Effect of craniovertebral decompression on CSF dynamics in Chiari malformation type I studied with computational fluid dynamics: Laboratory investigation.

OBJECT: The effect of craniovertebral decompression surgery on CSF flow dynamics in patients with Chiari malformation Type I (CM-I) has been incompletely characterized. The authors used computational fluid dynamics to calculate the effect of decompression surgery on CSF flow dynamics in the posterior fossa and upper cervical spinal canal. METHODS: Oscillatory flow was simulated in idealized 3D models of the normal adult and the CM-I subarachnoid spaces (both previously described) and in 3 models of CM-I post-craniovertebral decompressions. The 3 postoperative models were created from the CM model by virtually modifying the CM model subarachnoid space to simulate surgical decompressions of different magnitudes. Velocities and pressures were computed with the Navier-Stokes equations in Star-CD for multiple cycles of CSF flow oscillating at 80 cycles/min. Pressure gradients and velocities were compared for 8 levels extending from the posterior fossa to the C3-4 level. Relative pressures and peak velocities were plotted by level from the posterior fossa to C3-4. The heterogeneity of flow velocity distribution around the spinal cord was compared between models. RESULTS: Peak systolic velocities were generally lower in the postoperative models than in the preoperative CM model. With the 2 larger surgical defects, peak systolic velocities were brought closer to normal model velocities (equal values at C-3 and C-4) than with the smallest surgical defect. For the smallest defect, peak velocities were decreased, but not to levels in the normal model. In the postoperative models, heterogeneity in flow velocity distribution around the spinal cord increased from normal model levels as the degree of decompression increased. Pressures in the 5 models differed in magnitude and in pattern. Pressure gradients along the spinal canal in the normal and CM models were nonlinear, with steeper gradients below C3-4 than above. The CM model had a steeper pressure gradient than the normal model above C3-4 and the same gradient below. The postoperative models had lower pressure gradients than the CM model above C2-3. The most conservative decompression had lower pressure gradients than the normal model above C2-3. The two larger decompression defects had CSF pressure gradients below those in the normal model above C2-3. These 2 models had a less steep gradient above C-3 and a steeper gradient below. CONCLUSIONS: In computer simulations, craniovertebral surgical defects generally diminished CSF velocities and CSF pressures.

An assessment of swinger techniques for the playground swing oscillatory motion.

Much attention has been devoted to how playground swing amplitudes are built up by swinger techniques, i.e. body actions. However, very little attention has been given to the requirements that such swinger techniques place on the swinger himself. The purpose of this study was to find out whether different swinger techniques yield significantly different maximum torques, endurance and coordinative skills, and also to identify preferable techniques. We modelled the seated swinger as a rigid dumbbell and compared three different techniques. A series of computer simulations were run with each technique, testing the performance with different body rotational speeds, delayed onset of body rotation and different body mass distributions, as swing amplitudes were brought up towards 90°. One technique was found to be extremely sensitive to the timing of body actions, limiting swing amplitudes to 50° and 8° when body action was delayed by 0.03 and 0.3 s, respectively. Two other more robust techniques reached 90° even with the largest of these delays, although more time (and endurance) was needed. However, these two methods also differed with respect to maximum torque and endurance, and none was preferable in both these aspects, being dependent on the swinger goals and abilities.

Synchronizing computer simulations with measurement data for a case of atrial flutter.

Atrial flutter is a common supraventricular tachycardia that can be treated using radiofrequency catheter ablation, a procedure that is guided by electroanatomical mapping systems. In this paper, we propose an algorithm for incorporating mapping data into computer simulations of atrial electrical activity with the purpose of creating a more accurate map of electrical activation. The algorithm takes as input the extracellular potential values recorded at a number of sites throughout the atria and estimates the activation time for the entire atrial domain. We test the algorithm using synthetic mapping data and an anatomically detailed atrial geometry with an activation pattern typical of atrial flutter. The results show that the algorithm performs well with synthetic mapping data with information from relatively few mapping sites and in the presence of modeling and measurement error.

On the frequency of automaticity during ischemia in simulations based on stochastic perturbations of the Luo-Rudy 1 model.

