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  • Open Access

    ARTICLE

    An Improved Mathematical Approach for Determination of Molecular Kinetics in Living Cells with FRAP

    Tanmay Lele1,1, Philmo Oh1,1, Jeffrey A. Nickerson1,1,2,2, Donald E. Ingber1,1,3,3

    Molecular & Cellular Biomechanics, Vol.1, No.3, pp. 181-190, 2004, DOI:10.3970/mcb.2004.001.181

    Abstract The estimation of binding constants and diffusion coefficients of molecules that associate with insoluble molecular scaffolds inside living cells and nuclei has been facilitated by the use of Fluorescence Recovery after Photobleaching (FRAP) in conjunction with mathematical modeling. A critical feature unique to FRAP experiments that has been overlooked by past mathematical treatments is the existence of an `equilibrium constraint': local dynamic equilibrium is not disturbed because photobleaching does not functionally destroy molecules, and hence binding-unbinding proceeds at equilibrium rates. Here we describe an improved mathematical formulation under the equilibrium constraint which provides a more accurate estimate of molecular reaction… More >

  • Open Access

    ARTICLE

    Using a Musculoskeletal Mathematical Model to Analyze Fatigue of the Muscles in the Lower Limbs during Different Motions

    Kaito Watanabe1, Masaki Izawa1, Ayumi Takahashi1, Kazuhito Misaji1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.114, No.2, pp. 191-207, 2018, DOI:10.3970/cmes.2018.114.191

    Abstract Under the aim of finding effective rehabilitation solutions, the difference between the extents of fatigue of each muscle used in different motions are compared. Previous research suggested methods for estimating muscle torque and muscle tension on the basis of a musculoskeletal model. As a result, it has become possible to quantitatively identify the extent of fatigue in each muscle during motion. Therefore, to evaluate muscle fatigue more quantitatively, driving power and angular momentum are focused on. Based on the driving torque of joints and the muscle torque calculated by using a three-dimensional musculoskeletal model, a method for calculating the driving… More >

  • Open Access

    ARTICLE

    Mechanism Based Pharmacokinetic Pharmacodynamic Modeling of Vildagliptin as an Add-on to Metformin for Subjects with Type 2 Diabetes

    Marziyeh Eftekhari1, Omid Vahidi1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.114, No.2, pp. 153-171, 2018, DOI:10.3970/cmes.2018.114.153

    Abstract Various drugs are used to maintain normoglycemia in subjects with type 2 diabetes mellitus. The combination of the drugs from different classes in one single tablet may enhance the effectiveness of the anti-diabetic drugs. To investigate the impact of combining drugs on the glucose regulation of subjects with type 2 diabetes, we propose a pharmacokinetic/pharmacodynamics (PK/PD) mathematical modeling approach for a combination of metformin and vildagliptin drugs. In the proposed modeling approach, two separate PK models representing oral administration of metformin and vildagliptin for diabetic subjects are interconnected to a PD model comprising a detailed compartmental physiological model representing the… More >

  • Open Access

    ARTICLE

    Role of Tumor Microvessel Architecture and Function in Chemotherapeutic Drug Delivery: A Three-Dimensional Numerical Study

    Yan Cai1,1, Zhiyong Li1,2,*

    Molecular & Cellular Biomechanics, Vol.14, No.2, pp. 59-81, 2017, DOI:10.3970/mcb.2017.014.057

    Abstract To investigate the dynamic changes of solid tumor and neo-vasculature in response to chemotherapeutic agent, we proposed a multi-discipline three-dimensional mathematical model by coupling tumor growth, angiogenesis, vessel remodelling, microcirculation and drug delivery. The tumor growth is described by the cell automaton model, in which three cell phenotypes (proliferating cell, quiescent cell and necrotic cell) are assumed to reflect the dynamics of tumor progress. A 3D tree-like architecture network with different orders for vessel diameter is generated as pre-existing vasculature in host tissue. The chemical substances including oxygen, vascular endothelial growth factor, extra-cellular matrix and matrix degradation enzymes are calculated… More >

  • Open Access

    ARTICLE

    A Coupled Mathematical Model of Cell Migration, Vessel Cooption and Tumour Microenvironment during the Initiation of Micrometastases

    Yan Cai1,2,3, Jie Wu4, Zhiyong Li1,2

    Molecular & Cellular Biomechanics, Vol.12, No.4, pp. 231-248, 2015, DOI:10.3970/mcb.2015.012.231

