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Sample size calculation based on normal approximations is often associated with the loss of statistical power for a single-arm trial with a time-to-event endpoint. Recently, Wu (2015) derived the exact variance for the one-sample log-rank test under the alternative and showed that a single-arm one-stage study based on exact variance often has power above the nominal level while the type I error rate is controlled. We extend this approach to a single-arm two-stage design by using exact variances of the one-sample log-rank test for the first stage and the two stages combined. The empirical power of the proposed two-stage optimal designs is often not guaranteed under a two-stage design setting, which could be due to the asymptotic bi-variate normal distribution used to estimate the joint distribution of the test statistics. We adjust the nominal power level in the design search to guarantee the simulated power of the identified optimal design being above the nominal level. The sample size and the study time savings of the proposed two-stage designs are substantial as compared to the one-stage design.

In recent years, subgroup analysis has emerged as an important tool to identify unknown subgroup memberships. However, subgroup analysis is still under-studied for longitudinal data. In this paper, we propose a structured mixed-effects approach for longitudinal data to model subgroup distribution and identify subgroup membership simultaneously. In the proposed structured mixed-effects model, the heterogeneous treatment effect is modeled as a random effect from a two-component mixture model, while the membership of the mixture model is incorporated using a logistic model with respect to some covariates. One advantage of our approach is that we are able to derive the estimation of the treatment effects through an EM-type algorithm which keeps the subgroup membership unchanged over time. Our numerical studies and real data example demonstrate that the proposed model outperforms other competing methods.

Transcatheter aortic valve replacement (TAVR) is a minimally invasive procedure that provides an effective alternative to open-heart surgical valve replacement for treating advanced calcific aortic valve disease patients. However, complications, such as valve durability, device migration, paravalvular leakage (PVL), and thrombogenicity may lead to increased overall post-TAVR morbidity and mortality. A series of numerical studies involving a self-expandable TAVR valve were performed to evaluate these complications. Structural studies were performed with finite element (FE) analysis, followed by computational fluid dynamics (CFD) simulations, and fluid-structure interaction (FSI) analysis. The FE analysis was utilized to study the effect of TAVR valve implantation depth on valve anchorage in the Living Heart Human Model, which is capable of simulating beating heart during repeated cardiac cycles. The TAVR deployment cases where no valve migration was observed were then used to calculate the post-deployment thrombogenic potential via CFD simulations. FSI analysis followed to further assess the post-deployment TAVR hemodynamic performance for different implantation depths. The deployed valves PVL, geometric and effective orifice areas, and the leaflets structural and flow stress magnitudes were compared to determine the device optimal landing zone. The combined structural and hemodynamic analysis indicated that with the TAVR valve deployed at an aft ventricle position an optimal performance was achieved in the specific anatomy studied. Given the TAVR’s rapid expansion to younger lower-risk patients, the comprehensive numerical methodology proposed here can potentially be used as a predictive tool for both procedural planning and valve design optimization to minimize the reported complications.

Laser has been widely used in the treatment of vascular skin diseases, such as port wine stain, due to the effect of selective photothermolysis in laser on biological tissue. The 755 nm alexandrite laser was expected to achieve better curative effect than the commonly used 585 or 595 nm pulsed dye laser (PDL) because of its deeper tissue penetration. In this study, the dorsal chamber model and microscopic visualization system were used to observe morphology changes on 42 blood vessels before and after irradiation with the 755 nm laser. Results showed that thermal effects of blood vessels intensified with the increase in energy, and high energy was required to produce the same thermal effect as the extension of pulse width. Different from 595 and 1064 nm lasers, partial vessel contraction was dominant thermal effect caused by the 755 nm laser. The bleeding injury rate and thermal effect of the 755 nm laser were between those of 595 nm PDL and 1064 nm Nd:YAG laser. The simulation results proved that 595 nm PDLs were effective for small and shallow target blood vessels. The 755 nm alexandrite lasers were effective in the treatment of hypertrophic and resistant blood vessels to PDL in the skin with low or moderate melanin concentration. The 1064 nm Nd:YAG laser was effective in the treatment of deeply buried and enlarged target blood vessels in the skin with high melanin concentration. The simulation results were supported by published clinical observations.

Multidimensional correlation magnetic resonance imaging (MRI) is an emerging imaging modality that is capable of disentangling highly heterogeneous and opaque systems according to chemical and physical interactions of water within them. Using this approach, the conventional three dimensional MR scalar images are replaced with spatially resolved multidimensional spectra. The ensuing abundance in microstructural and chemical information is a blessing that incorporates a real challenge: how does one distill and refine it into images while retaining its significant components? In this paper we introduce a general framework that preserves the spectral information from spatially resolved multidimensional data. Equal weight is given to significant spectral components at the single voxel level, resulting in a summarized image spectrum. This spectrum is then used to define spectral regions of interest that are utilized to reconstruct images of sub-voxel components. Using numerical simulations we first show that, contrary to the conventional approach, the proposed framework preserves spectral resolution, and in turn, sensitivity and specificity of the reconstructed images. The retained spectral resolution allows, for the first time, to observe an array of distinct $${T}_{1}$$ T 1 −$${T}_{2}$$ T 2 −$$\langle D\rangle $$ ⟨ D ⟩ components images of the human brain. The robustly generated images of sub-voxel components overcome the limited spatial resolution of MRI, thus advancing multidimensional correlation MRI to fulfilling its full potential.

Polyhydroxybutyrate (PHB) is biodegradable and biocompatible polyester that has been recently used for developing different drug delivery systems (DDS). Microspheres as DDS, consist of a polymeric matrix with a diameter of 1–125 μm which contains a substance entrapped, and then released mainly through diffusion. In order to make DDS viable for commercial applications, it is essential to develop models that describe and predict the substance release kinetic. In this study, microspheres of PHB with curcumin entrapped were synthesized; the release of curcumin was studied and modeled. As a first approach, a physical model was introduced, in which mass transference was considered analogous to heat transference. The proposed model was based on local mass balance through the classical diffusion equation and total mass balance imposed through an integro-differential equation. The total mass balance introduced nonlinearities in the dynamics of the drug within the fluid; therefore, a semi-analytical approach based on the heat balance integral method was applied to solve the proposed model. Finally, by using the experimental rate of release of curcumin, the semi-analytical solutions to the proposed model were compared with the experimental release data, showing the importance of adding mass balance in the nonlinear mathematical model in order to describe more accurately the release kinetics.

