Thomas Woolley - Academia.edu (original) (raw)
Papers by Thomas Woolley
Physical Review E, 2011
Numerous mathematical models exploring the emergence of complexity within developmental biology i... more Numerous mathematical models exploring the emergence of complexity within developmental biology incorporate diffusion as the dominant mechanism of transport. However, self-organizing paradigms can exhibit the biologically undesirable property of extensive sensitivity, as illustrated by the behavior of the French-flag model in response to intrinsic noise and Turing’s model when subjected to fluctuations in initial conditions. Domain growth is known to be a stabilizing factor for the latter, though the interaction of intrinsic noise and domain growth is underexplored, even in the simplest of biophysical settings. Previously, we developed analytical Fourier methods and a description of domain growth that allowed us to characterize the effects of deterministic domain growth on stochastically diffusing systems. In this paper we extend our analysis to encompass stochastically growing domains. This form of growth can be used only to link the meso- and macroscopic domains as the “box-splitting” form of growth on the microscopic scale has an ill-defined thermodynamic limit. The extension is achieved by allowing the simulated particles to undergo random walks on a discretized domain, while stochastically controlling the length of each discretized compartment. Due to the dependence of diffusion on the domain discretization, we find that the description of diffusion cannot be uniquely derived. We apply these analytical methods to two justified descriptions, where it is shown that, under certain conditions, diffusion is able to support a consistent inhomogeneous state that is far removed from the deterministic equilibrium, without additional kinetics. Finally, a logistically growing domain is considered. Not only does this show that we can deal with nonmonotonic descriptions of stochastic growth, but it is also seen that diffusion on a stationary domain produces different effects to diffusion on a domain that is stationary “on average.”
Physical Review E, 2011
A central challenge in developmental biology is understanding the creation of robust spatiotempor... more A central challenge in developmental biology is understanding the creation of robust spatiotemporal heterogeneity. Generally, the mathematical treatments of biological systems have used continuum, mean-field hypotheses for their constituent parts, which ignores any sources of intrinsic stochastic effects. In this paper we consider a stochastic space-jump process as a description of diffusion, i.e., particles are able to undergo a random walk on a discretized domain. By developing analytical Fourier methods we are able to probe this probabilistic framework, which gives us insight into the patterning potential of diffusive systems. Further, an alternative description of domain growth is introduced, with which we are able to rigorously link the mean-field and stochastic descriptions. Finally, through combining these ideas, it is shown that such stochastic descriptions of diffusion on a deterministically growing domain are able to support the nucleation of states that are far removed from the deterministic mean-field steady state.
Annals of Pharmacotherapy, 2001
To determine the accuracy of three automatic monitors (arm, wrist, finger) for blood pressure mea... more To determine the accuracy of three automatic monitors (arm, wrist, finger) for blood pressure measurement manufactured by Omron compared with a standard mercury sphygmomanometer. PRIMRY END POINT: Difference in the mean blood pressure readings from each monitor; the secondary end point was difference in pulse readings. A single-visit, crossover trial tested each device twice on the left arm of each participant; the average of the two readings was recorded. The pulse readings from each monitor were also recorded. ANOVA was used to compare mean blood pressure readings and pulse readings from each device. A total of 55 persons (mean age 53 y; 36 women) met inclusion criteria and completed the study. The mean systolic and diastolic readings obtained from the electronic arm unit were comparable to the mercury readings (124.4/78.02 vs. 129.45/77.87 mm Hg, respectively; p > 0.05 for both readings). The mean results obtained from the wrist and finger monitors differed significantly from those of the mercury readings (145.44/89.58 and 113.94/69.07 mm Hg, respectively; p < 0.05 for both monitors compared with control). No difference was measured in the mean pulse readings between the comparisons (p = 0.72). The absolute difference in systolic and diastolic blood pressure readings from control varied the least wih the arm monitor. Compared with the mercury sphygmomanometer, the arm monitor was the most accurate in measuring blood pressure. The wrist and finger monitors resulted in statistically significant mean systolic and diastolic differences compared with the mercury sphygmomanometer.
Annals of Pharmacotherapy, 2001
To determine the accuracy of three automatic monitors (arm, wrist, finger) for blood pressure mea... more To determine the accuracy of three automatic monitors (arm, wrist, finger) for blood pressure measurement manufactured by Omron compared with a standard mercury sphygmomanometer. PRIMRY END POINT: Difference in the mean blood pressure readings from each monitor; the secondary end point was difference in pulse readings. A single-visit, crossover trial tested each device twice on the left arm of each participant; the average of the two readings was recorded. The pulse readings from each monitor were also recorded. ANOVA was used to compare mean blood pressure readings and pulse readings from each device. A total of 55 persons (mean age 53 y; 36 women) met inclusion criteria and completed the study. The mean systolic and diastolic readings obtained from the electronic arm unit were comparable to the mercury readings (124.4/78.02 vs. 129.45/77.87 mm Hg, respectively; p > 0.05 for both readings). The mean results obtained from the wrist and finger monitors differed significantly from those of the mercury readings (145.44/89.58 and 113.94/69.07 mm Hg, respectively; p < 0.05 for both monitors compared with control). No difference was measured in the mean pulse readings between the comparisons (p = 0.72). The absolute difference in systolic and diastolic blood pressure readings from control varied the least wih the arm monitor. Compared with the mercury sphygmomanometer, the arm monitor was the most accurate in measuring blood pressure. The wrist and finger monitors resulted in statistically significant mean systolic and diastolic differences compared with the mercury sphygmomanometer.
