Brain mechanics For neurosurgery: modeling issues

 Brain biomechanics has been investigated for more than 30 years. In particular, finite element analyses and other powerful computational methods have long been used to provide quantitative results in the investigation of dynamic processes such as head trauma. Nevertheless, the potential of these methods to simulate and predict the outcome of quasi-static processes such as neurosurgical procedures and neuropathological processes has only recently been explored. Some inherent difficulties in modeling brain tissues, which have impeded progress, are discussed in this work. The behavior of viscoelastic and poroelastic constitutive models is compared in simple 1-D simulations using the ABAQUS finite element platform. In addition, the behaviors of quasi-static brain constitutive models that have recently been proposed are compared. We conclude that a compressible viscoelastic solid model may be the most appropriate for modeling neurosurgical procedures. Received: 19 March 2002 / Accepted: 6 June 2002 Work is supported by a generous grant from the Whitaker Foundation. We would like to also thank Dr. Christos Davatzikos (Johns Hopkins School of Medicine, Baltimore, Maryland) for his help.     

Molecular mechanics modeling of azobenzene-based photoswitches

We present an extension of the generalized amber force field to allow the modeling of azobenzenes by means of classical molecular mechanics. TD-DFT calculations were employed to derive different interaction models for 4-hydroxy-4'-methyl-azobenzene, including the ground (S(0)) and S(1) excited state. For both states, partial charges and the -N = N- torsion potentials were characterized. On this basis, we pave the way to large-scale model simulations involving azobenzene molecular switches. Using the example of an isolated molecule, the mechanics of cyclic switching processes are demonstrated by classical molecular dynamics simulations.     

Compartment modeling from tracer experiments

Anelementary system is defined as two compartments, one the immediate and unique precursor of the other. By synthesizing a number of elementary systems, we can obtain a system with any givenweight, transfer time anddispersion. A criterion is presented to choose the best model of a given system, i.e. a system with the same above parameters and composed of a minimum number of elementary systems. Supported in part by NIH grant NO. GM-572. Supported by PHS Training grant No. 2T01 HE05138-17 from the National Heart Institute.     

Calcium-dependent activation of human neutrophils by a synthetic ionophore

Synthetic block copolymers composed of polyoxyethylene and poly-oxypropylene have been demonstrated to possess ionophore activity selective for monovalent cations and to cause histamine release from mouse mast cells and human basophils. We now report calcium-dependent release of granule contents from human neutrophils by the most active of these agents, TI30R2. At a concentration of 100 micrograms/ml (12.5 microM), net lysozyme release ranged from 17-40% after 30 minutes incubation at 37 degrees. Lysozyme release was dose-dependent over stimulus concentrations of 5-50 micrograms/ml (0.625-6.25 microM). Release was dependent upon the presence of extracellular calcium. T130R2 did not induce the release of superoxide anions over 30 minutes of incubation. As T130R2 induces sodium influx into cells, it is likely that a depolarizing influx of sodium ions in the presence of extracellular calcium constitutes a sufficient signal for granule release but not superoxide production by human neutrophils.     

Design of experiments for predictive microbial modeling

Summary Good predictive microbial models can be built with appropriate data from well-designed experiments. Anyone setting up an experiment should consider the sources of variability, possible screening experiments, optimum spacing between points on a continuous scale, and the most appropriate type of design, e.g. factorial, screening, or central composite.     

Extramuscular myofascial force transmission: experiments and finite element modeling