Purpose Intracranial aneurysms are malformations forming bulges on the walls of brain arteries. A flow diverter device is a fine braided wire structure used for the endovascular treatment of brain aneurysms. This work presents a rig and a protocol for the measurement of the hydrodynamic resistance of flow diverter stents. Hydrodynamic resistance is interpreted here as the pressure loss versus volumetric flow rate function through the mesh structure. The difficulty of the measurement is the very low flow rate range and the extreme sensitivity to contamination and disturbances. Methods Rigorous attention was paid to reproducibility, hence a strict protocol was designed to ensure controlled circumstances and accuracy. Somewhat unusually, the history of the development of the rig, including the pitfalls was included in the paper. In addition to the hydrodynamic resistance measurements, the geometrical properties—metallic surface area, pore density, deployed and unconstrained length and diameter—of the stent deployment were measured. Results Based on our evaluation method a confidence band can be determined for a given deployment scenario. Collectively analysing the hydrodynamic resistance and the geometric indices, a deeper understanding of an implantation can be obtained. Our results suggest that to correctly interpret the hydrodynamic resistance of a scenario, the deployment length has to be considered. To demonstrate the applicability of the measurement, as a pilot study the results of four intracranial flow diverter stents of two types and sizes have been reported in this work. The results of these measurements even on this small sample size provide valuable information on differences between stent types and deployment scenarios.

Quantiles are widely used in both theoretical and applied statistics, and it is important to be able to deploy appropriate quantile estimators. To improve performance in the lower and upper quantiles, especially with small sample sizes, a new quantile estimator is introduced which is a weighted average of all order statistics. The new estimator, denoted NO, has desirable asymptotic properties. Moreover, it offers practical advantages over four estimators in terms of efficiency in most experimental settings. The Harrell-Davis quantile estimator, the default quantile estimator of the R programming language, the Sfakianakis-Verginis SV2 quantile estimator and a kernel quantile estimator. The NO quantile estimator is also utilized in comparing two independent groups with a percentile bootstrap method and, as expected, it is more successful than other estimators in controlling Type I error rates.

Fracture healing and growth of the bones are highly related to the stress level. Numerical analysis of stresses is the most effective means to determine the stress level, but it usually requires sufficient resolution to ensure an accurate description of geometry features of bones. In this paper, high-fidelity smoothed finite element method (S-FEM) skull models are created using computed tomography (CT) and micro-computed tomography (μCT) images of a juvenile pig skull. The material properties of the heterogeneous bone are modeled by a varying distribution of Young's modulus mapped to each element and smoothing domain to accurately capture the high heterogeneity. Different types of S-FEM models, including node-based, edge-based, and face-based, are developed for this high-fidelity modeling work. It is found that S-FEM has higher accuracy, in terms of displacements, stresses, and strain energy, compared to the traditional finite element method (FEM). Graphical abstract.

We propose a latent topic model with a Markov transition for process data, which consists of time-stamped events recorded in a log file. Such data are becoming more widely available in computer-based educational assessment with complex problem-solving items. The proposed model can be viewed as an extension of the hierarchical Bayesian topic model with a hidden Markov structure to accommodate the underlying evolution of an examinee's latent state. Using topic transition probabilities along with response times enables us to capture examinees' learning trajectories, making clustering/classification more efficient. A forward-backward variational expectation-maximization (FB-VEM) algorithm is developed to tackle the challenging computational problem. Useful theoretical properties are established under certain asymptotic regimes. The proposed method is applied to a complex problem-solving item in the 2012 version of the Programme for International Student Assessment (PISA).

In this research, the hemodynamic performance of a 23-mm On-X bileaflet mechanical heart valve (BMHV) was investigated with the realistic geometry model of the valve and the deformable aorta in accelerating systole. In addition, the effect of ascending aorta flexibility and aortic annulus calcification on the complex blood flow characteristics were investigated. The geometry of the aorta is derived from the medical images, and the Ogden model has been utilized for the mechanical behavior of the ascending aorta. The 3D numerical simulation by a two-way Fluid-Structure Interaction (FSI) analysis using the Arbitrary Lagrangian–Eulerian (ALE) method was performed throughout the accelerating systolic phase. The dynamics of the leaflets are investigated, and blood flow characteristics such as velocities, vorticities as well as viscous and turbulent shear stress were precisely captured in the flow domain specifically in the hinge region. Streamline results are in accordance with the previously reported data, which show that the flared On-X valves inlet yields a more uniform flow in accelerating systole. Simulations show that aorta flexibility or valve annulus calcification causes variations up to 7% in maximum fluid velocity and 20% in Turbulence Kinetic Energy (TKE). In this study, the complex flow field characteristics in the new generation of BMHVs considering aorta flexibility with healthy and calcified annulus were investigated. It was found that the blood flow around the hinges region is in the danger of hemolysis and platelet activation and subsequently thromboembolism. Furthermore, the results show that similar to vessel wall deformation, considering the probable annulus calcification after valve replacement is also essential.

In this paper, we formulate a stage-structured predator–prey model with mutual interference, in which includes two discrete delays. By theoretical analysis, we establish the stability of the unique positive equilibrium and the existence of Hopf bifurcation when the maturation delay for predators is used as the bifurcation parameter. Our results exhibit that the maturation delay for preys does not affect the stability of the positive equilibrium. However, the maturation delay for predator is able to destabilize the positive equilibrium and causes periodic solutions. Numerical simulations are carried out to illustrate the theoretical results and display the differential impacts of two type delays and mutual interference.

A deterministic model of onchocerciasis disease dynamics is considered in a community partitioned into compartments based on the disease status. Public health education is offered in the community during the implementation of mass treatment using ivermectin drugs. Also, larviciding and trapping strategies are implemented in the vector population with the aim of controlling population growth of black flies. We fit the model to the data to check the suitability of the model. Expressions are derived for the influence on the reproduction numbers of these strategies. Numerical results show that the dynamics of onchocerciasis and the growth of black flies are best controlled when the four strategies are implemented simultaneously. Also, the results suggest that for the elimination of the disease in the society there is a need for finding another drug which will be implemented to ineligible human as well as killing the adult worms instead of ivermectin.

