Analysis of the main soft tissue stress associated with flexible flatfoot deformity: a finite element study

Biomechanics and Modeling in Mechanobiology - A better understanding of soft tissue stress and its role in supporting the medial longitudinal arch in flexible flatfoot could help to guide the...     

Simulation of planar soft tissues using a structural constitutive model: Finite element implementation and validation

Computational implementation of physical and physiologically realistic constitutive models is critical for numerical simulation of soft biological tissues in a variety of biomedical applications. It is well established that the highly nonlinear and anisotropic mechanical behaviors of soft tissues are an emergent behavior of the underlying tissue microstructure. In the present study, we have implemented a structural constitutive model into a finite element framework specialized for membrane tissues. We noted that starting with a single element subjected to uniaxial tension, the non-fibrous tissue matrix must be present to prevent unrealistic tissue deformations. Flexural simulations were used to set the non-fibrous matrix modulus because fibers have little effects on tissue deformation under three-point bending. Multiple deformation modes were simulated, including strip biaxial, planar biaxial with two attachment methods, and membrane inflation. Detailed comparisons with experimental data were undertaken to insure faithful simulations of both the macro-level stress–strain insights into adaptations of the fiber architecture under stress, such as fiber reorientation and fiber recruitment. Results indicated a high degree of fidelity and demonstrated interesting microstructural adaptions to stress and the important role of the underlying tissue matrix. Moreover, we apparently resolve a discrepancy in our 1997 study (Billiar and Sacks, 1997. J. Biomech. 30 (7), 753–756) where we observed that under strip biaxial stretch the simulated fiber splay responses were not in good agreement with the experimental results, suggesting non-affine deformations may have occurred. However, by correctly accounting for the isotropic phase of the measured fiber splay, good agreement was obtained. While not the final word, these simulations suggest that affine fiber kinematics for planar collagenous tissues is a reasonable assumption at the macro level. Simulation tools such as these are imperative in the design and simulation of native and engineered tissues.     

Patient-specific modeling of dyssynchronous heart failure: A case study

The development and clinical use of patient-specific models of the heart is now a feasible goal. Models have the potential to aid in diagnosis and support decision-making in clinical cardiology. Several groups are now working on developing multi-scale models of the heart for understanding therapeutic mechanisms and better predicting clinical outcomes of interventions such as cardiac resynchronization therapy. Here we describe the methodology for generating a patient-specific model of the failing heart with a myocardial infarct and left ventricular bundle branch block. We discuss some of the remaining challenges in developing reliable patient-specific models of cardiac electromechanical activity, and identify some of the main areas for focusing future research efforts. Key challenges include: efficiently generating accurate patient-specific geometric meshes and mapping regional myofiber architecture to them; modeling electrical activation patterns based on cellular alterations in human heart failure, and estimating regional tissue conductivities based on clinically available electrocardiographic recordings; estimating unloaded ventricular reference geometry and material properties for biomechanical simulations; and parameterizing systemic models of circulatory dynamics from available hemodynamic measurements.     

Enantioseparation of citalopram enantiomers by capillary electrophoresis: Method development through experimental design and computational modeling

Citalopram (CIT) is a frequently used modern antidepressant that inhibits selectively serotonin reuptake in the brain. It has a chiral center in its structure and is used in therapy as both racemic mixture and pure enantiomer as its pharmacological effect is almost entirely associated with S-CIT. The aim of this study was the development of a simple and rapid capillary electrophoresis (CE) method for the separation and quantification of CIT enantiomers. To establish the optimum chiral selector, several native and derivatized, neutral, and ionized cyclodextrins (CDs) were examined at different pH levels. An experimental design strategy was adopted for method optimization; a fractional factorial design was applied for screening purposes to identify significant experimental factors followed by a face-centered central composite design used for optimization purposes. Computational modeling was used to obtain information on the interaction energy and the geometry of the complexes to aid in the understanding of chiral separation mechanism. The best results were obtained when using a 25-mM phosphate buffer at pH 7.0, 3-mM CM-β-CD as chiral selector, 17.5°C temperature, 15-kV voltage, and 50 mbar/s hydrodynamic injection. The separation time was fast, below 3 min, and the migration order was S-CIT followed by R-CIT. The analytical performance of the method was verified in terms of precision, linearity, accuracy, sensibility, and robustness, and the method was applied for the determination of CIT enantiomers from pharmaceutical preparations.     

