Quantifying uncertainty in parameter estimates for stochastic models of collective cell spreading using approximate Bayesian computation

Wound healing and tumour growth involve collective cell spreading, which is driven by individual motility and proliferation events within a population of cells. Mathematical models are often used to interpret experimental data and to estimate the parameters so that predictions can be made. Existing methods for parameter estimation typically assume that these parameters are constants and often ignore any uncertainty in the estimated values. We use approximate Bayesian computation (ABC) to estimate the cell diffusivity, D, and the cell proliferation rate, λ, from a discrete model of collective cell spreading, and we quantify the uncertainty associated with these estimates using Bayesian inference. We use a detailed experimental data set describing the collective cell spreading of 3T3 fibroblast cells. The ABC analysis is conducted for different combinations of initial cell densities and experimental times in two separate scenarios: (i) where collective cell spreading is driven by cell motility alone, and (ii) where collective cell spreading is driven by combined cell motility and cell proliferation. We find that D can be estimated precisely, with a small coefficient of variation (CV) of 2–6%. Our results indicate that D appears to depend on the experimental time, which is a feature that has been previously overlooked. Assuming that the values of D are the same in both experimental scenarios, we use the information about D from the first experimental scenario to obtain reasonably precise estimates of λ, with a CV between 4 and 12%. Our estimates of D and λ are consistent with previously reported values; however, our method is based on a straightforward measurement of the position of the leading edge whereas previous approaches have involved expensive cell counting techniques. Additional insights gained using a fully Bayesian approach justify the computational cost, especially since it allows us to accommodate information from different experiments in a principled way.

A semi-alternating direction method for a 2-D fractional FitzHugh–Nagumo monodomain model on an approximate irregular domain

A FitzHugh-Nagumo monodomain model has been used to describe the propagation of the electrical potential in heterogeneous cardiac tissue. In this paper, we consider a two-dimensional fractional FitzHugh-Nagumo monodomain model on an irregular domain. The model consists of a coupled Riesz space fractional nonlinear reaction-diffusion model and an ordinary differential equation, describing the ionic fluxes as a function of the membrane potential. Secondly, we use a decoupling technique and focus on solving the Riesz space fractional nonlinear reaction-diffusion model. A novel spatially second-order accurate semi-implicit alternating direction method (SIADM) for this model on an approximate irregular domain is proposed. Thirdly, stability and convergence of the SIADM are proved. Finally, some numerical examples are given to support our theoretical analysis and these numerical techniques are employed to simulate a two-dimensional fractional Fitzhugh-Nagumo model on both an approximate circular and an approximate irregular domain.

A Crank--Nicolson ADI spectral method for a two-dimensional riesz space fractional nonlinear reaction-diffusion equation

In this paper, a new alternating direction implicit Galerkin--Legendre spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation is developed. The temporal component is discretized by the Crank--Nicolson method. The detailed implementation of the method is presented. The stability and convergence analysis is strictly proven, which shows that the derived method is stable and convergent of order $2$ in time. An optimal error estimate in space is also obtained by introducing a new orthogonal projector. The present method is extended to solve the fractional FitzHugh--Nagumo model. Numerical results are provided to verify the theoretical analysis.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation

In this paper, we consider a two-sided space-fractional diffusion equation with variable coefficients on a finite domain. Firstly, based on the nodal basis functions, we present a new fractional finite volume method for the two-sided space-fractional diffusion equation and derive the implicit scheme and solve it in matrix form. Secondly, we prove the stability and convergence of the implicit fractional finite volume method and conclude that the method is unconditionally stable and convergent. Finally, some numerical examples are given to show the effectiveness of the new numerical method, and the results are in excellent agreement with theoretical analysis.

A Novel High Order Space-Time Spectral Method for the Time Fractional Fokker--Planck Equation

The fractional Fokker-Planck equation is an important physical model for simulating anomalous diffusions with external forces. Because of the non-local property of the fractional derivative an interesting problem is to explore high accuracy numerical methods for fractional differential equations. In this paper, a space-time spectral method is presented for the numerical solution of the time fractional Fokker-Planck initial-boundary value problem. The proposed method employs the Jacobi polynomials for the temporal discretization and Fourier-like basis functions for the spatial discretization. Due to the diagonalizable trait of the Fourier-like basis functions, this leads to a reduced representation of the inner product in the Galerkin analysis. We prove that the time fractional Fokker-Planck equation attains the same approximation order as the time fractional diffusion equation developed in [23] by using the present method. That indicates an exponential decay may be achieved if the exact solution is sufficiently smooth. Finally, some numerical results are given to demonstrate the high order accuracy and efficiency of the new numerical scheme. The results show that the errors of the numerical solutions obtained by the space-time spectral method decay exponentially.