In this paper, a delayed diffusive predator-prey model with schooling behaviour and Allee effect is investigated. The existence and local stability of equilibria of model without time delay and diffusion are given. Regarding the conversion rate as bifurcation parameter, Hopf bifurcation of diffusive system without time delay is obtained. In addition, the local stability of the coexistent equilibrium and existence of Hopf bifurcation of system with time delay are discussed. Moreover, the properties of Hopf bifurcation are studied based on the centre manifold and normal form theory for partial functional differential equations. Finally, some numerical simulations are also carried out to confirm our theoretical results.

In this paper, we consider a nonautonomous predator-prey system with Beddington-DeAngelis functional response and explore the global stability of boundary solution. Based on the dynamics of logistic equation, some new sufficient conditions on the global asymptotic stability of boundary solution are presented for general time-dependence case. Our main results indicate that (i) the long-term ineffective predation behaviour or high mortality of predator species will lead the predator species to extinction, even if the intraspecies competition of predator species is weak or no intraspecies competition; (ii) the long-term intense intraspecific competition may lead the predator species to extinction, even though the long-term accumulative predation benefit is higher than the death lose. When all parameters are periodic functions with common period, a necessary and sufficient condition on the global stability of boundary periodic solution is obtained. In addition, some numerical simulations are performed to illustrate the theoretical results.

In this paper, we propose and investigate a stochastic Holling type-II predator–prey model with prey refuge and fear effect. We first prove the existence and uniqueness of the global positive solution. Then we perform the survival analysis of the model, including the existence of a unique ergodic stationary distribution and the extinction of the model. Numerical simulations are carried out to validate our analytical results. Our findings indicate that the white noise is adverse to the growth of predator and prey populations, and the increase of fear effect will lead to the decrease of predator density, but with no obvious effect on prey density.

A logistic type stochastic control model for cost-effective single-species population management subject to an ambiguous jump intensity is presented based on the modern multiplier-robust formulation. The Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation for finding the optimal control is then derived. Mathematical analysis of the HJBI equation from the viewpoint of viscosity solutions is carried out with an emphasis on the non-linear and non-local term, which is a key term arising due to the jump ambiguity. We show that this term can be efficiently handled in the framework of viscosity solutions by utilizing its monotonicity property. A numerical scheme to discretize the HJBI equation is presented as well. Our model is finally applied to management of algae population in river environment. Optimal management policies ranging from the short-term to long-term viewpoints are numerically investigated.

In this work, we study a non-autonomous differential equation model for the interaction of wild and sterile mosquitoes. Suppose that the number of sterile mosquitoes released in the field is a given nonnegative continuous function. We determine a threshold [Formula: see text] for the number of sterile mosquitoes and provide a sufficient condition for the origin [Formula: see text] to be globally asymptotically stable based on the threshold [Formula: see text]. For the case when the number of sterile mosquitoes keeps at a constant level, we find that the origin [Formula: see text] is globally asymptotically stable if and only if the constant number [Formula: see text] of sterile mosquitoes released in the field is above [Formula: see text].

We study the occurrence of chaos in the Atkinson-Allen model of four competing species, which plays the role as a discrete-time Lotka-Volterra-type model. We show that in this model chaos can be generated by a cascade of quasiperiod-doubling bifurcations starting from a supercritical Neimark-Sacker bifurcation of the unique positive fixed point. The chaotic attractor is contained in a globally attracting invariant manifold of codimension one, known as the carrying simplex. Biologically, our study implies that the invasion attempts by an invader into a trimorphic population under Atkinson-Allen dynamics can lead to chaos.

Scarlet fever is an acute respiratory infectious disease and the incidence rate is increasing from 2011 throughout the world. In this paper, the mathematical models are proposed, which incorporate both direct transmissions and indirect transmissions of scarlet fever. The threshold conditions for disease invasion are obtained in terms of the basic reproduction number. The peak value, final size and epidemic time in a seasonal prevalence are investigated numerically. Furthermore, the effects of seasonal fluctuations on disease outbreak are also studied on the basis of real data in China.

The silver, magnesium oxide and gyrotactic microorganism-based hybrid nanofluid flow inside the conical space between disc and cone is addressed in the perspective of thermal energy stabilization. Different cases have been discussed between the spinning of cone and disc in the same or counter wise directions. The hybrid nanofluid has been synthesized in the presence of silver Ag and magnesium oxide MgO nanoparticulate. The viscous dissipation and the magnetic field factors are introduced to the modeled equations. The parametric continuation method (PCM) is utilized to numerically handle the modeled problem. Magnesium oxide is chemically made up of Mg2+ and O2- ions that are bound by a strong ionic connection and can be made by pyrolyzing Mg(OH)2 (magnesium hydroxide) and MgCO3 (magnesium carbonate) at high temperature (700–1500 °C). For metallurgical, biomedical and electrical implementations, it is more efficient. Similarly, silver nanoparticle's antibacterial properties could be employed to control bacterial growth. It has been observed that a circulating disc with a stationary cone can achieve the optimum cooling of the cone-disk apparatus while the outer edge temperature remains fixed. The thermal energy profile remarkably upgraded with the magnetic effect, the addition of nanoparticulate in base fluid and Eckert number.

The present study considers the mathematical modelling of unsteady non-Newtonian hydro-magnetic nanohemodynamics through a rigid cylindrical artery featuring two different stenoses (composite and irregular).\ud The Ostwald-De Waele power-law fluid model is adopted to simulate the non-Newtonian characteristics of\ud blood. Inspired by drug delivery applications for cardiovascular treatments, blood is considered doped with\ud a homogenous suspension of biocompatible nanoparticles. The arterial vessel exhibits the permeability\ud effect (lateral influx/efflux), and an external magnetic field is also applied in the radial direction to the flow.\ud A combination of the Buongiorno and Tiwari-Das nanoscale models is adopted. The strongly nonlinear\ud nature of the governing equations requires a robust numerical method, and therefore the finite difference\ud technique is deployed to solve the resulting equations. Validation of solutions for the pure blood case\ud (absence of nanoparticles) is included. Comprehensive solutions are presented for shear-thickening (n=1.5)\ud and shear-thinning (n=0.5) blood flow for the effects of crucial nanoscale thermophysical, solutal\ud parameters, and hydrodynamic parameters. Comparison of profiles (velocity, temperature, wall shear stress,\ud and flow rate) is also made for composite and irregular stenosis. Colour visualization of streamline plots is\ud included for pure blood and nano mediated blood both with and without applied magnetic field. The\ud inclusion of nanoparticles (Cu/blood) within blood increases the axial velocity of blood. By applying\ud external magnetic field in the radial direction, axial velocity is significantly damped whereas much less\ud dramatic alterations are computed in blood temperature and concentration profiles. The simulations are\ud relevant to the diffusion of nano-drugs in magnetic targeted treatment of stenosed arterial diseases.