    Abstract We propose a coupled mathematical model for the detailed quantitative analyses of initial microtumour and micrometastases formation by including cancer cell migration, host vessel cooption and changes in microenvironment. Migrating cells are included as a new phenotype to describe the migration behaviour of malignant tumour cells. Migration probability of a migrating cell is assumed to be influenced by local chemical microenvironment. Pre-existing vessel cooption and remodelling are introduced according to the local haemodynamical microenvironment, such as interstitial pressure and vessel wall permeability. After the tumour cells and tumour vessels distribution are updated, the chemical substances are coupled calculated with the… More >

  • Open Access

    ARTICLE

    Mathematical Model for Skeletal Muscle to Simulate the Concentric and Eccentric Contraction

    Chetan Kuthe, R. V. Uddanwadiker, P. M. Padole, A. A. Ramteke§

    Molecular & Cellular Biomechanics, Vol.12, No.1, pp. 1-16, 2015, DOI:10.3970/mcb.2015.012.001

    Abstract Skeletal muscles are responsible for the relative motion of the bones at the joints and provide the required strength. They exhibit highly nonlinear mechanical behaviour and are described by nonlinear hyperelastic constitutive relations. It is distinct from other biological soft tissue. Its hyperelastic or viscoelastic behaviour is modelled by using CE, SEE, and PEE. Contractile element simulates the behaviour of skeletal muscle when it is subjected to eccentric and concentric contraction. This research aims to estimate the stress induced in skeletal muscle in eccentric and concentric contraction with respect to the predefined strain. With the use of mathematical model for… More >

  • Open Access

    ARTICLE

    Bone Tissue Formation under Ideal Conditions in a Scaffold Generated by a Reaction-Diffusion System

    Marco A.Velasco, Diego A. Garzón-Alvarado

    Molecular & Cellular Biomechanics, Vol.10, No.2, pp. 137-157, 2013, DOI:10.3970/mcb.2013.010.137

    Abstract The design of porous scaffolds for tissue engineering requires methods to generate geometries in order to control the stiffness and the permeability of the implant among others characteristics. This article studied the potential of the reaction-diffusion systems to design porous scaffolds for bone regeneration. We simulate the degradation of the scaffold material and the formation of new bone tissue over canal-like, spherical and ellipsoid structures obtained by this approach. The simulations show that the degradation and growth rates are affected by the form of porous structures. The results have indicated that the proposed method has potential as a tool to… More >

  • Open Access

    ARTICLE

    A Mathematical Model of Cell Reorientation in Response to Substrate Stretching

    Konstantinos A. Lazopoulos1, Dimitrije Stamenović2

    Molecular & Cellular Biomechanics, Vol.3, No.1, pp. 43-48, 2006, DOI:10.3970/mcb.2006.003.043

    Abstract It is well documented that in response to substrate stretching adhering cells alter their orientation. Generally, the cells reorient away from the direction of the maximum substrate strain, depending upon the magnitude of the substrate strain and the state of cell contractility. Theoretical models from the literature can describe only some aspects of this phenomenon. In the present study, we developed a more comprehensive mathematical model of cell reorientation than the current models. Using the framework of theory of non-linear elasticity, we found that the problem of cell reorientation was a stability problem, with the global (Maxwell's) criterion for stability.… More >

  • Open Access

    ARTICLE

    Quantifying Roll Feel of a Car by Using a Musculoskeletal Mathematical Model

    Masaki Izawa1, Ryota Araki1, Tatsuro Suzuki1, Kaito Watanabe2, Kazuhito Misaji3,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.118, No.3, pp. 493-507, 2019, DOI:10.31614/cmes.2019.04470

    Abstract Primary purpose of this research is to create a three-dimensional musculoskeletal mathematical model of a driver of a car using a motion capture system. The model is then used in an analysis of drive torque around joints and attached muscles as a vehicle travels in different travel modes and damping force settings to examine ‘burdens’ for the driver. Previous studies proposed a method of quantifying the degree of musculoskeletal load in simple human motion from the changes in drive torque around joints and attached muscles. However, examination of the level of burdens for the driver while driving using this method… More >

  • Open Access

    ARTICLE

    The Accuracy of Mathematical Models in Simulator Distributed Computing

    I. Kvasnica1, P. Kvasnica2

    CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.6, pp. 447-462, 2015, DOI:10.3970/cmes.2015.107.447

    Abstract The issue of simulation of decentralized mathematical models is discussed in the paper. The authors’ knowledge is based on a theory of design of decentralized computer control systems. Their knowledge is gained in the process of designing mathematical models that are simulated. A decomposed control system is required to meet the conditions of observation and control. The methodology of a multi-model design is based on main principles of object orientation such as abstraction, hierarchy, and modularity. Modelling on a parallel architecture has an impact on a simulator system. The system is defined by the equations shown below. An important part… More >

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