A method for optimal fit of patient-specific fracture fixation plates

Anatomically pre-contoured fracture fixation plates are a treatment option for bone fractures. A well-fitting plate can be used as a tool for anatomical reduction of the fractured bone. However, recent studies showed that some plates fit poorly for many patients due to considerable shape variations between bones of the same anatomical site. Therefore, the plates have to be manually fitted and deformed by surgeons to fit each patient optimally. The process is time-intensive and labor-intensive, and could lead to adverse clinical implications such as wound infection or plate failure. This paper proposes a new iterative method to simulate the patient-specific deformation of an optimally fitting plate for pre-operative planning purposes. We further demonstrate the validation of the method through a case study. The proposed method involves the integration of four commercially available software tools, Matlab, Rapidform2006, SolidWorks, and ANSYS, each performing specific tasks to obtain a plate shape that fits optimally for an individual tibia and is mechanically safe. A typical challenge when crossing multiple platforms is to ensure correct data transfer. We present an example of the implementation of the proposed method to demonstrate successful data transfer between the four platforms and the feasibility of the method.

An improved modal strain energy method for structural damage detection, 2D simulation

Structural damage detection using modal strain energy (MSE) is one of the most efficient and reliable structural health monitoring techniques. However, some of the existing MSE methods have been validated for special types of structures such as beams or steel truss bridges which demands improving the available methods. The purpose of this study is to improve an efficient modal strain energy method to detect and quantify the damage in complex structures at early stage of formation. In this paper, a modal strain energy method was mathematically developed and then numerically applied to a fixed-end beam and a three-story frame including single and multiple damage scenarios in absence and presence of up to five per cent noise. For each damage scenario, all mode shapes and natural frequencies of intact structures and the first five mode shapes of assumed damaged structures were obtained using STRAND7. The derived mode shapes of each intact and damaged structure at any damage scenario were then separately used in the improved formulation using MATLAB to detect the location and quantify the severity of damage as compared to those obtained from previous method. It was found that the improved method is more accurate, efficient and convergent than its predecessors. The outcomes of this study can be safely and inexpensively used for structural health monitoring to minimize the loss of lives and property by identifying the unforeseen structural damages.

Generalized element load method for first- and second-order element solutions with element load effect

The finite element method in principle adaptively divides the continuous domain with complex geometry into discrete simple subdomain by using an approximate element function, and the continuous element loads are also converted into the nodal load by means of the traditional lumping and consistent load methods, which can standardise a plethora of element loads into a typical numerical procedure, but element load effect is restricted to the nodal solution. It in turn means the accurate continuous element solutions with the element load effects are merely restricted to element nodes discretely, and further limited to either displacement or force field depending on which type of approximate function is derived. On the other hand, the analytical stability functions can give the accurate continuous element solutions due to element loads. Unfortunately, the expressions of stability functions are very diverse and distinct when subjected to different element loads that deter the numerical routine for practical applications. To this end, this paper presents a displacement-based finite element function (generalised element load method) with a plethora of element load effects in the similar fashion that never be achieved by the stability function, as well as it can generate the continuous first- and second-order elastic displacement and force solutions along an element without loss of accuracy considerably as the analytical approach that never be achieved by neither the lumping nor consistent load methods. Hence, the salient and unique features of this paper (generalised element load method) embody its robustness, versatility and accuracy in continuous element solutions when subjected to the great diversity of transverse element loads.

Wonder and method

In this paper, my aim is to address the twin concerns raised in this session - models of practice and geographies or spaces of practice - through regarding a selection of works and processes that have arisen from my recent research. Setting up this discussion, I first present a short critique of the idea of models of creative practice, recognising possible problems with the attempt to generalise or abstract its complexities. Working through a series of portraits of my working environment, I will draw from Lefebvre’s Rhythmanalysis as a way of understanding an art practice both spatially and temporally, suggesting that changes and adjustments can occur through attending to both intuitions and observations of the complex of rhythmic layers constantly at play in any event. Reflecting on my recent studio practice I explore these rhythms through the evocation of a twin axis: the horizontal and the vertical and the arcs of difference or change that occur between them, in both spatial and temporal senses. What this analysis suggests is the idea that understanding does not only emerge from the construction of general principles, derived from observation of the particular, but that the study of rhythms allows us to maintain the primacy of the particular. This makes it well suited to a study of creative methods and objects, since it is to the encounter with and expression of the particular that art practices, most certainly my own, are frequently directed.