Loop-mediated isothermal amplification or LAMP has been identified to be an efficient technology for point-of-care diagnostics. Paper-based LAMP technique has tremendous potential in replacing the existing tube-based technology as the manufacturing cost of a paper-based device is comparatively lower and easy-to-use. LAMP-based paper diagnostic device for Mycobacterium tuberculosis (MTB) detection is of extreme importance as it will help in early and rapid diagnosis of the affected patients. The fabrication of these devices requires assessment of design parameters on the extent of LAMP amplification reaction. Hence, CFD studies would be extremely beneficial from the design perspective. The current work presents an insight into the CFD simulations for LAMP amplification reaction on a porous paper membrane (nitrocellulose membrane). The convection-diffusion-reaction model is solved on a COMSOL Multiphysics 5.0 platform. Studies on effect of pore size, aspect ratio and initial DNA concentration on the extent of DNA amplification reaction have been carried out. The current paper-based technique is effective in detecting a minimum of 5 copies of DNA contrasting the previous semi-quantitative technique which demonstrated the detection of minimum 98 copies. Overall, the simulation results displayed almost 96% enhancement in the DNA amplification rate on paper membrane. Graphical abstract Graphical abstract for the computational study of DNA amplification reaction via LAMP technique on a porous paper membrane.

The sacrum is a large trilateral bone located at the base of the vertebral column serving to transfer the body weight from the trunk to the pelvis and lower extremities. Over the years, an abundance of sacral anatomical divergences has been reported, including numerical and/or morphological variations of sacral entities. The majority of these anatomical alternations has been incidentally identified during radiological investigations, surgical procedures or discovered in anatomical, anthropological and forensic research studies. Throughout international literature, however, there is a scarcity of an integrative recording of all known anatomical variations of the sacrum in a single study. This constitutes the objective of the present paper: to provide an exhaustive systematic review of the relevant literature, as well as to thoroughly describe all the recognized deviations of the sacrum structure, while highlighting the aspects of their clinical significance.

Air absorption can be a significant source of attenuation, which should be considered in long-duration wideband acoustics simulations. In this short contribution, a time-domain model for three-dimensional wave propagation including viscothermal and relaxation effects (air absorption) is developed and coupled with locally reactive impedance wall conditions through a conservative energy framework. The model is discretised with a finite-difference time-domain method, and numerical stability is established with a discrete energy balance. Numerical examples are presented to demonstrate the proposed method.

The process of integrating observations into a numerical model of an evolving dynamical system, known as data assimilation, has become an essential tool in computational science. These methods, however, are computationally expensive as they typically involve large matrix multiplication and inversion. Furthermore, it is challenging to incorporate a constraint into the procedure, such as requiring a positive state vector. Here we introduce an entirely new approach to data assimilation, one that satisfies an information measure and uses the unnormalized Kullback-Leibler divergence, rather than the standard choice of Euclidean distance. Two sequential data assimilation algorithms are presented within this framework and are demonstrated numerically. These new methods are solved iteratively and do not require an adjoint. We find them to be computationally more efficient than Optimal Interpolation (3D-Var solution) and the Kalman filter whilst maintaining similar accuracy. Furthermore, these Kullback-Leibler data assimilation (KL-DA) methods naturally embed constraints, unlike Kalman filter approaches. They are ideally suited to systems that require positive valued solutions as the KL-DA guarantees this without need of transformations, projections, or any additional steps. This Kullback-Leibler framework presents an interesting new direction of development in data assimilation theory. The new techniques introduced here could be developed further and may hold potential for applications in the many disciplines that utilize data assimilation, especially where there is a need to evolve variables of large-scale systems that must obey physical constraints.

Chemical exchange saturation transfer (CEST) methods measure the effect of magnetization exchange between solutes and water. While CEST methods are often implemented using a train of off-resonant shaped rf pulses, they are typically analyzed as if the irradiation is continuous. This approximation does not account for exchange of rotated magnetization, unique to pulsed irradiation and exploited by chemical exchange rotation transfer (CERT) methods. In this work, we derive and test an analytic solution for the steady-state water signal under pulsed irradiation by extending a previous work to include the effects of pulse shape. The solution is largely accurate at all offsets, but this accuracy diminishes at higher exchange rates and when applying pulse shapes with large root-mean-squared to mean ratios (such as multi-lobe sinc pulses).

A microfluidic array was constructed for trapping single cell and loading identical dynamic biochemical stimulation for gain a better understanding of Ca2+ signaling at single cell resolution in the present study. This microfluidic array consists of multiple radially aligned flow channels with equal intersection angles, which was designed by a combination of stagnation point flow and physical barrier. Numerical simulation results and trajectory analysis have shown the effectiveness of this single cell trapping device. Fluorescent experiment results demonstrated the effects of flow rate and frequency of dynamic stimulus on the profiles of biochemical concentration which exposed on captured cells. In this microarray, the captured single cells in each trapping channels were able to receive identical extracellular dynamic biochemical stimuli which being transmitted from the entrance in the middle of the microfluidic array. Besides, after loading dynamic Adenosine Triphosphate (ATP) stimulation on captured cells by this device, consistent average intracellular Ca2+ dynamics phase and cellular heterogeneity were observed in captured single K562 cells. Furthermore, this device is able to be used for investigating cellular respond on single cell resolution to temporally varying environments by modulating the stimulation signal in terms of concentration, pattern, and duration of exposure.

