Investigation of the influence of reflection on the attenuation of cancellous bone

The model proposed in this paper is based on the fact that the reflection might have a significant contribution to the attenuation of the acoustic waves propagating through the cancellous bone. The numerical implementation of the mentioned effect is realized by the development of a new representative volume element that includes an infinitesimally thin ‘transient’ layer on the contact surface of the bone and the marrow. This layer serves to model the amplitude transformation of the incident wave by the transition through media with different acoustic impedances and to take into account the energy loss due to the reflection. The proposed representative volume element together with the multiscale finite element is used to simulate the wave propagation and to evaluate the attenuation coefficient for samples with different effective densities in the dependence of the applied excitation frequency. The obtained numerical values show a very good agreement with the experimental results. Moreover, the model enables the determination of the upper and the lower bound for the attenuation coefficient.     

A finite element model for analyzing shear wave propagation observed in magnetic resonance elastography

Magnetic resonance elastography (MRE) is a novel non-invasive approach to determine material stiffness by using a conventional magnetic resonance imaging (MRI) system incorporated with an oscillating motion-sensitizing gradient to detect nodal displacements produced by a shear excitation wave. The effects of material properties, excitation frequency, boundary conditions, and applied tension on shear wavelength measurement must be examined before MRE can become a useful diagnostic tool. We propose finite element (FE) modeling as a robust method to systematically study the effects of these parameters. An axisymmetric FE model was generated with ABAQUS to simulate agarose gel phantoms. The effects of material stiffness, density, and excitation frequency on propagating shear wavelength were examined individually. The effect of the boundary conditions on shear wavelength was also demonstrated. Results of shear wavelength from MRE measurement were compared with the results of FE model, which showed good agreement between the methods.     

Novel Multiscale Modeling Tool Applied to Pseudomonas aeruginosa Biofilm Formation

Multiscale modeling is used to represent biological systems with increasing frequency and success. Multiscale models are often hybrids of different modeling frameworks and programming languages. We present the MATLAB-NetLogo extension (MatNet) as a novel tool for multiscale modeling. We demonstrate the utility of the tool with a multiscale model of Pseudomonas aeruginosa biofilm formation that incorporates both an agent-based model (ABM) and constraint-based metabolic modeling. The hybrid model correctly recapitulates oxygen-limited biofilm metabolic activity and predicts increased growth rate via anaerobic respiration with the addition of nitrate to the growth media. In addition, a genome-wide survey of metabolic mutants and biofilm formation exemplifies the powerful analyses that are enabled by this computational modeling tool.     

Predictive multiscale computational model of shoe-floor coefficient of friction

Understanding the frictional interactions between the shoe and floor during walking is critical to prevention of slips and falls, particularly when contaminants are present. A multiscale finite element model of shoe-floor-contaminant friction was developed that takes into account the surface and material characteristics of the shoe and flooring in microscopic and macroscopic scales. The model calculates shoe-floor coefficient of friction (COF) in boundary lubrication regime where effects of adhesion friction and hydrodynamic pressures are negligible. The validity of model outputs was assessed by comparing model predictions to the experimental results from mechanical COF testing. The multiscale model estimates were linearly related to the experimental results (p < 0.0001). The model predicted 73% of variability in experimentally-measured shoe-floor-contaminant COF. The results demonstrate the potential of multiscale finite element modeling in aiding slip-resistant shoe and flooring design and reducing slip and fall injuries.     

A mathematical model of combination therapy using the EGFR signaling network

An increasing awareness of the significance of abnormal signal transduction in tumors and the concomitant development of target-based drugs to selectively modulate aberrantly-activated signaling pathways has given rise to a variety of promising new strategies in cancer treatment. This paper uses mathematical modeling to investigate a novel type of combination therapy in which multiple nodes in a signaling cascade are targeted simultaneously with selective inhibitors, pursuing the hypothesis that such an approach may induce the desired signal attenuation with lower doses of the necessary agents than when one node is targeted in isolation. A mathematical model is presented which builds upon previous theoretical work on EGFR signaling, simulating the effect of administering multiple kinase inhibitors in various combinations. The model demonstrates that attenuation of biochemical signals is significantly enhanced when multiple upstream processes are inhibited, in comparison with the inhibition of a single upstream process. Moreover, this enhanced attenuation is most pronounced in signals downstream of serially-connected target points. In addition, the inhibition of serially-connected processes appears to have a supra-additive (synergistic) effect on the attenuation of downstream signals, owing to the highly non-linear relationships between network parameters and signals.     

