Modeling the dynamics of risk of altitude decompression sickness

A probabilistic model of decompression sickness is modified by introducing corrections that determine more precisely the risk of tissue injury by gas bubbles as a function of blood supply and bubble nucleation intensity. Parameters of the “worst” virtual tissues and theoretical curves corresponding to empirical data on the cumulative probability of decompression sickness symptoms for some altitude decompression procedures are determined. The parameters are shown to depend on final pressure, physical load, and duration of preoxygenation.     

A new class of biophysical models for predicting the probability of decompression sickness in scuba diving.

Interconnected compartmental models have been used for decades in physiology and medicine to account for the observed multi-exponential washout kinetics of a variety of solutes (including inert gases) both from single tissues and from the body as a whole. They are used here as the basis for a new class of biophysical probabilistic decompression models. These models are characterized by a relatively well-perfused, risk-bearing, central compartment and one or two non-risk-bearing, relatively poorly perfused, peripheral compartment(s). The peripheral compartments affect risk indirectly by diffusive exchange of dissolved inert gas with the central compartment. On the basis of the accuracy of their respective predictions beyond the calibration regime, the three-compartment interconnected models were found to be significantly better than the two-compartment interconnected models. The former, on the basis of a number of criteria, was also better than a two-compartment parallel model used for comparative purposes. In these latter comparisons, the models all had the same number of fitted parameters (four), were based on linear kinetics, had the same risk function, and were calibrated against the same dataset. The interconnected models predict that inert gas washout during decompression is relatively fast, initially, but slows rapidly with time compared with the more uniform washout rate predicted by an independent parallel compartment model. If empirically verified, this may have important implications for diving practice.     

A model for influence of exercise on formation and growth of tissue bubbles during altitude decompression

In response to exercise performed before or after altitude decompression, physiological changes are suspected to affect the formation and growth of decompression bubbles. We hypothesized that the work to change the size of a bubble is done by gas pressure gradients in a macro- and microsystem of thermodynamic forces and that the number of bubbles formed through time follows a Poisson process. We modeled the influence of tissue O(2) consumption on bubble dynamics in the O(2) transport system in series against resistances, from the alveolus to the microsystem containing the bubble and its surrounding tissue shell. Realistic simulations of experimental decompression procedures typical of actual extravehicular activities were obtained. Results suggest that exercise-induced elevation of O(2) consumption at altitude leads to bubble persistence in tissues. At the same time, exercise-enhanced perfusion leads to an overall suppression of bubble growth. The total volume of bubbles would be reduced unless increased tissue motion simultaneously raises the rate of bubble formation through cavitation processes, thus maintaining or increasing total bubble volume, despite the exercise.     

A comparison between a new model and current models for estimating trunk segment inertial parameters

Modeling of the body segments to estimate segment inertial parameters is required in the kinetic analysis of human motion. A new geometric model for the trunk has been developed that uses various cross-sectional shapes to estimate segment volume and adopts a non-uniform density function that is gender-specific. The goal of this study was to test the accuracy of the new model for estimating the trunk's inertial parameters by comparing it to the more current models used in biomechanical research. Trunk inertial parameters estimated from dual X-ray absorptiometry (DXA) were used as the standard. Twenty-five female and 24 male college-aged participants were recruited for the study. Comparisons of the new model to the accepted models were accomplished by determining the error between the models’ trunk inertial estimates and that from DXA. Results showed that the new model was more accurate across all inertial estimates than the other models. The new model had errors within 6.0% for both genders, whereas the other models had higher average errors ranging from 10% to over 50% and were much more inconsistent between the genders. In addition, there was little consistency in the level of accuracy for the other models when estimating the different inertial parameters. These results suggest that the new model provides more accurate and consistent trunk inertial estimates than the other models for both female and male college-aged individuals. However, similar studies need to be performed using other populations, such as elderly or individuals from a distinct morphology (e.g. obese). In addition, the effect of using different models on the outcome of kinetic parameters, such as joint moments and forces needs to be assessed.     

A theoretical model for estimating the margination constant of leukocytes

Background  

Blood leukocytes constitute two interchangeable sub-populations, the marginated and circulating pools. These two sub-compartments are found in normal conditions and are potentially affected by non-normal situations, either pathological or physiological. The dynamics between the compartments is governed by rate constants of margination (M) and return to circulation (R). Therefore, estimates of M and R may prove of great importance to a deeper understanding of many conditions. However, there has been a lack of formalism in order to approach such estimates. The few attempts to furnish an estimation of M and R neither rely on clearly stated models that precisely say which rate constant is under estimation nor recognize which factors may influence the estimation.     