This paper presents an investigation on the interstitial fluid pressure and stress reductions in a vascularized solid tumor using a thermal therapy approach. The solid tumor is modeled as a fluid infiltrated poroelastic medium with a pressure source subjected to spatial heating. The distributions of temperature, interstitial fluid pressure, strains and stresses in a spherical tumor are obtained using a thermoporoelasticity theory in which the extracellular solid matrix and the interstitial fluid have different coefficient of thermal expansion (CTE). The numerical results for a solid tumor subjected to uniform spatial heating indicate that the CTE of the solid matrix of the tumor plays a crucial role in the reductions in the fluid pressure and effective stresses caused by the thermal therapy. The pore pressure and effective stresses are reduced when the CTE of the solid matrix is higher than that of the interstitial fluid. The reductions in fluid pressure and stresses may become significant depending on the difference between the CTEs of the solid matrix and interstitial fluid. The reductions reach the maximum at the tumor center and decrease with increasing radial distance from the tumor center. Finally, the thermally induced fluid flow is directed from the surface towards the center thereby potentially improving the microcirculation in the solid tumor.

In the analysis of current life science datasets, we often encounter scenarios in which the application of asymptotic theory to hypothesis testing can be problematic. Besides improved asymptotic results, permutation/simulation-based tests are a general approach to address this issue. However, these randomized tests can impose a massive computational burden, for example, in scenarios in which large numbers of statistical tests are computed, and the specified significance level is very small. Stopping rules aim to assess significance with the smallest possible number of draws while controlling the probabilities of errors due to statistical uncertainty. In this communication, we derive a general stopping rule, QUICK-STOP, based on the sequential testing theory that is easy to implement, controls the error probabilities rigorously, and is nearly optimal in terms of expected draws. In a simulation study, we show that our approach outperforms current stopping approaches for general randomized tests by factor 10 and does not impose an additional computational burden. We illustrate our approach by applying our stopping rule to a single variant analysis of a whole-genome sequencing study for lung function.

According to recent studies, cancer is an evolving complex ecosystem. It means that tumor cells are well differentiated and involved in heterotypic interactions with their microenvironment competing for available resources to proliferate and survive. In this paper, we propose a chemo-mechanical model for the growth of specific subtypes of an invasive breast carcinoma. The model suggests that a carcinoma is a heterogeneous entity comprising cells of different phenotypes, which perform different functions in a tumor. Every cell is represented by an elastic polygon changing its form and size under pressure from the tissue. The mechanical model is based on the elastic potential energy of the tissue including the effects of contractile forces within the cell perimeter and the elastic resistance to stretching or compressing the cell with respect to the reference area. A tissue can evolve via mechanisms of cell division and intercalation. The phenotype of each cell is determined by its environment and can dynamically change via an epithelial-mesenchymal transition and vice versa. The phenotype defines the cell adhesion to the adjacent tissue and the ability to divide. In this part, we focus on the forms of collective migration of large groups of cells. Numerical simulations show the different architectural subtypes of invasive carcinoma. For each communication, we examine the dynamics of the cell population and evaluate the complexity of the pattern in terms of the synergistic paradigm. The patterns are compared with the morphological structures previously identified in clinical studies.

In-stent restenosis (ISR) is related to local haemodynamics in the arteries after stent intervention. However, the haemodynamics of stents implanted into tapered vessels is rarely studied and remains unclear. This study aimed to study the haemodynamic performance of a stent in a tapered artery to reveal the haemodynamic differences between tapered and cylindrical stents after stent implantation and guide the stent selection for the treatment of coronary artery stenosis. Cylindrical and tapered stents were implanted into the tapered arteries. A model of a cylindrical stent implanted into a cylindrical artery was established as the contrast model. Using the finite element method, the flow velocity and wall shear stress distribution of the three models were compared. At t1, t2, t3 and t4, the flow rate of the tapered artery with tapered stents (TT) after the implantation increased by 8.59, 3.80, 12.81 and 3.66%, respectively. In addition, the wall shear stress in the tapered arteries of TT was 23.48, 36.67, 13.00 and 8.06% higher than that of the tapered arteries with cylindrical stents (TC). The implantation of a tapered stent in the tapered artery can effectively improve intravascular haemodynamics. The tapered stent allows the tapered artery to obtain better haemodynamics and reduces the probability of ISR.

Pure iron and its biocompatible and biodegradable alloys have a high potential to be used for temporary load bearing medical implants. Nevertheless, the formation of passive iron oxide and hydroxide layers, which lead to a considerably low degradation rate at the physiological environment, has highly restricted their application. Herein we used numerical and experimental methods to evaluate the effect of severe shot peening, as a scalable mechanical surface treatment, on adjusting the performance of pure iron for biomedical applications. The developed numerical model was used to identify the range of peening parameters that would promote grain refinement on the pure iron surface. Experimental tests were then performed to analyze the gradient structure and the characteristics of the interface free surface layer created on peened samples. The results indicated that severe shot peening could notably increase the surface roughness and wettability, induce remarkable surface deformation and grain refinement, enhance surface hardness and generate high in-depth compressive residual stresses. The increased surface roughness besides the high concentration of micro cracks and dislocation density in the grain refined top layer promoted pure iron's degradation in the biologically simulated environment. Statement of Significance: Biodegradable metallic materials with resorbable degradation products have a high potential to be used for temporary implants such as screws, pins, staples, etc. They can eliminate the need for implant retrieval surgery after the damaged tissue is healed, and result in reduced patient suffering besides lowered hospitalization costs. Pure iron is biodegradable and is an essential nutrient in human body; however, its application as biomedical implant is highly restricted by its slow degradation rate in physiological environment. We applied a scalable surface treatment able to induce grain refinement and increase surface roughness. This treatment enhances mechanical performance of pure iron and accelerates its degradation rate, paving the way for its broader applications for biomedical implants.

Magnetohydrodynamic (MHD) bioconvective flow of Williamson nanomaterial in frame of gyrotactic microorganisms is addressed. Nanomaterial characterizes gyrotactic microorganism. Bioconvection is generated by buoyancy forces in the communication of nanoparticles and motile microorganisms. The use of gyrotactic microorganisms into nanofluid here is just to stabilize the nanoparticles to suspend due to a phenomenon called bioconvection. Newtonian conditions for thermal, solutal and motile microorganism are employed. The transformed nonlinear systems of momentum, energy, nanoparticles concentration and motile microorganisms density are solved numerically through the bvp4c technique. Significance of various variables on physical quantities is explained graphically.