Modeling and simulation of chemomechanics at the cell-matrix interface

Chemomechanical characteristics of the extracellular materials with which cells interact can have a profound impact on cell adhesion and migration. To understand and modulate such complex multiscale processes, a detailed understanding of the feedback between a cell and the adjacent microenvironment is crucial. Here, we use computational modeling and simulation to examine the cell-matrix interaction at both the molecular and continuum lengthscales. Using steered molecular dynamics, we consider how extracellular matrix (ECM) stiffness and extracellular pH influence the interaction between cell surface adhesion receptors and extracellular matrix ligands, and we predict potential consequences for focal adhesion formation and dissolution. Using continuum level finite element simulations and analytical methods to model cell-induced ECM deformation as a function of ECM stiffness and thickness, we consider the implications toward design of synthetic substrata for cell biology experiments that intend to decouple chemical and mechanical cues.Key words: cell adhesion, focal adhesion, steered molecular dynamics, finite element, chemomechanics, multiscale modeling, elasticity theory     

Nonlinear hierarchical multiscale modeling of cortical bone considering its nanoscale microstructure

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone consists of mineral platelet with nanometer size embedded in a protein matrix, it is similar to the microstructure of soft matrix nanocomposites reinforced with hard nanostructures. Considering a representative volume element (RVE) of the microstructure of bone as the microscale problem in our hierarchical multiscale modeling scheme, the global behavior of bone is obtained under various macroscopic loading conditions. This scheme may be suitable for modeling arbitrary bone geometries subjected to a variety of loading conditions. Using the presented method, mechanical properties of cortical bone including elastic moduli and Poisson's ratios in two major directions and shear modulus is obtained for different mineral volume fractions.     

Dimensionless parameters to summarize the influence of microbial growth and inhibition on the bioremediation of groundwater contaminants

Monod expressions are preferred over zero- and first-order decay expressions in modeling contaminants biotransformation in groundwater because they better represent complex conditions. However, the wide-range of values reported for Monod parameters suggests each case-study is unique. Such uniqueness restricts the usefulness of modeling, complicates an interpretation of natural attenuation and limits the utility of a bioattenuation assessment to a small number of similar cases. In this paper, four Monod-based dimensionless parameters are developed that summarize the effects of microbial growth and inhibition on groundwater contaminants. The four parameters represent the normalized effective microbial growth rate (η), the normalized critical contaminant/substrate concentration (S*), the critical contaminant/substrate inhibition factor (N), and the bioremediation efficacy (η*). These parameters enable contaminated site managers to assess natural attenuation or augmented bioremediation at multiple sites and then draw comparisons between disparate remediation activities, sites and target contaminants. Simulations results are presented that reveal the sensitivity of these dimensionless parameters to Monod parameters and varying electron donor/acceptor loads. These simulations also show the efficacy of attenuation (η*) varying over space and time. Results suggest electron donor/acceptor amendments maintained at relative concentrations S* between 0.5 and 1.5 produce the highest remediation efficiencies. Implementation of the developed parameters in a case study proves their usefulness.     

Multiscale Systems Analysis of Root Growth and Development: Modeling Beyond the Network and Cellular Scales

Over recent decades, we have gained detailed knowledge of many processes involved in root growth and development. However, with this knowledge come increasing complexity and an increasing need for mechanistic modeling to understand how those individual processes interact. One major challenge is in relating genotypes to phenotypes, requiring us to move beyond the network and cellular scales, to use multiscale modeling to predict emergent dynamics at the tissue and organ levels. In this review, we highlight recent developments in multiscale modeling, illustrating how these are generating new mechanistic insights into the regulation of root growth and development. We consider how these models are motivating new biological data analysis and explore directions for future research. This modeling progress will be crucial as we move from a qualitative to an increasingly quantitative understanding of root biology, generating predictive tools that accelerate the development of improved crop varieties.     