A comparison of the parameter estimating procedures for the Michaelis-Menten model

The performance of four parameter estimating procedures for the estimation of the adjustable parameters in the Michaelis-Menten model, the maximum initial rate Vmax, and the Michaelis-Menten constant Km, including Lineweaver & Burk transformation (L-B), Eadie & Hofstee transformation (E-H), Eisenthal & Cornish-Bowden transformation (ECB), and Hsu & Tseng random search (H-T) is compared. The analysis of the simulated data reveals the followings: (i) Vmax can be estimated more precisely than Km. (ii) The sum of square errors, from the smallest to the largest, follows the sequence H-T, E-H, ECB, L-B. (iii) Considering the sum of square errors, relative error, and computing time, the overall performance follows the sequence H-T, L-B, E-H, ECB, from the best to the worst. (iv) The performance of E-H and ECB are on the same level. (v) L-B and E-H are appropriate for pricesly measured data. H-T should be adopted for data whose error level are high. (vi) Increasing the number of data points has a positive effect on the performance of H-T, and a negative effect on the performance of L-B, E-H, and ECB.     

A biophysical model of the mitochondrial respiratory system and oxidative phosphorylation

A computational model for the mitochondrial respiratory chain that appropriately balances mass, charge, and free energy transduction is introduced and analyzed based on a previously published set of data measured on isolated cardiac mitochondria. The basic components included in the model are the reactions at complexes I, III, and IV of the electron transport system, ATP synthesis at F₁F₀ ATPase, substrate transporters including adenine nucleotide translocase and the phosphate–hydrogen co-transporter, and cation fluxes across the inner membrane including fluxes through the K⁺/H⁺ antiporter and passive H⁺ and K⁺ permeation. Estimation of 16 adjustable parameter values is based on fitting model simulations to nine independent data curves. The identified model is further validated by comparison to additional datasets measured from mitochondria isolated from rat heart and liver and observed at low oxygen concentration. To obtain reasonable fits to the available data, it is necessary to incorporate inorganic-phosphate-dependent activation of the dehydrogenase activity and the electron transport system. Specifically, it is shown that a model incorporating phosphate-dependent activation of complex III is able to reasonably reproduce the observed data. The resulting validated and verified model provides a foundation for building larger and more complex systems models and investigating complex physiological and pathophysiological interactions in cardiac energetics.     

A three-dimensional constitutive model for the stress relaxation of articular ligaments

A new nonlinear constitutive model for the three-dimensional stress relaxation of articular ligaments is proposed. The model accounts for finite strains, anisotropy, and strain-dependent stress relaxation behavior exhibited by these ligaments. The model parameters are identified using published uniaxial stress–stretch and stress relaxation data on human medial collateral ligaments (MCLs) subjected to tensile tests in the fiber and transverse to the fiber directions (Quapp and Weiss in J Biomech Eng Trans ASME 120:757–763, 1998; Bonifasi-Lista et al. in J Orthop Res 23(1):67–76, 2005). The constitutive equation is then used to predict the nonlinear elastic and stress relaxation response of ligaments subjected to shear deformations in the fiber direction and transverse to the fiber direction, and an equibiaxial extension. A direct comparison with stress relaxation data collected by subjecting human MCLs to shear deformation in the fiber direction is presented in order to demonstrate the predictive capabilities of the model.     

A microstructural model for the anisotropic drained stiffness of articular cartilage

A constitutive model for articular cartilage is developed to study directional load sharing within the soft biological tissue. Cartilage is idealized as a composite structure whose static mechanical response is dominated by distortion of a sparse fibrous network and by changes in fixed charge density. These histological features of living cartilage are represented in a microstructural analog of the tissue, linking the directionality of mechanical stiffness to the orientation of microstructure. The discretized 'model tissue' is used to define a stiffness tensor relating drained stress and strain over a regime of large deformation. The primary goal of this work was to develop a methodology permitting more complete treatment of anisotropy in the stiffness of cartilage. The results demonstrate that simple oriented microscopic behaviors can combine to produce complicated larger scale response. For the illustrative example of a homogeneous specimen subjected to confined compression, the model predicts a nonlinear anisotropic drained response, with inherent uncertainty at cellular size scales.     

A test of a model for estimating production in the sea

Primary productivity was measured in the sea off the coasts of Florida and Georgia with the radiocarbon method at four stations during March, 1971. Integral photosynthesis per square meter surface was determined with a mathematical model from empirical data gathered from in situ and shipboard incubation experiments. The mathematical model provided shipboard incubators to be used to estimate primary production rates while overcoming the problem of relating light quality and quantity simulated by the incubators to that found in the euphotic zone. The use of shipboard incubation can allow for measurements to be made on a moving vessel, more stations visited per day and water samples incubated at a constant light intensity. Primary productivity at the four sampling stations ranged from 0.026 to 0.042 mg C/M² hr.     