Hormone therapy is one of the popular therapeutic methods for prostate cancer. Intermittent androgen suppression (IAS) is the method which stops and resumes hormone therapy repeatedly. The efficacy of IAS differs depending on patients; both the cases have been reported where the relapse of cancer happened and did not happen, for the patients who had undergone IAS. For the patients who cannot avoid the relapse of cancer by IAS, we should delay the relapse of cancer as later as possible. Here we compared some practical methods of determining when to stop and restart hormone therapy for IAS using an existing mathematical model of prostate cancer. The method we suggest is to determine the ratio of on-treatment period and off-treatment period sparsely for each cycle, namely the “sparse search.” We also compared the performance of the sparse search with the exhaustive search and the model predictive control. We found that the sparse search can find a good treatment schedule without failure, and the computational cost is not so high compared to the exhaustive method. In addition, we focus on the model predictive control (MPC) method which has been applied to the scheduling of IAS in some existing studies. The MPC is computationary efficient, although it does not always find an optimal schedule in the numerical experiments here. We believe that the MPC method might be also promising because of its reasonable computational costs and its possibility of expanding of the model.

PURPOSE: Patient-specific models of the heart can be used to improve the diagnosis of cardiac diseases, but practical application of these models can be impeded by the computational costs and numerical uncertainties of fitting mechanistic models to clinical measurements from individual patients. Reliable and efficient tuning of these models within clinically appropriate error bounds is a requirement for practical deployment in the time-constrained environment of the clinic. METHODS: We developed an optimization framework to tune parameters of patient-specific mechanistic models using routinely-acquired non-invasive patient data more efficiently than manual methods. We employ a hybrid particle swarm and pattern search optimization algorithm, but the framework can be readily adapted to use other optimization algorithms. RESULTS: We apply the proposed framework to tune full-cycle lumped parameter circulatory models using clinical data. We show that our framework can be easily adapted to optimize cross-species models by tuning the parameters of the same circulation model to four canine subjects. CONCLUSIONS: This work will facilitate the use of biomechanics and circulatory cardiac models in both clinical and research environments by ameliorating the tedious process of manually fitting the parameters.

The adhesion morphology of a cell monolayer results in a mechanical force inside cells, between cells, or between cells and substrates. The mechanical force regulates the differentiation of stem cells, but its influence on cell fusion is seldom studied. The present study is focused on osteoclast precursors, RAW264.7 monocytes, which can fuse into multinucleated cells (MNCs) responsible for bone resorption. Cells were cultured on circular and ring-like patterned substrates. Then, cell fusion, cell-substrate traction force, and force-sensitive molecules in different regions were measured and analyzed. Results showed that MNCs mainly appeared in the interior of the ring-like pattern and the central zone of the circular pattern, where both cell-substrate traction force and in-plane maximal shear stress were smaller than that at the patterns' edge. The immunostaining results revealed that F-actin, vinculin, β-catenin, and E-cadherin were highly distributed at the edge of patterns. High seeding density of cells promoted mechanical force-dependent fusion. When calcium-dependent cell-cell connections were inhibited by E-cadherin antibody or low-calcium medium, the fusion into MNCs was greatly reduced. Thus, the morphology of cell monolayer decides the mechanical state of cell-substrate interaction and cell-cell connection, ultimately regulating the fusion of osteoclast precursors.

More than eighty percent of pancreatic cancer involves ductal adenocarcinoma with an abundant desmoplastic extracellular matrix surrounding the solid tumor entity. This aberrant tumor microenvironment facilitates a strong resistance of pancreatic cancer to medication. Although various therapeutic strategies have been reported to be effective in mice with pancreatic cancer, they still need to be tested quantitatively in wider animal-based experiments before being applied as therapies. To aid the design of experiments, we develop a cell-based mathematical model to describe cancer progression under therapy with a specific application to pancreatic cancer. The displacement of cells is simulated by solving a large system of stochastic differential equations with the Euler–Maruyama method. We consider treatment with the PEGylated drug PEGPH20 that breaks down hyaluronan in desmoplastic stroma followed by administration of the chemotherapy drug gemcitabine to inhibit the proliferation of cancer cells. Modeling the effects of PEGPH20 + gemcitabine concentrations is based on Green’s fundamental solutions of the reaction–diffusion equation. Moreover, Monte Carlo simulations are performed to quantitatively investigate uncertainties in the input parameters as well as predictions for the likelihood of success of cancer therapy. Our simplified model is able to simulate cancer progression and evaluate treatments to inhibit the progression of cancer. Electronic supplementary material The online version of this article (10.1007/s10237-019-01219-0) contains supplementary material, which is available to authorized users.

Modeling tumor growth in biological systems is a challenging problem with important consequences for diagnosis and treatment of various forms of cancer. This growth process requires large simulation complexity due to evolving biological and chemical processes in living tissue and interactions of cellular and vascular constituents in living organisms. Herein, we describe with a phase-field model, namely the Cahn-Hilliard equation the intricate interactions between the tumors and their host tissue. The spatial discretization uses highly-continuous isogeometric elements. For fast simulation of the time-dependent Cahn-Hilliard equation, we employ an alternating directions implicit methodology. Thus, we reduce the original problems to Kronecker products of 1 D matrices that can be factorized in a linear computational cost. The implementation enables parallel multi-core simulations and shows good scalability on shared-memory multi-core machines. Combined with the high accuracy of isogeometric elements, our method shows high efficiency in solving the Cahn-Hilliard equation on tensor-product meshes.

Column selection and experimental design are recognized to be wear-and-tear processes to obtain a good fingerprinting result with comprehensive two dimensional gas chromatography (GC × GC). The processes involve a large number of experiments for analysis of each sample due to the optimized conditions depending on the selected column sets. In this study, the analytical solutions of time summation model combined with temperature dependent linear solvation energy relationship (LSER) were derived for constant flow separation in GC × GC. The derived equations allow calculation of analyte retention time in first and second dimensional separation (1tR and 2tR), under temperature program separation employing any column combination with known LSER database. As a result, optimization software was developed enabling simulation of several hundred thousand GC × GC results (fingerprints) for separation of each sample. Good correlations between our predicted results and the results obtained with the previously established numerical approach, were obtained with the R2 of 1.000 and 0.998 for simulation of 1tR and 2tR, respectively. The developed approaches were further applied to simulation of 96,000 individual fingerprints in temperature programmed GC × GC, with the focus on application of 16 column sets including non-ionic liquid and ionic liquid (IL) stationary phases for separation of 678 model compounds. These approaches resulted in the computational time of 1 day compared with 1 year provided by the numerical method. Best column sets and experimental conditions (secondary column lengths and temperature programs) could then be extracted according to maximizing number of separated peaks in separation, which represents the quality of each fingerprinting.