The specific purpose of the present study was to show that extramuscular myofascial force transmission exclusively has substantial effects on muscular mechanics. Muscle forces exerted at proximal and distal tendons of the rat extensor digitorium longus (EDL) were measured simultaneously, in two conditions (1) with intact extramuscular connections (2) after dissecting the muscles' extramuscular connections to a maximum extent without endangering circulation and innervation (as in most in situ muscle experiments). A finite element model of EDL including the muscles' extramuscular connections was used to assess the effects of extramuscular myofascial force transmission on muscular mechanics, primarily to test if such effects lead to distribution of length of sarcomeres within muscle fibers. In condition (1), EDL isometric forces measured at the distal and proximal tendons were significantly different (F(dist) > F(prox), DeltaF approximates maximally 40% of the proximal force). The model results show that extramuscular myofascial force transmission causes distributions of strain in the fiber direction (shortening in the proximal, lengthening in the distal ends of fibers) at higher lengths. This indicates significant length distributions of sarcomeres arranged in series within muscle fibers. Stress distributions found are in agreement with the higher distal force measured, meaning that the muscle fiber is no longer the unit exerting equal forces at both ends. Experimental results obtained in condition (2) showed no significant changes in the length-force characteristics (i.e., proximo-distal force differences were maintained). This shows that a muscle in situ has to be distinguished from a muscle that is truly isolated in which case the force difference has to be zero. We conclude that extramuscular myofascial force transmission has major effects on muscle functioning.     

Homogenization modeling for the mechanics of perfused myocardium

Altered coronary perfusion can change the apparent diastolic stiffness of ventricular myocardium--the ‘garden hose’ effect. Our recent findings showed that myocardial strains are reduced during ventricular filling, primarily along the directions transverse to the coronary microvessels. In this article, we review hypotheses and theoretical models regarding the role that regional wall stress plays in the mechanical interaction between myocardium and coronary circulation. Various mechanisms have been used to explain the effects of the tissue stress on coronary flow, as well as the effect of coronary dynamics on myocardial mechanics. Many models of coronary pressure-flow relations using lumped parameter circuit analogs. Poroelasticity and swelling theories have been used to model the mechanics of perfused muscle. Here, we describe a new mathematical model of the mechanics of perfused myocardium derived using homogenization theory. In this model, perfused myocardium is treated as a nonlinear anisotropic elastic solid embedded with cylindrical vessels of known distensibility. The solid compartment is incompressible but the vascular compartment may change volume according to a simple relation between vessel diameter and perfusion pressure. The work done by the perfusion pressure in changing vascular volume contributes to the macroscopic strain energy and hence affects the stress and stiffness of the composite. Conversely, the stress in the tissue affects microvessel diameter and volume, since tractions transverse to the vessel axis oppose the internal blood pressure. Finite element simulations of passive filling show good agreement of model with experimental results.     

Multiscale modeling and mechanics of filamentous actin cytoskeleton

The adaptive structure and functional changes of the actin cytoskeleton are induced by its mechanical behavior at various temporal and spatial scales. In particular, the mechanical behaviors at different scales play important roles in the mechanical functions of various cells, and these multiscale phenomena require clarification. To establish a milestone toward achieving multiscale modeling and simulation, this paper reviews mathematical analyses and simulation methods applied to the mechanics of the filamentous actin cytoskeleton. The actin cytoskeleton demonstrates characteristic behaviors at every temporal and spatial scale, and mathematical models and simulation methods can be applied to each level of actin cytoskeletal structure ranging from the molecular to the network level. This paper considers studies on mathematical models and simulation methods based on the molecular dynamics, coarse-graining, and continuum dynamics approaches. Every temporal and spatial scale of actin cytoskeletal structure is considered, and it is expected that discrete and continuum dynamics ranging from functional expression at the molecular level to macroscopic functional expression at the whole cell level will be developed and applied to multiscale modeling and simulation.     

Exocytotic dynamics in human chromaffin cells: experiments and modeling

Chromaffin cells have been widely used to study neurosecretion since they exhibit similar calcium dependence of several exocytotic steps as synaptic terminals do, but having the enormous advantage of being neither as small or fast as neurons, nor as slow as endocrine cells. In the present study, secretion associated to experimental measurements of the exocytotic dynamics in human chromaffin cells of the adrenal gland was simulated by using a model that combines stochastic and deterministic approaches for short and longer depolarizing pulses, respectively. Experimental data were recorded from human chromaffin cells, obtained from healthy organ donors, using the perforated patch configuration of the patch-clamp technique. We have found that in human chromaffin cells, secretion would be mainly managed by small pools of non-equally fusion competent vesicles, slowly refilled over time. Fast secretion evoked by brief pulses can be predicted only when 75% of one of these pools (the “ready releasable pool” of vesicles, abbreviated as RRP) are co-localized to Ca^2?+? channels, indicating an immediately releasable pool in the range reported for isolated cells of bovine and rat (Álvarez and Marengo, J Neurochem 116:155–163, 2011). The need for spatial correlation and close proximity of vesicles to Ca^2?+? channels suggests that in human chromaffin cells there is a tight control of those releasable vesicles available for fast secretion.     