Computational modeling of the arterial wall based on layer-specific histological data

Arterial walls typically have a heterogeneous structure with three different layers (intima, media, and adventitia). Each layer can be modeled as a fiber-reinforced material with two families of relatively stiff collagenous fibers symmetrically arranged within an isotropic soft ground matrix. In this paper, we present two different modeling approaches, the embedded fiber (EF) approach and the angular integration (AI) approach, to simulate the anisotropic behavior of individual arterial wall layers involving layer-specific data. The EF approach directly incorporates the microscopic arrangement of fibers that are synthetically generated from a random walk algorithm and captures material anisotropy at the element level of the finite element formulation. The AI approach smears fibers in the ground matrix and treats the material as homogeneous, with material anisotropy introduced at the constitutive level by enhancing the isotropic strain energy with two anisotropic terms. Both approaches include the influence of fiber dispersion introduced by fiber angular distribution (departure of individual fibers from the mean orientation) and take into consideration the dispersion caused by fiber waviness, which has not been previously considered. By comparing the numerical results with the published experimental data of different layers of a human aorta, we show that by using histological data both approaches can successfully capture the anisotropic behavior of individual arterial wall layers. Furthermore, through a comprehensive parametric study, we establish the connections between the AI phenomenological material parameters and the EF parameters having straightforward physical or geometrical interpretations. This study provides valuable insight for the calibration of phenomenological parameters used in the homogenized modeling based on the fiber microscopic arrangement. Moreover, it facilitates a better understanding of individual arterial wall layers, which will eventually advance the study of the structure–function relationship of arterial walls as a whole.     

Top down and bottom up engineering of bone

The goal of this retrospective article is to place the body of my lab's multiscale mechanobiology work in context of top-down and bottom-up engineering of bone. We have used biosystems engineering, computational modeling and novel experimental approaches to understand bone physiology, in health and disease, and across time (in utero, postnatal growth, maturity, aging and death, as well as evolution) and length scales (a single bone like a femur, m; a sample of bone tissue, mm-cm; a cell and its local environment, μm; down to the length scale of the cell's own skeleton, the cytoskeleton, nm). First we introduce the concept of flow in bone and the three calibers of porosity through which fluid flows. Then we describe, in the context of organ-tissue, tissue-cell and cell-molecule length scales, both multiscale computational models and experimental methods to predict flow in bone and to understand the flow of fluid as a means to deliver chemical and mechanical cues in bone. Addressing a number of studies in the context of multiple length and time scales, the importance of appropriate boundary conditions, site specific material parameters, permeability measures and even micro-nanoanatomically correct geometries are discussed in context of model predictions and their value for understanding multiscale mechanobiology of bone. Insights from these multiscale computational modeling and experimental methods are providing us with a means to predict, engineer and manufacture bone tissue in the laboratory and in the human body.     

Effect of the background activity of a network of excitatory neuron-like elements on the conduction of excitation

Calculation on a mathematical model showed that for distortion-free conduction of excitation through a net of excitatory elements (EEs) a system is necessary of optimum correlation of EEs parameters, links between them and of external influences. When these parameters are deviated from their optimum values, excitation is conducted through the net either with attenuation or with intensification (as a result of divergence and convergence of the influences of the previous layer on the following one). The background activity which is above threshold of impulse activity emergence and which is created by common effects on all EEs, prevents the revealing of the input EEs activation at the net output. Near-threshold tonic net activation facilitates excitation conduction through it. Periodic net activity facilitates excitation conduction through it only under optimum correlation of its parameters and the time of its conduction through the net. At disturbance of this condition, excitation conduction through the net is limited.     

Multiscale Analysis of Biological Systems

It is argued that multiscale approaches are necessary for an explanatory modeling of biological systems. A first step, besides common to the multiscale modeling of physical and living systems, is a bottom-up integration based on the notions of effective parameters and minimal models. Top-down effects can be accounted for in terms of effective constraints and inputs. Biological systems are essentially characterized by an entanglement of bottom-up and top-down influences following from their evolutionary history. A self-consistent multiscale scheme is proposed to capture the ensuing circular causality. Its differences with standard mean-field self-consistent equations and slow-fast decompositions are discussed. As such, this scheme offers a way to unravel the multilevel architecture of living systems and their regulation. Two examples, genome functions and biofilms, are detailed.     

