Bruce Bukiet

Measurement of balance in computer posturography: Comparison of methods—A brief review

Some symptoms related to disequilibrium may not be detected by a clinical exam. Therefore, objective study is important in assessing balance. In this paper, methods to measure balance in computer posturography are compared. Center of pressure (COP) displacement, equilibrium score (ES) and postural stability index (PSI), the main measures of assessing balance are described and their merits and disadvantages are discussed. Clinicians should apply that measure which suits the specific strategies in a specific situation. Measuring devices such as Force plate, Balance Master and Equitest are also discussed. Although the Balance Master and Equitest devices are more costly compared to the force plate only, they are more useful for assessing balance relevant to daily life activities that might result in falls.

A Markov Chain Approach to Baseball

Most earlier mathematical studies of baseball required particular models for advancing runners based on a small set of offensive possibilities. Other efforts considered only teams with players of identical ability. We introduce a Markov chain method that considers teams made up of players with different abilities and which is not restricted to a given model for runner advancement. Our method is limited only by the available data and can use any reasonable deterministic model for runner advancement when sufficiently detailed data are not available. Furthermore, our approach may be adapted to include the effects of pitching and defensive ability in a straightforward way. We apply our method to find optimal batting orders, run distributions per half inning and per game, and the expected number of games a team should win. We also describe the application of our method to test whether a particular trade would benefit a team.

RESIDUAL STRESSES IN OSCILLATING THORACIC ARTERIES REDUCE CIRCUMFERENTIAL STRESSES AND STRESS GRADIENTS

The purpose of this paper is to examine the effects of residual stresses and strains in the oscillating arteries on the stress distribution in the vascular wall. We employ a static theory of large elastic deformations for orthotropic material (Chuong and Fung, 1986, J. biomech. Engng 108, 189-192) with the acceleration term added to make the theory dynamic. We use the static elastic parameters of residual stresses in our analysis because the dynamic parameters are not available in the literature. Our analysis reveals that the effect of considering the residual stresses is to decrease the very large circumferential stresses at the inner wall by 62% and reduces the stress gradient through the arterial wall by 94% compared to the case when residual stresses are ignored. Thus, because the arteries do contain residual stresses, the consequent lower stresses at the inner wall and the reduced stress gradient may reduce the progression of atheroma. Our computations show that the stress gradients do not depend on the heart rate.

Optimal patterns for suturing wounds

A mathematical model for computing stresses in sutured human skin wounds is presented. The model uses the incremental law of elasticity and elastic constants valid for in vivo orthotropic skin. The model is applied to compute the principal stress and displacements resulting from suturing small elliptical and circular wounds in a large flat sheet of skin, in order to determine the optimal suturing patterns. It is observed that the average stress index for a circular wound sutured toward the center is almost double that of a wound sutured transverse to the diameter. Thus, the latter type of suturing pattern is preferable. Similarly, suturing an elliptical wound transversely produces a lower average stress index than a circular wound of the same area. It is also found that the optimal ratio of semi-major to semi-minor axis of an elliptical wound is near 3 (for abdominal wounds), i.e., this ratio produces the most uniform stresses along the wound edges, where wound healing is slowest. Since high stresses have adverse effects on healing and blood flow, this work, depicting regions of high stresses, may be used along with other biological factors to help predict regions of slower healing in sutured wounds.

Postural stability index is a more valid measure of stability than equilibrium score.

Researchers, therapists, and physicians often use equilibrium score (ES) from the Sensory Organization Test, a key test in the NeuroCom EquiTest System (a dynamic posturography system) to assess stability. ES reflects the overall coordination of the visual, proprioceptive, and vestibular systems for maintaining standing posture. In our earlier article, we proposed a new measure of anterior-posterior (A-P) postural stability called the Postural Stability Index (PSI), which accounts for more biomechanical aspects than ES. This article showed that PSI provides a clinically important adjunct to ES. In the present article, we show that PSI can provide an acceptable index even if a person falls during the trial, whereas ES assigns a zero score for any fall. We also show that PSI decreases as ankle stiffness increases, which is intuitive, while ES exhibits the opposite behavior. Ankle stiffness is generally recognized as an indicator of postural stability. These results suggest that PSI is a more valid measure of A-P stability than ES.

