This dissertation develops uncertainty quantification methodologies for modeling, response analysis and optimization of diverse dynamical systems. Two distinct application platforms are considered pertaining to engineering dynamics and precision medicine. First, the recently developed Wiener path integral (WPI) technique for determining, accurately and in a computationally efficient manner, the stochastic response of diverse dynamical systems is employed for solving a high-dimensional, nonlinear system of stochastic differential equations governing the dynamics of a representative model of electrostatically coupled micromechanical oscillators. Compared to alternative modeling and solution treatments in the literature, the current development exhibits the following novelties: a) typically adopted linear, or higher-order polynomial, approximations of the nonlinear electrostatic forces are circumvented; and b) stochastic modeling is employed, for the first time, by considering a random excitation component representing the effect of diverse noise sources on the system dynamics. Further, the WPI technique is enhanced and extended based on a Bayesian compressive sampling (CS) treatment. Specifically, sparse expansions for the system response joint PDF are utilized. Next, exploiting the localization capabilities of the WPI technique for direct evaluation of specific PDF points leads to an underdetermined linear system of equations for the expansion coefficients. Furthermore, relying on a Bayesian CS solution formulation yields a posterior distribution for the expansion coefficient vector. In this regard, a significant advantage of the herein-developed methodology relates to the fact that the uncertainty of the response PDF estimates obtained by the WPI technique is quantified. Also, an adaptive scheme is proposed based on the quantified uncertainty of the estimates for the optimal selection of PDF sample points. This yields considerably fewer boundary value problems to be solved as part of the WPI technique, and thus, the associated computational cost is significantly reduced. Second, modeling and analysis of the physiological mechanism of dynamic cerebral autoregulation (DCA) is pursued based on the concept of diffusion maps. Specifically, a state-space description of DCA dynamics is considered based on arterial blood pressure (ABP), cerebral blood flow velocity (CBFV), and their time derivatives. Next, an eigenvalue analysis of the Markov matrix of a random walk on a graph over the dataset domain yields a low-dimensional representation of the intrinsic dynamics. Further dimension reduction is made possible by accounting only for the two most significant eigenvalues. The value of their ratio indicates whether the underlying system is governed by active or hypoactive dynamics, indicating healthy or impaired DCA function, respectively. The reliability of the technique is assessed by considering healthy individuals and patients with unilateral carotid artery stenosis or occlusion. It is shown that the proposed ratio of eigenvalues can be used as a reliable and robust biomarker for assessing how active the intrinsic dynamics of the autoregulation is and for indicating healthy versus impaired DCA function. Further, an alternative joint time-frequency analysis methodology based on generalized harmonic wavelets is utilized for assessing DCA performance in patients with preeclampsia within one week postpartum, which is associated with an increased risk for postpartum maternal cerebrovascular complications. The results are compared with normotensive postpartum individuals and healthy non-pregnant female volunteers and suggest a faster, but less effective response of the cerebral autoregulatory mechanism in the first week postpartum, regardless of preeclampsia diagnosis.

