent is a major factor which determines its reliability after implantation into a stenosed non-vascular cavity. This paper presents the effect of the main structural parameters on the mechanical properties of braided stents. A parametric analysis of a commercial stent model is developed using the commercial finite element code ANSYS. As a consequence of the analytical results that the pitch of wire has a greater effect than other structural parameters, a new design of a variable pitch stent is presented to improve mechanical properties of these braided stents. The effect of structural parameters on mechanical properties is compared for both stent models: constant and variable pitches. When the pitches of the left and right quarters of the stent are 50% larger and 100% larger than that of the central portion, respectively, the radial stiffness in the central portion increases by 10% and 38.8%, while the radial stiffness at the end portions decreases by 128% and 164.7%, the axial elongation by 25.6% and 56.6% and the bending deflection by 3.96% and 10.15%. It has been demonstrated by finite element analysis that the variable pitch stent can better meet the clinical requirements.     

Mpg1, a fission yeast protein required for proper septum structure,is involved in cell cycle progression through cell-size checkpoint

Using a yeast two-hybrid screen we isolated a gene from Schizosaccharomyces pombe which corresponds to the previously uncharacterized ORF SPCC1906.01. We have designated this gene as mpg1, based on the putative function of its product as a mannose-1-phosphatase guanyltransferase. Mpg1 shows strong similarity to other GDP-mannose-1-phosphate guanyltransferases involved in the maintenance of cell wall integrity and/or glycosylation. This homology, together with the protein's localization pattern demonstrated in this work, strongly suggests that Mpg1 is involved in cell wall and septum synthesis. Moreover, cells lacking Mpg1 present a defect in glycosylation, are more sensitive to Lyticase, and show an aberrant septum structure from the start of its deposition, indicating that the Mpg1 function is necessary for the correct assembly of the septum. Interestingly, lack of Mpg1 clearly affects cell cycle progression: mpg1 null mutants arrest as septated and bi-nucleated 4C cells, without an actomyosin ring. Wee1 is required for the G2/M arrest induced in the absence of Mpg1, since the blockade is circumvented when Wee1 is inactivated. Wee1 is part of a cell-size checkpoint that prevents entry into mitosis before cells reach a critical size. The results presented in this work demonstrate that the G2/M arrest induced in the absence of Mpg1 is mediated by this cell size checkpoint, since oversized mutant cells enter mitosis. The mpg1 loss-of-function mutant, therefore, provides a good model in which to study how cells coordinate cell growth and cell division.     

Modeling and simulation of novel antenna for the treatment of hepatocellular carcinoma using finite element method

In this article, new interstitial antenna operating at a frequency of 2.45 GHz for the treatment of hepatocellular carcinoma (HCC) using microwave ablation has been investigated. This antenna is basically an asymmetrical miniaturized choke dipole antenna with a pointed needle at the tip. A commercial finite element method (FEM) package, COMSOL Multiphysics 3.4a, has been used to simulate the performance of needle tip choke antenna. The performance of the antenna has been evaluated numerically, taking into account the specific absorption rate, antenna impedance matching and geometry of the obtained thermal lesion, and the temperature distribution plot obtained shows that maximum temperature was attained in this simulation. The antenna is also capable of creating a spherical-shaped ablation zone. The size and shape of the ablation zone can be slightly adjusted by adjusting the choke position in order to maintain spherical ablation zones.