Modeling flows with curved detonation waves

Abstract The nonzero width of a curved detonation front has a significant effect on its propagation. Physically, the curvature effect is a small but important correction. In numerical simulations, the curvature effect tends to be greatly exaggerated due to an artificially large width of an underresolved wave. In the context of reactive fluid flow, a detonation wave consists of a lead shock followed by a thin reaction zone. The curvature effect is determined by the dynamics within the reaction zone; in particular, the competition between a source term for the rate of chemical energy release and a geometric source term due to front curvature. When the width of the reaction zone is small compared with the radius of curvature of the front, the reaction zone can be approximated as quasi-steady and be modeled locally by a system of ordinary differential equations (ODEs) in which the front curvature enters as a parameter. Front curvature breaks the Galilean invariance and the quasi-steady approximation is only valid in a distinguished frame determined by both the front curvature and the tangential velocity divergence ahead of the front. The quasi-steady ODEs determine the reaction zone profile to leading order and can be viewed as an extension of the ZND model. However, the source terms in the ODEs lead to modified Hugoniot jump conditions that take into account front curvature and reaction zone width. When the reaction zone is underresolved, a calculation in effect reduces to a “capturing algorithm” in which the burn model plays an analogous role for detonation waves as artificial viscosity does for shock waves. In particular, the reaction zone has an unphysically large width that is proportional to the cell size. As a consequence of the modified jump conditions, the numerical reaction zone width gives rise to an artificial curvature effect. This causes numerical solutions to depend on the cell size and orientation of a detonation front relative to the grid. Two algorithms that eliminate numerical curvature effects are discussed, detonation shock dynamics and front tracking.

Mathematical analysis of the flow of hyaluronic acid around fascia during manual therapy motions.

CONTEXT More research is needed to understand the flow characteristics of hyaluronic acid (HA) during motions used in osteopathic manipulative treatment and other manual therapies. OBJECTIVE To apply a 3-dimensional mathematical model to explore the relationship between the 3 manual therapy motions (constant sliding, perpendicular vibration, and tangential oscillation) and the flow characteristics of HA below the fascial layer. METHODS The Squeeze Film Lubrication theory of fluid mechanics for flow between 2 plates was used, as well as the Navier-Stokes equations. RESULTS The fluid pressure of HA increased substantially as fascia was deformed during manual therapies. There was a higher rate of pressure during tangential oscillation and perpendicular vibration than during constant sliding. This variation of pressure caused HA to flow near the edges of the fascial area under manipulation, and this flow resulted in greater lubrication. The pressure generated in the fluid between the muscle and the fascia during osteopathic manipulative treatment causes the fluid gap to increase. Consequently, the thickness between 2 fascial layers increases as well. Thus, the presence of a thicker fluid gap can improve the sliding system and permit the muscles to work more efficiently. CONCLUSION The mathematical model employed by the authors suggests that inclusion of perpendicular vibration and tangential oscillation may increase the action of the treatment in the extracellular matrix, providing additional benefits in manual therapies that currently use only constant sliding motions.

Computational method to evaluate ankle postural stiffness with ground reaction forces.

We examined an existing method for evaluating postural sway based on force-plate technology. Through an improved mathematical model of postural dynamics, we propose a new method, which better evaluated postural sway and, in addition, computed ankle moment and ankle postural stiffness directly from the measured ground reaction forces. An example is detailed that demonstrates the utility of this approach. The proposed method does not involve filtering or numerical integration and considers the platform inclination. Results from normal subjects show a linear relation between the ankle moment and the sway angle during quiet standing.

STRESSES AND STRAINS IN THE PASSIVE LEFT VENTRICLE

In this paper, we estimate the stresses and strains from the equatorial region down to the apex of the heart by modeling the passive left ventricle as a frustrum of a thick hollow cone. Large deformation theory has been employed in this analysis. Furthermore, the effects of residual stresses and the anisotropy due to muscle fiber orientation have been included. It is observed that circumferential stress, which is the most important physiologically, decreases considerably at the endocardium and is more evenly distributed through the wall when residual stresses are taken into account. The stresses also decrease as we go from the equatorial region to the apex. Because heart muscles physically have residual stresses, the consequent lower stress gradient through the wall enhances the diastolic function of the left ventricle.

STRESSES AND STRAINS IN THE LEFT VENTRICULAR WALL APPROXIMATED AS A THICK CONICAL SHELL USING LARGE DEFORMATION THEORY

In this paper, stress and strain equations are developed for the left ventricle mainly to find the influence of the ventricle’s shape on wall stresses. Here, the ventricle is assumed to be a thick-walled truncated conical shell and large elastic deformation theory is applied. Our model is compared to corresponding results approximating the left ventricle as a spherical shell. Clinically relevant parameters such as the myocardial stiffness constant, the stretch ratios and the stresses and strains have been computed using available canine data. The conical model leads to more realistic results than the spherical model and enables one to evaluate stresses and strains from base to apex instead of only at the equatorial region as in a cylindrical model.