Vortex structures, as one of the most important features of cardiac flow, have a crucial impact on the left ventricle function and pathological conditions. These swirling flows are closely related to the presence of turbulence in left ventricle which is investigated in the current study. Using an extended model of the left heart, including a fluid-structure interaction (FSI) model of the mitral valve with a realistic geometry, the effect of using two numerical turbulent models, k-ε and Spalart-Allmaras (SA), on diastolic flow patterns is studied and compared with results from laminar flow model. As a result of the higher dissipation rate in turbulent models (k-ε and SA), vortices are larger and stronger in the laminar flow model. Comparing E/A ratio in the three models (Laminar, k-ε, and SA) with experimental data from healthy subjects, it is concluded that the results from k-ε model are more accurate.

During intraerythrocytic development, the human malaria parasite Plasmodium falciparum alters the mechanical deformability of its host cell. The underpinning biological processes involve gain in parasite mass, changes in the membrane protein compositions, reorganization of the cytoskeletons and its coupling to the plasma membrane, and formation of membrane protrusions, termed knobs. The hemoglobinopathies S and C are known to partially protect carriers from severe malaria, possibly through additional changes in the erythrocyte biomechanics, but a detailed quantification of cell mechanics is still missing. Here, we combined flicker spectroscopy and a mathematical model and demonstrated that knob formation strongly suppresses membrane fluctuations by increasing membrane-cytoskeleton coupling. We found that the confinement increased with hemoglobin S but decreases with hemoglobin C in spite of comparable knob densities and diameters. We further found that the membrane bending modulus strongly depends on the hemoglobinopathetic variant, suggesting increased amounts of irreversibly oxidized hemichromes bound to membranes., Fröhlich et al. show that membrane protrusions of malaria parasite-infected blood cells reduce their membrane fluctuation due to the enforced coupling of membrane and cytoskeleton. Differential cellular mechanics of blood cells possessing variant hemoglobins that protect people from malaria suggests that oxidative stress may explain the selective advantage of certain hemoglobin variants.

Onset of flow transition in a sinusoidally oscillating flow through a rigid, constant area circular pipe with a smooth sinusoidal obstruction in the center of the pipe is studied by performing direct numerical simulations, with resolutions close to the Kolmogorov microscales. The studied pipe is stenosed in the center with a 75% reduction in area in two distinct configurations-one that is symmetric to the axis of the parent pipe and the other that is offset by 0.05 diameters to introduce an eccentricity, which disturbs the flow thereby triggering the onset of flow transition. The critical Reynolds number at which the flow transitions to turbulence for a zero-mean oscillatory flow through a stenosis is shown to be nearly tripled in comparison with studies of pulsating unidirectional flow through the same stenosis. The onset of transition is further explored with three different flow pulsation frequencies resulting in a total of 90 simulations conducted on a supercomputer. It is found that the critical Reynolds number at which the oscillatory flow transitions is not affected by the pulsation frequencies. The locations of flow breakdown and re-stabilization post-stenosis are, however, respectively shifted closer to the stenosis throat with increasing pulsation frequencies. The results show that oscillatory physiological flows, while more stable, exhibit fluctuations due to geometric complexity and have implications in studies of dispersion and solute transport in the cerebrospinal fluid flow and understanding of pathological conditions.

An explicit immersed boundary-lattice Boltzmann method is applied to numerically investigate the dynamics of primary cilium in pulsatile blood flows with two-way fluid-structure interaction considered. To well characterize the effect of cilium basal body on cilium dynamics, the cilium base is modeled as a nonlinear rotational spring attached to the cilium's basal end as proposed by Resnick (Biophys J 109:18-25, 2015. https://doi.org/10.1016/j.bpj.2015.05.031). After several careful validations, the fluid-cilium interaction system is investigated in detail at various pulsatile flow conditions that are characterized by peak Reynolds numbers ([Formula: see text]) and Womersley numbers ([Formula: see text]). The periodic flapping of primary cilium observed in our simulations is very similar to the in vivo ciliary oscillation captured by O'Connor et al. (Cilia 2:8, 2013. https://doi.org/10.1186/2046-2530-2-8). The cilium's dynamics is found to be closely related to the [Formula: see text] and [Formula: see text]. Increase the [Formula: see text] or decrease the [Formula: see text] bring to an increase in the cilium's flapping amplitude, tip angular speed, basal rotation, and maximum tensile stress. It is also demonstrated that by reducing the [Formula: see text] or enhancing the [Formula: see text] to a certain level, one can shift the flapping pattern of cilium from its original two-side one to a one-side one, making the stretch only happen on one particular side. During the flapping process, the location of the maximum tensile stress is not always found at the basal region; instead, it is able to propagate from time to time within a certain distance to the base. Due to the obstruction of the primary cilium, the distribution of wall shear stress no longer remains uniform as in the absence of cilia. It oscillates in space with the minimum magnitude which is always found near where the cilium is located. The presence of cilium also reduces the overall level of wall shear stress, especially at the region near the cilium's anchor point.

Two dimensional, steady state, and incompressible blood and bile flows through the liver lobules are numerically simulated. Two different geometric models A and B are proposed to study the effects of lobule structure on the fluid flow behaviour. In Model A, the lobule tissue is represented as a hexagonal shape porous medium with a set of flow channels at its vertices accounting for the hepatic artery, portal and central veins along with bile ductules. Model B is a channelized porous medium constructed by adding a set of flow channels, representing the bile canaliculies and lobule sinusoids, to Model A. The bile and blood flow through the lobule is simulated by the finite element approach, based on the Darcy/Brinkman equations in the lobule tissue and the Navier-Stokes (or Stokes) equations in the flow channels. In Model B, a transmission factor on the boundaries of the bile canaliculies is introduced to connect the bile and blood flows. First, a single regular lobule is utilized to exhibit the fluid flow pattern through the liver lobule represented by proposed geometric models. Then, the model is extended to a group of liver lobules to demonstrate the flow through a liver slice represented by irregular lobules. Numerical results indicate that the Darcy and Brinkman equations provide nearly the same solutions for Model A and similar solutions with a little difference for Model B. It is shown that the existence of sinusoids and bile canaliculies inside the liver lobules has noticeable effects on its fluid flow pattern, in terms of pressure and velocity fields.