The Impact of Tissue Morphology,Cross-Section and Turgor Pressure on the Mechanical Properties of the Leaf Petiole in Plants

This paper describes a study of petiole structural morphology in which tissue materials, cross-sectional geometry, layer-architecture and hydrostatic condition are variables that affect the overall structural properties of the organ. Philodendron melinonii is selected as a model species for characterizing the mechanical properties of the petiole. The shape of the petiole is modeled through the polar parameterization of the Lame's curves, i.e. Gielis formulation. A multiscale model of bending stiffness is proposed to capture the impact of changing the constituent tissues and the cross-sectional geometry. Stiffness and density of different tissues are used to plot the domain bounded by the limiting curve of the respective tissue material. Shape parameters and the respective tissue properties are used to generate structural efficiency maps displaying property domains within which fall all possible combinations of tissues that are shaped into a certain geometry during growth. The turgor pressure is also taken into account to show how the domain of the effective material properties changes with water content. Finite element analysis besides experimental data is used to validate the theoretical results. The maps may offer a source of inspiration for biomimetic design, as they help to gain insight into the efficiency of biological beams described by different tissues properties, geometry and turgidity.     

Multiscale modeling of cancellous bone considering full coupling of mechanical,electric and magnetic effects

Modeling of cancellous bone has important applications in the detection and treatment of fatigue fractures and diseases like osteoporosis. In this paper, we present a fully coupled multiscale approach considering mechanical, electric and magnetic effects by using the multiscale finite element method and a two-phase material model on the microscale. We show numerical results for both scales, including calculations for a femur bone, comparing a healthy bone to ones affected by different stages of osteoporosis. Here, the magnetic field strength resulting from a small mechanical impact decreases drastically for later stages of the disease, confirming experimental research.

     

Interaction between pancreatic β cell and electromagnetic fields: A systematic study toward finding the natural frequency spectrum of β cell system

Interaction between biological systems and environmental electric or magnetic fields has gained attention during the past few decades. Although there are a lot of studies that have been conducted for investigating such interaction, the reported results are considerably inconsistent. Besides the complexity of biological systems, the important reason for such inconsistent results may arise due to different excitation protocols that have been applied in different experiments. In order to investigate carefully the way that external electric or magnetic fields interact with a biological system, the parameters of excitation, such as intensity or frequency, should be selected purposefully due to the influence of these parameters on the system response. In this study, pancreatic β cell, the main player of blood glucose regulating system, is considered and the study is focused on finding the natural frequency spectrum of the system using modeling approach. Natural frequencies of a system are important characteristics of the system when external excitation is applied. The result of this study can help researchers to select proper frequency parameter for electrical excitation of β cell system. The results show that there are two distinct frequency ranges for natural frequency of β cell system, which consist of extremely low (or near zero) and 100–750 kHz frequency ranges. There are experimental works on β cell exposure to electromagnetic fields that support such finding.     

On the application of wave scattering theory for the diagnosis of muscle diseases

This investigation is concerned with a scattering matrix approach which is proposed for the non-destructive, differential diagnosis of muscle diseases. A number of muscle diseases are classified according to their various pathological indications and appropriate material parameters are derived for utilization as input data for a theoretical model. In the mathematical analysis phase of the model, Waterman's T-matrix approach in conjunction with statistical averaging for both position and orientation of muscle fibers are employed to obtain the attenuation due to geometric dispersion for a wide range of frequencies. The numerical results not only exhibit qualitative agreement with existing experimental data for normal muscle but also display differentiable patterns for the various muscle disease cases. The formulation is an improvement over the previously applied scattering theory in that it obtains the attenuation over a continuous frequency spectrum.     

A real time hyperelastic tissue model

Real-time soft tissue modeling has a potential application in medical training, procedure planning and image-guided therapy. This paper characterizes the mechanical properties of organ tissue using a hyperelastic material model, an approach which is then incorporated into a real-time finite element framework. While generalizable, in this paper we use the published mechanical properties of pig liver to characterize an example application. Specifically, we calibrate the parameters of an exponential model, with a least-squares method (LSM) using the assumption that the material is isotropic and incompressible in a uniaxial compression test. From the parameters obtained, the stress–strain curves generated from the LSM are compared to those from the corresponding computational model solved by ABAQUS and also to experimental data, resulting in mean errors of 1.9 and 4.8%, respectively, which are considerably better than those obtained when employing the Neo-Hookean model. We demonstrate our approach through the simulation of a biopsy procedure, employing a tetrahedral mesh representation of human liver generated from a CT image. Using the material properties along with the geometric model, we develop a nonlinear finite element framework to simulate the behaviour of liver during an interventional procedure with a real-time performance achieved through the use of an interpolation approach.