A stochastic differential equation analysis of cerebrospinal fluid dynamics

<p>Abstract</p> <p>Background</p> <p>Clinical measurements of intracranial pressure (ICP) over time show fluctuations around the deterministic time path predicted by a classic mathematical model in hydrocephalus research. Thus an important issue in mathematical research on hydrocephalus remains unaddressed--modeling the effect of noise on CSF dynamics. Our objective is to mathematically model the noise in the data.</p> <p>Methods</p> <p>The classic model relating the temporal evolution of ICP in pressure-volume studies to infusions is a nonlinear differential equation based on natural physical analogies between CSF dynamics and an electrical circuit. Brownian motion was incorporated into the differential equation describing CSF dynamics to obtain a nonlinear stochastic differential equation (SDE) that accommodates the fluctuations in ICP.</p> <p>Results</p> <p>The SDE is explicitly solved and the dynamic probabilities of exceeding critical levels of ICP under different clinical conditions are computed. A key finding is that the probabilities display strong threshold effects with respect to noise. Above the noise threshold, the probabilities are significantly influenced by the resistance to CSF outflow and the intensity of the noise.</p> <p>Conclusions</p> <p>Fluctuations in the CSF formation rate increase fluctuations in the ICP and they should be minimized to lower the patient's risk. The nonlinear SDE provides a scientific methodology for dynamic risk management of patients. The dynamic output of the SDE matches the noisy ICP data generated by the actual intracranial dynamics of patients better than the classic model used in prior research.</p

Mindful Aging: The Effects of Regular Brief Mindfulness Practice on Electrophysiological Markers of Cognitive and Affective Processing in Older Adults

There is growing interest in the potential benefits of mindfulness meditation practices in terms of counteracting some of the cognitive effects associated with aging. Pursuing this question, the aim of the present study was to investigate the influence of mindfulness training on executive control and emotion regulation in older adults, by means of studying behavioral and electrophysiological changes. Participants, 55 to 75 years of age, were randomly allocated to an 8-week mindful breath awareness training group or an active control group engaging in brain training exercises. Before and after the training period, participants completed an emotional-counting Stroop task, designed to measure attentional control and emotion regulation processes. Concurrently, their brain activity was measured by means of 64-channel electroencephalography. The results show that engaging in just over 10 min of mindfulness practice five times per week resulted in significant improvements in behavioral (response latency) and electrophysiological (N2 event-related potential) measures related to general task performance. Analyses of the underlying cortical sources (Variable Resolution Electromagnetic Tomography, VARETA) indicate that this N2-related effect is primarily associated with changes in the right angular gyrus and other areas of the dorsal attention network. However, the study did not find the expected specific improvements in executive control and emotion regulation, which may be due to the training instructions or the relative brevity of the intervention. Overall, the results indicate that engaging in mindfulness meditation training improves the maintenance of goal-directed visuospatial attention and may be a useful strategy for counteracting cognitive decline associated with aging

Adding noise to Markov cohort state-transition model in decision modeling and cost-effectiveness analysis.

Following its introduction over 30 years ago, the Markov cohort state-transition model has been used extensively to model population trajectories over time in health decision modeling and cost-effectiveness analysis studies. We recently showed that a cohort model represents the average of a continuous-time stochastic process on a multidimensional integer lattice governed by a master equation, which represents the time-evolution of the probability function of an integer-valued random vector. By leveraging this theoretical connection, this study introduces an alternative modeling method using a stochastic differential equation (SDE) approach, which captures not only the mean behavior but also the variance of the population process. We show the derivation of an SDE model from first principles, describe an algorithm to construct an SDE and solve the SDE via simulation for use in practice, and demonstrate the two applications of an SDE in detail. The first example demonstrates that the population trajectories, and their mean and variance, from the SDE and other commonly used methods in decision modeling match. The second example shows that users can readily apply the SDE method in their existing works without the need for additional inputs beyond those required for constructing a conventional cohort model. In addition, the second example demonstrates that the SDE model is superior to a microsimulation model in terms of computational speed. In summary, an SDE model provides an alternative modeling framework which includes information on variance, can accommodate for time-varying parameters, and is computationally less expensive than a microsimulation for a typical cohort modeling problem

Reduced vertical displacement of the center of mass is not accompanied by reduced oxygen uptake during walking

Abstract The six determinants of gait proposed that the goal of gait is to minimize vertical displacement of the body’s center of mass (CoM) with the objective to optimize energy expenditure. On the contrary, recent investigations suggest that reduced vertical displacement leads to an increase in energy expenditure. However, these investigations had the included subjects deliberately changing their gait, which could bias the endpoint measures. The present study investigated the effect of reduced vertical displacement of the CoM on oxygen uptake and walking economy without imposing altered gait patterns. This was accomplished by having subjects walk on a curved treadmill and on a flat treadmill. Vertical displacement of the CoM (sacrum marker displacement), oxygen uptake, walking economy, stride characteristics and lower limb joint angles were measured. There were significant differences in stride characteristics and phase dependent differences in lower limb movement pattern between the two conditions which in size were comparable to the changes observed between different speeds. The vertical displacement of the CoM was significantly reduced on the curved treadmill. This was accompanied by an increase in oxygen uptake and walking economy. These results support recent assertions that the six determinants of gait do not serve to improve walking economy