Explicit finite element modeling of total knee replacement mechanics

Joint kinematics and contact mechanics dictate the success of current total knee replacement (TKR) devices. Efficient computer models present an effective way of evaluating these characteristics. Predicted contact stress and area due to articulations at the tibio-femoral and patello-femoral interfaces indicate potential clinical performance. Previous finite element (FE) knee models have generally been used to predict contact stresses and/or areas during static or quasi-static loading conditions. Explicit dynamic FE analyses have recently been used to efficiently predict TKR kinematics and contact mechanics during dynamic loading conditions. The objective of this study was to develop and experimentally validate an explicit FE TKR model that incorporates tibio-femoral and patello-femoral articulations. For computational efficiency, we developed rigid body analyses that can reasonably reproduce the kinematics, contact pressure distribution, and contact area of a fully deformable system. Results from the deformable model showed that the patello-femoral and tibio-femoral kinematics were in good agreement with experimental knee simulator measurements. Kinematic results from the rigid body analyses were nearly identical to those from the fully deformable model, and the contact pressure and contact area correlation was acceptable given the great reduction in analysis time. Component mesh density studied had little effect on the predicted kinematics, particularly for the patellar component, and small effects on the predicted contact pressure and area. These analyses have shown that, at low computational cost, a force-control dynamic simulation of a gait cycle can yield useful and predictable results.     

Circular dichroism of carotenoids in bacterial light-harvesting complexes: experiments and modeling

In this work we investigate the origin and characteristics of the circular dichroism (CD) spectrum of rhodopin glucoside and lycopene in the light-harvesting 2 complex of Rhodopseudomonas acidophila and Rhodospirillum molischianum, respectively. We successfully model their absorption and CD spectra based on the high-resolution structures. We assume that these spectra originate from seven interacting transition dipole moments: the first corresponds to the 0-0 transition of the carotenoid, whereas the remaining six represent higher vibronic components of the S2 state. From the absorption spectra we get an estimate of the Franck-Condon factors of these transitions. Furthermore, we investigate the broadening mechanisms that lead to the final shape of the spectra and get an insight into the interaction energy between carotenoids. Finally, we examine the consequences of rotations of the carotenoid transition dipole moment and of deformations in the light-harvesting 2 complex rings. Comparison of the modeled carotenoid spectra with modeled spectra of the bacteriochlorophyll QY region leads to a refinement of the modeling procedure and an improvement of all calculated results. We therefore propose that the combined carotenoid and bacteriochlorophyll CD can be used as an accurate reflection of the overall structure of the light-harvesting complexes.     

Muscle and prosthesis contributions to amputee walking mechanics: A modeling study

Unilateral, below-knee amputees have altered gait mechanics, which can significantly affect their mobility. Below-knee amputees lose the functional use of the ankle muscles, which are critical during walking to provide body support, forward propulsion, leg-swing initiation and mediolateral balance. Thus, either muscles must compensate or the prosthesis must provide the functional tasks normally provided by the ankle muscles. Three-dimensional (3D) forward dynamics simulations of amputee and non-amputee walking were generated to identify muscle and prosthesis contributions to amputee walking mechanics, including the subtasks of body support, forward propulsion, leg-swing initiation and mediolateral balance. Results showed that the prosthesis provided body support in the absence of the ankle muscles. The prosthesis contributed to braking from early to mid-stance and propulsion in late stance. The prosthesis also functioned like the uniarticular soleus muscle by transferring energy from the residual leg to the trunk to provide trunk propulsion. The residual-leg vasti and rectus femoris reduced their contributions to braking in early stance, which mitigated braking from the prosthesis during this period. The prosthesis did not replace the function of the gastrocnemius, which normally generates energy to the leg to initiate swing. As a result, lower overall energy was delivered to the residual leg. The prosthesis also acted to accelerate the body laterally in the absence of the ankle muscles. These results provide further insight into muscle and prosthesis function in below-knee amputee walking and can help guide rehabilitation methods and device designs to improve amputee mobility.     