A model for estimating the extent of variegation in mosaic tissues

A method is described which allows the size of patches of like cells in mosaic tissues to be estimated from the frequency with which small samples taken from the tissue contain both of the mosaic cell types. The mosaic patches are represented as close-packed geometric figures arranged in twoor three-dimensional tissues. Small samples drawn at random from these tissues will include portions of one or more patches; only those samples which include portions of two or more dissimilar patches (mixed samples) will contain both cell types. The expected frequency of mixed samples is calculated as a function of the shape of the mosaic patches, the frequency of the two mosaic cell types and the sample to patch size ratio. This expected frequency is not strongly dependent on patch shape for triangular, square and hexagonal patches in two dimensions or for cubic and orthotetrakaidekahedral patches in three dimensions. Elongation of square patches along one axis or of cubic patches along one or two axes results in slight increases in the expected frequency of mixed samples for given sample to patch size ratio.     

A displacement-based model for estimating the shear resistance of root-permeated soils

Aims

This paper presents a displacement-based model for predicting the relationship between the increase in shear resistance and shear displacement for soils permeated with an entire plant root system.

Methods

The root force in the root system is estimated based on the shear deformation developed in the soil. This displacement-based model takes a number of factors into account, including the distribution of the shear deformation in the soil, the root orientation, the mobilized root forces, and the root properties.

Results

The proposed model reasonably captures the relationship between the increase in the shear resistance (ΔS) and the shear displacement, as shown by a comparison of the predicted results with data from in situ shear tests.

Conclusions

Major findings are the following: (1) the ΔS value increases considerably with increasing b coefficients, which are used to describe the deformed shape of the shear zone, and Young’s moduli of roots at the early stage of shearing; (2) the ΔS value increases significantly with the τ value at large shear deformations; (3) short roots play an important role in the contribution of root systems to the shear resistance of the soil. However, the success of the model relies on the appropriate estimate of the deformation characteristics on the shear zone and the soil-root bond strength.     

种间竞争的一个新的数学模型—对经典的Lotka—Vol—terra竞争方程的扩充

本文根据营养动力学理论,建立了一类种间竞争的新的数学模型:它是单种群增长的Cui-Lawson模型,在种间竞争上的推广。新的种间竞争模型克服了经典的种间竞争的Lotka-Volteira方程的局限与不足,具有更广泛和复杂的行为,并在特殊条件下以Lotka-Volterra竞争方程为其特例。因此,新的种间竞争的数学模型是更一般的解释性模型,是对经典的Lotka-Voterra竞争方程的扩充。     

A new approach for estimating the efficiencies of the nucleotide substitution models

In this article, a new approach is presented for estimating the efficiencies of the nucleotide substitution models in a four-taxon case and then this approach is used to estimate the relative efficiencies of six substitution models under a wide variety of conditions. In this approach, efficiencies of the models are estimated by using a simple probability distribution theory. To assess the accuracy of the new approach, efficiencies of the models are also estimated by using the direct estimation method. Simulation results from the direct estimation method confirmed that the new approach is highly accurate. The success of the new approach opens a unique opportunity to develop analytical methods for estimating the relative efficiencies of the substitution models in a straightforward way.     

A real-time computational model for estimating kinematics of ankle ligaments

Background: An accurate assessment of ankle ligament kinematics is crucial in understanding the injury mechanisms and can help to improve the treatment of an injured ankle, especially when used in conjunction with robot-assisted therapy. A number of computational models have been developed and validated for assessing the kinematics of ankle ligaments. However, few of them can do real-time assessment to allow for an input into robotic rehabilitation programs. Method: An ankle computational model was proposed and validated to quantify the kinematics of ankle ligaments as the foot moves in real-time. This model consists of three bone segments with three rotational degrees of freedom (DOFs) and 12 ankle ligaments. This model uses inputs for three position variables that can be measured from sensors in many ankle robotic devices that detect postures within the foot–ankle environment and outputs the kinematics of ankle ligaments. Validation of this model in terms of ligament length and strain was conducted by comparing it with published data on cadaver anatomy and magnetic resonance imaging. Results: The model based on ligament lengths and strains is in concurrence with those from the published studies but is sensitive to ligament attachment positions. Conclusions: This ankle computational model has the potential to be used in robot-assisted therapy for real-time assessment of ligament kinematics. The results provide information regarding the quantification of kinematics associated with ankle ligaments related to the disability level and can be used for optimizing the robotic training trajectory.     

A model for estimating the medium properties of Avicel to ethanol conversion

Simultaneous saccharification and fermentation received an increasing level of attention over recent decades, with the primary focus on the development of improved enzyme and organism performance. Little literature is available on the effects of the various fermentation components on the apparent dynamic viscosity of the fermentation broth for use in reactor design and analysis. This work investigates density and settling properties of Avicel PH-101 particles and the effects of base medium composition, yeast concentration and cellulose particles on the apparent dynamic viscosity of the fermentation mixture. Dynamic viscosity measurements were obtained using a rotational viscometer equipped with a DG 26.7 double gap concentric cylinder measuring system. Results indicated that Avicel particles experience a greater drag force compared to similar sized spherical particles and have a measured density of 1,605.7 kg m^?3. The Ostwäld-de Waele formulation was used to describe the dynamic viscosity of the particles due to it shear-thinning nature. Correlation between the predicted particle effects and experimental results deviated with a root mean square error of 8.46 %.