This study analyzes the lethal clinical condition of aortic dissections from a numerical point of view. On the basis of previous contributions by Gültekin et al. (Comput Methods Appl Mech Eng 312:542-566, 2016 and 331:23-52, 2018), we apply a holistic geometrical approach to fracture, namely the crack phase-field, which inherits the intrinsic features of gradient damage and variational fracture mechanics. The continuum framework captures anisotropy, is thermodynamically consistent and is based on finite strains. The balance of linear momentum and the crack evolution equation govern the coupled mechanical and phase-field problem. The solution scheme features the robust one-pass operator-splitting algorithm upon temporal and spatial discretizations. Based on experimental data of diseased human thoracic aortic samples, the elastic material parameters are identified followed by a sensitivity analysis of the anisotropic phase-field model. Finally, we simulate an incipient propagation of an aortic dissection within a multi-layered segment of a thoracic aorta that involves a prescribed initial tear. The finite element results demonstrate a severe damage zone around the initial tear and exhibit a rather helical crack pattern, which aligns with the fiber orientation. It is hoped that the current contribution can provide some directions for further investigations of this disease.

A profound analysis of pressure and flow wave propagation in cardiovascular systems is the key in noninvasive assessment of hemodynamic parameters. Pulse transit time (PTT), which closely relates to the physical properties of the cardiovascular system, can be linked to variations of blood pressure and stroke volume to provide information for patient-specific clinical diagnostics. In this work, we present mathematical and numerical tools, capable of accurately predicting the PTT, local pulse wave velocity, vessel compliance, and pressure/flow waveforms, in a viscous hyperelastic cardiovascular network. A new one-dimensional framework, entitled cardiovascular flow analysis (CardioFAN), is presented to describe the pulsatile fluid-structure interaction in the hyperelastic arteries, where pertaining hyperbolic equations are solved using a high-resolution total variation diminishing Lax-Wendroff method. The computational algorithm is validated against well-known numerical, in vitro and in vivo data for networks of main human arteries with 55, 37 and 26 segments, respectively. PTT prediction is improved by accounting for hyperelastic nonlinear waves between two arbitrary sections of the arterial tree. Consequently, arterial compliance assignments at each segment are improved in a personalized model of the human aorta and supra-aortic branches with 26 segments, where prior in vivo data were available for comparison. This resulted in a 1.5% improvement in overall predictions of the waveforms, or average relative errors of 5.5% in predicting flow, luminal area and pressure waveforms compared to prior in vivo measurements. The open source software, CardioFAN, can be calibrated for arbitrary patient-specific vascular networks to conduct noninvasive diagnostics.

The solute transport distribution in a tumor is an important criterion in the evaluation of the cancer treatment efficacy. The fraction of killed cells after each treatment can quantify the therapeutic effect and plays as a helpful tool to evaluate the chemotherapy treatment schedules. In the present study, an image-based spatio-temporal computational model of a solid tumor is provided for calculation of interstitial fluid flow and solute transport. Current model incorporates heterogeneous microvasculature for angiogenesis instead of synthetic mathematical modeling. In this modeling process, a comprehensive model according to Convection-Diffusion-Reaction (CDR) equations is employed due to its high accuracy for simulating the binding and the uptake of the drug by tumor cells. Based on the velocity and the pressure distribution, transient distribution of the different drug concentrations (free, bound, and internalized) is calculated. Then, the fraction of killed cells is obtained according to the internalized concentration. Results indicate the dependence of the drug distribution on both time and space, as well as the microvasculature density. Free and bound drug concentration have the same trend over time, whereas, internalized and total drug concentration increases over time and reaches a constant value. The highest amount of concentration occurred in the tumor region due to the higher permeability of the blood vessels. Moreover, the fraction of killed cells is approximately 78.87% and 24.94% after treatment with doxorubicin for cancerous and normal tissues, respectively. In general, the presented methodology may be applied in the field of personalized medicine to optimize patient-specific treatments. Also, such image-based modeling of solid tumors can be used in laboratories that working on drug delivery and evaluating new drugs before using them for any in vivo or clinical studies.

Background Validating new techniques for fetal cardiovascular magnetic resonance (CMR) is challenging due to random fetal movement that precludes repeat measurements. Consequently, fetal CMR development has been largely performed using physical phantoms or postnatal volunteers. In this work, we present an open-source simulation designed to aid in the development and validation of new approaches for fetal CMR. Our approach, fetal extended Cardiac-Torso cardiovascular magnetic resonance imaging (Fetal XCMR), builds on established methods for simulating CMR acquisitions but is tailored toward the dynamic physiology of the fetal heart and body. We present comparisons between the Fetal XCMR phantom and data acquired in utero, resulting in image quality, anatomy, tissue signals and contrast. Methods Existing extended Cardiac-Torso models are modified to create maternal and fetal anatomy, combined according to simulated motion, mapped to CMR contrast, and converted to CMR data. To provide a comparison between the proposed simulation and experimental fetal CMR images acquired in utero, images from a typical scan of a pregnant woman are included and simulated acquisitions were generated using matching CMR parameters, motion and noise levels. Three reconstruction (static, real-time, and CINE), and two motion estimation methods (translational motion, fetal heart rate) from data acquired in transverse, sagittal, coronal, and short-axis planes of the fetal heart were performed to compare to in utero acquisitions and demonstrate feasibility of the proposed simulation framework. Results Overall, CMR contrast, morphologies, and relative proportions of the maternal and fetal anatomy are well represented by the Fetal XCMR images when comparing the simulation to static images acquired in utero. Additionally, visualization of maternal respiratory and fetal cardiac motion is comparable between Fetal XCMR and in utero real-time images. Finally, high quality CINE image reconstructions provide excellent delineation of fetal cardiac anatomy and temporal dynamics for both data types. Conclusion The fetal CMR phantom provides a new method for evaluating fetal CMR acquisition and reconstruction methods by simulating the underlying anatomy and physiology. As the field of fetal CMR continues to grow, new methods will become available and require careful validation. The fetal CMR phantom is therefore a powerful and convenient tool in the continued development of fetal cardiac imaging. Electronic supplementary material The online version of this article (10.1186/s12968-019-0539-2) contains supplementary material, which is available to authorized users.