Torsion of the human left ventricle: experimental analysis and computational modeling

We set a twofold investigation: we assess left ventricular (LV) rotation and twist in the human heart through 3D-echocardiographic speckle tracking, and use representative experimental data as benchmark with respect to numerical results obtained by solving our mechanical model of the LV. We aim at new insight into the relationships between myocardial contraction patterns and the overall behavior at the scale of the whole organ. It is concluded that torsional rotation is sensitive to transmural gradients of contractility which is assumed linearly related to action potential duration (APD). Pressure-volume loops and other basic strain measures are not affected by these gradients. Therefore, realistic torsional behavior of human LV may indeed correspond to the electrophysiological and functional differences between endocardial and epicardial cells recently observed in non-failing hearts. Future investigations need now to integrate the mechanical model proposed here with minimal models of human ventricular APD to drive excitation-contraction coupling transmurally.     

Exploring the binding dynamics of etoricoxib with human hemoglobin: A spectroscopic,calorimetric, and molecular modeling approach

Etoricoxib, widely used for the treatment of osteoarthritis, rheumatoid arthritis, ankylosing spondylitis, and related conditions has ample affinity to bind with globular proteins. Here, the molecular interaction between purified human hemoglobin (HHb), a major heme protein and etoricoxib, a cyclooxygenase-2 inhibitor was studied by various spectroscopic, calorimetric, and molecular modeling techniques. The binding affected hypochromic changes in the Soret band of hemoglobin (Hb) and induced remarkable quenching of the intrinsic fluorescence property of protein molecules. Synchronous fluorescence studies revealed alterations in tryptophan (Trp) and tyrosine (Tyr) microenvironments of HHb molecule in presence of etoricoxib. Flouremetric and isothermal titration calorimetric studies suggested two binding sites in HHb for etoricoxib at three different temperatures (298.15, 303.15, and 310.15 K). Negative values of Gibbs energy change (ΔG⁰) and enthalpy change (ΔH⁰) strongly suggest that it is spontaneous and exothermic reaction, mainly stabilized by hydrogen bonding as evidenced by sucrose binding assay. These findings support our in silico molecular docking study, which specified the binding site and the non-covalent interactions involved in the association. Moreover, the interaction impacts on structural integrity and functional aspects of HHb as confirmed by decreased α helicity, increased free iron release, increased rate of co-oxidation, and decreased rate of esterase activity. Overall, these studies conclude that etoricoxib leads to a remarkable alteration in the conformational aspects of binding to HHb.

Communicated by Ramaswamy H. Sarma.     

Rearrangement of the endoplasmic reticulum and calcium transient formation: the computational approach

Experiments affecting calcium signaling often lead to changes in the calcium transient height. The present work is designed to approach this effect theoretically. Use of computational model let us to follow results of precisely designed changes in the endoplasmic reticulum distribution as a possible cause of cytoplasmic free calcium ion level. Obtained results suggest that indeed, rearrangement of the endoplasmic reticulum elements may be responsible for modulation of calcium signal's strength. We have also noticed that even if the endoplasmic reticulum concentration levels are local, the resulting changes in free calcium concentration are global and evenly distributed throughout the cell. The used mathematical method proved to be a powerful tool which made us understand the chemical dynamics of nonequilibrium processes of calcium transient formation. Presented data show how Ca2+ signal resulting from IP3 provoked release of calcium from the endoplasmic reticulum may depend on the cytoskeleton structure.     