Vibration based baseline updating method to localize crack formation and propagation in reinforced concrete members

Structural Health Monitoring (SHM) schemes are useful for proper management of the performance of structures and for preventing their catastrophic failures. Vibration based SHM schemes has gained popularity during the past two decades resulting in significant research. It is hence evitable that future SHM schemes will include robust and automated vibration based damage assessment techniques (VBDAT) to detect, localize and quantify damage. In this context, the Damage Index (DI) method which is classified as non-model or output based VBDAT, has the ability to automate the damage assessment process without using a computer or numerical model along with actual measurements. Although damage assessment using DI methods have been able to achieve reasonable success for structures made of homogeneous materials such as steel, the same success level has not been reported with respect to Reinforced Concrete (RC) structures. The complexity of flexural cracks is claimed to be the main reason to hinder the applicability of existing DI methods in RC structures. Past research also indicates that use of a constant baseline throughout the damage assessment process undermines the potential of the Modal Strain Energy based Damage Index (MSEDI). To address this situation, this paper presents a novel method that has been developed as part of a comprehensive research project carried out at Queensland University of Technology, Brisbane, Australia. This novel process, referred to as the baseline updating method, continuously updates the baseline and systematically tracks both crack formation and propagation with the ability to automate the damage assessment process using output only data. The proposed method is illustrated through examples and the results demonstrate the capability of the method to achieve the desired outcomes.

An improved computational method in structural dynamics

Purpose – In structural, earthquake and aeronautical engineering and mechanical vibration, the solution of dynamic equations for a structure subjected to dynamic loading leads to a high order system of differential equations. The numerical methods are usually used for integration when either there is dealing with discrete data or there is no analytical solution for the equations. Since the numerical methods with more accuracy and stability give more accurate results in structural responses, there is a need to improve the existing methods or develop new ones. The paper aims to discuss these issues. Design/methodology/approach – In this paper, a new time integration method is proposed mathematically and numerically, which is accordingly applied to single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. Finally, the results are compared to the existing methods such as Newmark’s method and closed form solution. Findings – It is concluded that, in the proposed method, the data variance of each set of structural responses such as displacement, velocity, or acceleration in different time steps is less than those in Newmark’s method, and the proposed method is more accurate and stable than Newmark’s method and is capable of analyzing the structure at fewer numbers of iteration or computation cycles, hence less time-consuming. Originality/value – A new mathematical and numerical time integration method is proposed for the computation of structural responses with higher accuracy and stability, lower data variance, and fewer numbers of iterations for computational cycles.

Blast response of segmented bored tunnel using coupled SPH–FE method

Underground transport tunnels are vulnerable to blast events. This paper develops and applies a fully coupled technique involving the Smooth Particle Hydrodynamics and Finite Element techniques to investigate the blast response of segmented bored tunnels. Findings indicate that several bolts failed in the longitudinal direction due to redistribution of blast loading to adjacent tunnel rings. The tunnel segments respond as arch mechanisms in the transverse direction and suffered damage mainly due to high bending stresses. The novel information from the present study will enable safer designs of buried tunnels and provide a benchmark reference for future developments in this area.

Comparison of Body Composition Assessment Methods in Breast Cancer Survivors

Purpose/Objectives: To examine and compare the reliability of four body composition methods commonly used in assessing breast cancer survivors. Design: Cross-sectional. Setting: A rehabilitation facility at a university-based comprehensive cancer center in the southeastern United States. Sample: 14 breast cancer survivors aged 40-71 years. Methods: Body fat (BF) percentage was estimated via bioelectric impedance analysis (BIA), air displacement plethysmography (ADP), and skinfold thickness (SKF) using both three- and seven-site algorithms, where reliability of the methods was evaluated by conducting two tests for each method (test 1 and test 2), one immediately after the other. An analysis of variance was used to compare the results of BF percentage among the four methods. Intraclass correlation coefficient (ICC) was used to test the reliability of each method. Main Research Variable: BF percentage. Findings: Significant differences in BF percentage were observed between BIA and all other methods (three-site SKF, p < 0.001; seven-site SKF, p < 0.001; ADP, p = 0.002). No significant differences (p > 0.05) in BF percentage between three-site SKF, seven-site SKF, and ADP were observed. ICCs between test 1 and test 2 for each method were BIA = 1, ADP = 0.98, three-site SKF = 0.99, and seven-site SKF = 0.94. Conclusions: ADP and both SKF methods produce similar estimates of BF percentage in all participants, whereas BIA overestimated BF percentage relative to the other measures. Caution is recommended when using BIA as the body composition method for breast cancer survivors who have completed treatment but are still undergoing adjuvant hormonal therapy. Implications for Nursing: Measurements of body composition can be implemented very easily as part of usual care and should serve as an objective outcome measure for interventions designed to promote healthy behaviors among breast cancer survivors. - See more at: https://onf.ons.org/onf/38/4/comparison-body-composition-assessment-methods-breast-cancer-survivors#sthash.5djfTS1Q.dpuf