AIMS: To compute the effects of parameter perturbations for single ischemic cardiac cells, and to determine how perturbations influenced the tendency for the cells to undergo spontaneous depolarization (automaticity) during 20 min of acute ischemia. METHODS: A modified Luo-Rudy 1 cell model was used. Since the range of biological variation and measurement errors is largely unknown, we conducted our study of the consequences of perturbations under the assumption that cell model parameters have a normal distribution with a 10% standard deviation. A total of 10000 random cell realizations were tested while varying important Luo-Rudy cell model parameters. Ischemia was modelled by deterministic functions chosen for the expected values of crucial ion concentrations and gating parameters as they developed with time, while realizing the respective parameter values from static normal distributions with a 10% standard deviation. RESULTS AND CONCLUSION: It was found that the tendency towards automaticity did increase as the stochastic parameters were varied. In particular, cells with standard Luo-Rudy parameter values did not become automatic during ischemia, whereas a significant portion of the cells with randomized parameter values did. The relative importance of model parameter variations was also determined and a sodium m-gate activation parameter was identified as the most critical parameter. The frequency of arrhythmic events during acute ischemia is known to be bell-shaped, with a peak at around 7-8 min after the onset of ischemia. Our simulations display a similar peak in the frequency of automaticity.

Modelling the parallel bars in men's artistic gymnastics.

The modelling of the parallel bars-gymnast system is considered. A 2D frontal plane model for the parallel bars apparatus is developed, enabling technique and injury analysis to be undertaken when combined with an interacting gymnast body model. We also demonstrate how such a gymnast body model may be combined with the parallel bars model by use of a simplifying symmetry consideration about the gymnast's sagittal plane. This symmetry consideration implies that just half the gymnast body and one of the two bars, are needed in the total model. We found that midpoint vertical parallel bars dynamics may be modelled by three parameters, using a single damped spring-mass model with linear force-displacement characteristics. Horizontally, as opposed to the vertical direction, bar endpoints accounted for a substantial part (35%) of the midpoint movement, demanding two serially connected springs for this direction. One spring represented the absolute horizontal movement of the bar endpoints, while the other spring represented the superimposed horizontal movement of bar midpoint relative to the endpoints. Both horizontal springs had the same characteristics as the vertical spring, giving a total of nine parameters for the three-spring bar model. Bar parameters were estimated by fitting the modelled bar movements to corresponding measured movements caused by a 140 kg lateral pendulum below the bar midpoint. Validation was then undertaken by comparing model-predicted bar movements to corresponding measurements using lateral pendulums of 100 kg and 60 kg, respectively. Finally, a gymnast handstand position was modelled and used to compare model-predicted and measured bar oscillations following a somersault backwards to a handstand position. The model gave convincing predictions of bar movements both for the 100 kg (1 period, RMS error of 7.0 mm) and 60 kg (1 period, RMS error of 3.7 mm) pendulums, as well as for the somersault landing (2 periods, RMS error of 8.1 mm).

Solving the heart mechanics equations with Newton and quasi Newton methods--a comparison.

The non-linear elasticity equations of heart mechanics are solved while emulating the effects of a propagating activation wave. The dynamics of a 1 cm(3) slab of active cardiac tissue was simulated as the electrical wave traversed the muscular heart wall transmurally. The regular Newton (Newton-Raphson) method was compared to two modified Newton approaches, and also to a third approach that delayed update only of some selected Jacobian elements. In addition, the impact of changing the time step (0.01, 0.1 and 1 ms) and the relative non-linear convergence tolerance (10(-4), 10(-3) and 10(-2)) was investigated. Updating the Jacobian only when slow convergence occurred was by far the most efficient approach, giving time savings of 83-96%. For each of the four methods, CPU times were reduced by 48-90% when the time step was increased by a factor 10. Increasing the convergence tolerance by the same factor gave time savings of 3-71%. Different combinations of activation wave speed, stress rate and bulk modulus revealed that the fastest method became relatively even faster as stress rate and bulk modulus was decreased, while the activation speed had negligible influence in this respect.