TSAR,a new graph–theoretical approach to computational modeling of protein side‐chain flexibility: Modeling of ionization properties of proteins

A new graph–theoretical approach called thermodynamic sampling of amino acid residues (TSAR) has been elaborated to explicitly account for the protein side chain flexibility in modeling conformation‐dependent protein properties. In TSAR, a protein is viewed as a graph whose nodes correspond to structurally independent groups and whose edges connect the interacting groups. Each node has its set of states describing conformation and ionization of the group, and each edge is assigned an array of pairwise interaction potentials between the adjacent groups. By treating the obtained graph as a belief‐network—a well‐established mathematical abstraction—the partition function of each node is found. In the current work we used TSAR to calculate partition functions of the ionized forms of protein residues. A simplified version of a semi‐empirical molecular mechanical scoring function, borrowed from our Lead Finder docking software, was used for energy calculations. The accuracy of the resulting model was validated on a set of 486 experimentally determined pK_a values of protein residues. The average correlation coefficient (R) between calculated and experimental pK_a values was 0.80, ranging from 0.95 (for Tyr) to 0.61 (for Lys). It appeared that the hydrogen bond interactions and the exhaustiveness of side chain sampling made the most significant contribution to the accuracy of pK_a calculations. Proteins 2011; © 2011 Wiley‐Liss, Inc.     

A flexible state-space approach for the modeling of metabolic networks I: development of mathematical methods

We introduce a novel, flexible, optimization-based mathematical framework for the modeling of arbitrarily complex metabolic networks: topological metabolic analysis (TMA). The framework is adapted from state-space approaches used by Manousiouthakis and co-workers for the representation of complex heat- and mass-exchanger networks. We offer a thorough discussion of the mathematics and general theory underlying the framework, and discuss certain mathematical advantages of our modeling representation in comparison with other commonly used techniques (MFA and FBA). We employ a novel aggregate objective function for use with our basic constraint model, including a generalized least-squares term (for fitting available experimental measurements) and a linear design term (for representing biological or engineering goals). Using a case-study taken from recent literature (McKinlay et al., 2007), we demonstrate (among other benefits) the ability of this objective to identify alternate distinct-yet-equally optimal solutions for a given modeling problem. We also show that these solutions, obtained using only external metabolite uptake and secretion measurements, provide useful biological insights and compare favorably with solutions obtained on the basis of (13)C isotope-tracing data.     

MRI-based finite element modeling of facial mimics: a case study on the paired zygomaticus major muscles

Finite element simulation of facial mimics provides objective indicators about soft tissue functions for improving diagnosis, treatment and follow-up of facial disorders. There is a lack of in vivo experimental data for model development and validation. In this study, the contribution of the paired Zygomaticus Major (ZM) muscle contraction on the facial mimics was investigated using in vivo experimental data derived from MRI. Maximal relative differences of 7.7% and 37% were noted between MRI-based measurements and numerical outcomes for ZM and skin deformation behaviors respectively. This study opens a new direction to simulate facial mimics with in vivo data.     

Preliminary computational modeling of nitric oxide synthase 3 interactions with caveolin-1： influence of exon 7 Glu298Asp polymorphism

The significance of endothelial nitric oxide synthase 3 （NOS3） activity has been recognized for many years, however it was only recently that the complicated regulation of this constitutively expressed enzyme in endothelial cells was identified. A critical component of the NOS3 regulatory cyde in endothelial cells is its intracellnlar localization to caveolae. The caveolar coordination of NOS3, more specifically its interaction with caveolin-1 （Cav-1）, plays a major role in normal endothelial NOS3 activity and vascular bioavailability of nitric oxide. We have recently shown that the presence of NOS3 exon 7 Glu298Asp polymorphism caused diminished shear-dependent NOS activation, was less extensively associated with caveolae, and had a decreased degree of interaction with Cav-1. Here, we carried out preliminary investigations to identify possible mechanisms of the genotype-dependent endothelial cell responses we observed in our previous investigations. Through this approach we tested the hypothesis that computer simulations could provide insights regarding the contribution of this single nucleotide polymorphism to regulation of the NOS3 isoform. We observed that in the Glu/Asp and Asp/Asp mutant genotypes, the amount of NOS3 associated with Cav-1 was significantly lower. Additionally, we have shown, using a theoretical computational model, that mutation of an amino acid at position 298 might affect the protein-protein interactions and localization of the NOS3 protein. These alterations might also affect the protein function and explain the enhanced disease risk associated with the presence of Glu298Asp polymorphism in the NOS3 protein.     