The synthetic melanocortin (CKPV)2 exerts broad anti-inflammatory effects in human neutrophils

Natural melanocortin peptides exert broad effects on the host and they have remarkable therapeutic potential. However, successful use of melanocortins as therapeutic agents depends on the design of molecules that have more stable pharmacological profiles. The synthetic peptide (CKPV)(2), based on the C-terminal sequence of alpha-melanocyte stimulating hormone (alpha-MSH), has anti-tumor necrosis factor-alpha (TNF-alpha) effects in vitro and in vivo and is a promising candidate to treat inflammation. Because neutrophil activity is a major target for anti-inflammatory therapies, we determined whether (CKPV)(2) modulates human neutrophil functions in vitro. Incubation of freshly-separated human neutrophils with 10(-12)-10(-6)M (CKPV)(2) significantly inhibited activities relevant to the inflammatory reaction. Neutrophil migration toward the two chemoattractants interleukin 8 (IL-8) and N-formyl-methionyl-leucyl-phenylalanine (fMLP) was significantly inhibited by (CKPV)(2). (CKPV)(2) also inhibited reactive oxygen intermediate (ROI) production induced by phorbol 12-myristate 13-acetate (PMA), but not that induced by fMLP. Because these effects of (CKPV)(2) were abolished by the adenylyl cyclase inhibitor 2',5'-dideoxyadenosine (ddAdo), they appear to be cAMP-dependent. Finally, the peptide reduced lipopolysaccharide (LPS)-stimulated expression of TNF-alpha, interleukin-1beta (IL-1beta), interleukin-8 (IL-8), and intercellular adhesion molecule 1 (ICAM-1), as well as TNF-alpha protein release in cell supernatants. The data indicate that (CKPV)(2) modulates broad cAMP-dependent, anti-inflammatory pathways in human neutrophils.     

Nonkinetic modeling of the mechanical unfolding of multimodular proteins: theory and experiments

We introduce and discuss a novel approach called back-calculation for analyzing force spectroscopy experiments on multimodular proteins. The relationship between the histograms of the unfolding forces for different peaks, corresponding to a different number of not-yet-unfolded protein modules, is exploited in such a manner that the sole distribution of the forces for one unfolding peak can be used to predict the unfolding forces for other peaks. The scheme is based on a bootstrap prediction method and does not rely on any specific kinetic model for multimodular unfolding. It is tested and validated in both theoretical/computational contexts (based on stochastic simulations) and atomic force microscopy experiments on (GB1)₈ multimodular protein constructs. The prediction accuracy is so high that the predicted average unfolding forces corresponding to each peak for the GB1 construct are within only 5 pN of the averaged directly-measured values. Experimental data are also used to illustrate how the limitations of standard kinetic models can be aptly circumvented by the proposed approach.     

Fracture mechanics modeling of popping event during daughter cell separation

Most bacteria cells divide by binary fission which is part of a bacteria cell cycle and requires tight regulations and precise coordination. Fast separation of Staphylococcus Aureus (S. Aureus) daughter cells, named as popping event, has been observed in recent experiments. The popping event was proposed to be driven by mechanical crack propagation in the peripheral ring which connected two daughter cells before their separation. It has also been shown that after the fast separation, a small portion of the peripheral ring was left as a hinge. In the article, we develop a fracture mechanics model for the crack growth in the peripheral ring during S. Aureus daughter cell separation. In particular, using finite element analysis, we calculate the energy release rate associated with the crack growth in the peripheral ring, when daughter cells are inflated by a uniform turgor pressure inside. Our results show that with a fixed inflation of daughter cells, the energy release rate depends on the crack length non-monotonically. The energy release rate reaches a maximum value for a crack of an intermediate length. The non-monotonic relationship between the energy release rate and crack length clearly indicates that the crack propagation in the peripheral ring can be unstable. The computed energy release rate as a function of crack length can also be used to explain the existence of a small portion of peripheral ring remained as hinge after the popping event.