Recent evidence suggests that heat, a major byproduct of exercise, may be the mediator for many vascular adaptations that come from exercise. Thus, heat therapy that increases muscle temperature in a comparable way to exercise may be an advantageous alternative for enhancing cardiovascular health in individuals where treatment with exercise is either not possible or undesired. PURPOSE: Compare the effects of exercise and heat training on resistance artery function at rest and during exercise. METHODS: Thirty-five (18 female) healthy, untrained subjects completed a 6-week training program utilizing either high intensity knee extension (KE) exercise (40 min), localized heat therapy (pulsed shortwave diathermy; 120 min), or a sham heat therapy protocol (120 min). We randomly selected 8 subjects from each group to have a temperature probe inserted into their vastus lateralis muscle during one of their training sessions to evaluate the effect of the interventions on muscle temperature. We assessed resistance artery function at rest with the passive leg movement technique (PLM) prior to and after completion of the training protocols. We assessed peak exercise blood flow (KE peak flow) and peak power output (KE peak power) during the KE graded exercise test and prior to and after completion of the training protocols. RESULTS: Peak muscle treatment temperature was significantly different between all groups with those assigned to the diathermy heat training exhibiting a higher peak temperature (~40.80°C) than those in the exercise (~37.75°C, P < 0.001) and sham training groups (~36.10°C, P < 0.001). KE peak flow during PLM increased to the same extent (P = 0.625) in both the exercise (~10.5% increase, P = 0.009) and heating groups (~8.5% increase, P = 0.044); but tended to decrease in the sham group (P = 0.087). KE peak flow increased in the exercise group (~19%, P = 0.005), but did not change in the heat group (P = 0.523) and decreased in the sham group (~7%, P = 0.020). Peak vascular conductance during KE significantly increased by ~25% in the exercise (P = 0.030) and heat (P = 0.012) groups. KE peak power increased in the exercise group by ~27% (P = 0.001) but did not significantly change in the heat (P = 0.175) and sham groups (P = 0.111). The change in vascular function, assessed via PLM, showed a correlation with both ∆KE peak flow (R = 0.55, P = 0.01) and ∆KE peak power (R = 0.56, P = .010). Likewise, ∆KE peak flow showed a strong association with ∆KE peak power (R = 0.64, P < 0.001). CONCLUSION: Localized diathermy heat treatment increased resistance artery function at rest and during exercise to a similar extent as single-leg KE exercise training but did not yield significant improvements in performance. Thus, heat training mimics some but not all of the benefits associated with exercise and may be used to replace exercise treatment to some extent.

Low-load blood flow restriction (LLBFR) training has been shown to elicit greater increases in muscle hypertrophy and strength compared to traditional low-load training, yet few studies have compared the effectiveness of different LLBFR protocols. To our knowledge, no previous study has compared the acute neuromuscular changes induced by two common LLBFR protocols: 30-15-15-15 repetitions (BFR-75) and four sets of repetitions performed to volitional failure (BFR-F). Therefore, the purpose of this study was to use surface electromyography (sEMG) to compare changes in muscle excitation and fatigue during BFR-75 and BFR-F protocols. Ten women (mean ± SD age = 22 ± 3.5 years) volunteered to participate in this investigation. Participants performed isokinetic, unilateral, concentric-eccentric, leg extension muscle actions at 30% maximal voluntary isometric contraction torque with BFR applied at 60% arterial occlusion pressure using a 12-centimeter-wide cuff. The sEMG amplitude and frequency values were measured from the rectus femoris muscle during the beginning and end of each set of exercise and analyzed using separate 2 [condition (BFR-75 and BFR-F)] x 8 [time (B1, E1, B2, E2, B3, E3, B4, E4)] repeated measures ANOVAs. For sEMG amplitude, there was no significant 2-way interaction (p = 0.486; ηₚ² = 0.118) or significant main effect for condition (p = 0.617; ηₚ² = 0.038), but there was a significant main effect for time (p < 0.001; ηₚ² = 0.520). SEMG amplitude increased across time during both protocols (B1 < E1, E2, B3, E3, B4, E4, p ≤ 0.001–0.049). For sEMG frequency, there was no significant 2-way interaction (p = 0.847; ηₚ² = 0.064) or significant main effect for condition (p = 0.825; ηₚ² = 0.007), but there was a significant main effect for time (p = 0.006; ηₚ² = 0.478). SEMG frequency decreased across time during both protocols (B1 > E1, B2, E2, B3, E3, B4, E4, p = 0.002–0.035). Thus, the implementation of the BFR-75 and BFR-F protocols elicited comparable neuromuscular responses that were consistent with fatiguing exercise, but investigators and clinicians may consider other factors such as participant/patient comfort, time, and rating of perceived exertion when determining which protocol to use.

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