Effects of selective harvest on antler size in white-tailed deer: A modeling approach

Selective harvesting in wild deer (Odocoileus spp.) populations is a common practice that may influence antler size. However, in free-ranging populations, response due to selection is unknown or difficult to quantify because antlers are influenced by nutrition and population demographics. We used quantitative genetic models to predict how white-tailed deer (O. virginianus) antlers would respond to selection and what variables (i.e., population size, age structure, mating ratio, and heritability) most affected antler size. We validated our quantitative genetics program by comparing model results with a population of deer used for controlled breeding experiments; modeled antler points (AP) and score increased (2.2–4.3 AP and 48.5–97.7 cm, respectively) after 8 years of selection, similar to observed increases in AP (3.2) and score (92.3 cm) from the controlled population. In modeled free-ranging populations, mating ratio, age structure, and heritability were more important in influencing antler size than size of the population. However, response to selection in free-ranging populations was lower (0.1–0.9 AP) than controlled breeding populations even after 20 years of selection. These results show that selective harvesting of free-ranging white-tailed deer may be inefficient to change population-level genetic characteristics related to antler size. Response of antlers in free-ranging deer will be less than controlled populations, and possibly modeled free-ranging simulations, because individual reproductive success of males is lower, breeding is done by a large group of males, and reproductive and survival rates are lower. These factors, and others, reduce the amount of improvement that can be made to antlers due to selection. Therefore, selective harvesting in free-ranging populations should be justified for managing population demographics and dynamics, but not for changing the genetic characteristics of populations. © 2011 The Wildlife Society.     

Transients of delayed fluorescence induction signal and photosynthetic antennas: A possible relationship. Mathematical modeling approach

A mathematical model was developed for resolved temporal transients of experimentally recorded delayed fluorescence (DF) induction signal. During an intermittent light regime, antennas of the photosynthetic apparatus were treated as targets, repeatedly hit by potentially absorbable photons within a series of consecutive light flashes. Formulas were derived for the number of antennas, cumulatively hit by a specific number of photons, as a function of the flash serial number (time). Model parameters included number of absorbable photons in one flash, antenna sizes, and their number. A series of induction curves were analyzed, obtained from a Zea mays leaf segment and differing in the previous dark period (t _d). Each curve, consisting of the two most prominent DF transients (C and D), was fitted with several model types, differing in the number of absorbed photons. For both transients, the best fitting result was achieved when DF induction was linked to the second absorbed photon. As expected, model parameters related to antenna sizes showed weaker dependence on t _d than those referring to antenna number. With restrictions applied to this model, the two DF induction transients may be related to two classes of photosynthetic antennas. Their different sizes may have a predominant influence on the efficiency of photon absorption and possibly time-dependent appearance of DF transients. Published in Russian in Fiziologiya Rastenii, 2006, Vol. 53, No. 3, pp. 325–335. The text was submitted by the authors in English.     

A joint modeling approach for analyzing marker data in the presence of a terminal event

In many medical studies, markers are contingent on recurrent events and the cumulative markers are usually of interest. However, the recurrent event process is often interrupted by a dependent terminal event, such as death. In this article, we propose a joint modeling approach for analyzing marker data with informative recurrent and terminal events. This approach introduces a shared frailty to specify the explicit dependence structure among the markers, the recurrent, and terminal events. Estimation procedures are developed for the model parameters and the degree of dependence, and a prediction of the covariate‐specific cumulative markers is provided. The finite sample performance of the proposed estimators is examined through simulation studies. An application to a medical cost study of chronic heart failure patients from the University of Virginia Health System is illustrated.     

Mathematical modeling of intracellular transport processes and the creatine kinase systems: a probability approach

A probability approach was used to describe mitochondrial respiration in the presence of substrates, ATP, ADP, Cr and PCr. Respiring mitochondria were considered as a three-component system, including: 1) oxidative phosphorylation reactions which provide stable ATP and ADP concentrations in the mitochondrial matrix; 2) adenine nucleotide translocase provides exchange transfer of matrix adenine nucleotides for those from outside, supplied from medium and by creatine kinase; 3) creatine kinase, starting these reactions when activated by the substrates from medium. The specific feature of this system is close proximity of creatine kinase and translocase molecules. This results in high probability of direct activations of translocase by creatine kinase-derived ADP or ATP without their leak into the medium. In turn, the activated translocase with the same high probability directly provides creatine kinase with matrix-derived ATP or ADP. The catalytic complexes of creatine kinase formed with ATP from matrix together with those formed from medium ATP provide activation of the forward creatine kinase reaction coupled to translocase activation. Simultaneously the catalytic complexes of creatine kinase formed with ADP from matrix together with those formed from medium ADP provide activation of the reverse creatine kinase reaction coupled to translocase activation. The considered probabilities were arranged into a mathermatical model. The model satisfactorily simulates the available experimental data by several groups of investigators. The results allow to consider the observed kinetic and thermodynamic iriegularities in behavior of structurally bound creatine kinase as a direct consequence of its tight coupling to translocase.     

A scenario-based approach to modeling development: a prototype model of C. elegans vulval fate specification

Studies of developmental biology are often facilitated by diagram “models” that summarize the current understanding of underlying mechanisms. The increasing complexity of our understanding of development necessitates computational models that can extend these representations to include their dynamic behavior. Here we present a prototype model of Caenorhabditis elegans vulval precursor cell fate specification that represents many processes crucial for this developmental event but that are hard to integrate using other modeling methodologies. We demonstrate the integrative capabilities of our methodology by comprehensively incorporating the contents of three seminal papers, showing that this methodology can lead to comprehensive models of developmental biology. The prototype computational model was built and is run using a language (Live Sequence Charts) and tool (the Play-Engine) that facilitate the same conceptual processes biologists use to construct and probe diagram-type models. We demonstrate that this modeling approach permits rigorous tests of mutual consistency between experimental data and mechanistic hypotheses and can identify specific conflicting results, providing a useful approach to probe developmental systems.     

A computational model of cell migration coupling the growth of focal adhesions with oscillatory cell protrusions

Cell migration is a highly integrated process where actin turnover, actomyosin contractility, and adhesion dynamics are all closely linked. In this paper, we propose a computational model investigating the coupling of these fundamental processes within the context of spontaneous (i.e. unstimulated) cell migration. In the unstimulated cell, membrane oscillations originating from the interaction between passive hydrostatic pressure and contractility are sufficient to lead to the formation of adhesion spots. Cell contractility then leads to the maturation of these adhesion spots into focal adhesions. Due to active actin polymerization, which reinforces protrusion at the leading edge, the traction force required for cell translocation can be generated. Computational simulations first show that the model hypotheses allow one to reproduce the main features of fibroblast cell migration and established results on the biphasic aspect of the cell speed as a function of adhesion strength. The model also demonstrates that certain temporal parameters, such as the adhesion proteins recycling time and adhesion lifetimes, influence cell motion patterns, particularly cell speed and persistence of the direction of migration. This study provides some elements, which allow a better understanding of spontaneous cell migration and enables a first glance at how an individual cell would potentially react once exposed to a stimulus.