Physical Review E, 2011
Numerous mathematical models exploring the emergence of complexity within developmental biology i... more Numerous mathematical models exploring the emergence of complexity within developmental biology incorporate diffusion as the dominant mechanism of transport. However, self-organizing paradigms can exhibit the biologically undesirable property of extensive sensitivity, as illustrated by the behavior of the French-flag model in response to intrinsic noise and Turing’s model when subjected to fluctuations in initial conditions. Domain growth is known to be a stabilizing factor for the latter, though the interaction of intrinsic noise and domain growth is underexplored, even in the simplest of biophysical settings. Previously, we developed analytical Fourier methods and a description of domain growth that allowed us to characterize the effects of deterministic domain growth on stochastically diffusing systems. In this paper we extend our analysis to encompass stochastically growing domains. This form of growth can be used only to link the meso- and macroscopic domains as the “box-splitting” form of growth on the microscopic scale has an ill-defined thermodynamic limit. The extension is achieved by allowing the simulated particles to undergo random walks on a discretized domain, while stochastically controlling the length of each discretized compartment. Due to the dependence of diffusion on the domain discretization, we find that the description of diffusion cannot be uniquely derived. We apply these analytical methods to two justified descriptions, where it is shown that, under certain conditions, diffusion is able to support a consistent inhomogeneous state that is far removed from the deterministic equilibrium, without additional kinetics. Finally, a logistically growing domain is considered. Not only does this show that we can deal with nonmonotonic descriptions of stochastic growth, but it is also seen that diffusion on a stationary domain produces different effects to diffusion on a domain that is stationary “on average.”
Physical Review E, 2011
A central challenge in developmental biology is understanding the creation of robust spatiotempor... more A central challenge in developmental biology is understanding the creation of robust spatiotemporal heterogeneity. Generally, the mathematical treatments of biological systems have used continuum, mean-field hypotheses for their constituent parts, which ignores any sources of intrinsic stochastic effects. In this paper we consider a stochastic space-jump process as a description of diffusion, i.e., particles are able to undergo a random walk on a discretized domain. By developing analytical Fourier methods we are able to probe this probabilistic framework, which gives us insight into the patterning potential of diffusive systems. Further, an alternative description of domain growth is introduced, with which we are able to rigorously link the mean-field and stochastic descriptions. Finally, through combining these ideas, it is shown that such stochastic descriptions of diffusion on a deterministically growing domain are able to support the nucleation of states that are far removed from the deterministic mean-field steady state.
Annals of Pharmacotherapy, 2001
To determine the accuracy of three automatic monitors (arm, wrist, finger) for blood pressure mea... more To determine the accuracy of three automatic monitors (arm, wrist, finger) for blood pressure measurement manufactured by Omron compared with a standard mercury sphygmomanometer. PRIMRY END POINT: Difference in the mean blood pressure readings from each monitor; the secondary end point was difference in pulse readings. A single-visit, crossover trial tested each device twice on the left arm of each participant; the average of the two readings was recorded. The pulse readings from each monitor were also recorded. ANOVA was used to compare mean blood pressure readings and pulse readings from each device. A total of 55 persons (mean age 53 y; 36 women) met inclusion criteria and completed the study. The mean systolic and diastolic readings obtained from the electronic arm unit were comparable to the mercury readings (124.4/78.02 vs. 129.45/77.87 mm Hg, respectively; p > 0.05 for both readings). The mean results obtained from the wrist and finger monitors differed significantly from those of the mercury readings (145.44/89.58 and 113.94/69.07 mm Hg, respectively; p < 0.05 for both monitors compared with control). No difference was measured in the mean pulse readings between the comparisons (p = 0.72). The absolute difference in systolic and diastolic blood pressure readings from control varied the least wih the arm monitor. Compared with the mercury sphygmomanometer, the arm monitor was the most accurate in measuring blood pressure. The wrist and finger monitors resulted in statistically significant mean systolic and diastolic differences compared with the mercury sphygmomanometer.
Annals of Pharmacotherapy, 2001
To determine the accuracy of three automatic monitors (arm, wrist, finger) for blood pressure mea... more To determine the accuracy of three automatic monitors (arm, wrist, finger) for blood pressure measurement manufactured by Omron compared with a standard mercury sphygmomanometer. PRIMRY END POINT: Difference in the mean blood pressure readings from each monitor; the secondary end point was difference in pulse readings. A single-visit, crossover trial tested each device twice on the left arm of each participant; the average of the two readings was recorded. The pulse readings from each monitor were also recorded. ANOVA was used to compare mean blood pressure readings and pulse readings from each device. A total of 55 persons (mean age 53 y; 36 women) met inclusion criteria and completed the study. The mean systolic and diastolic readings obtained from the electronic arm unit were comparable to the mercury readings (124.4/78.02 vs. 129.45/77.87 mm Hg, respectively; p > 0.05 for both readings). The mean results obtained from the wrist and finger monitors differed significantly from those of the mercury readings (145.44/89.58 and 113.94/69.07 mm Hg, respectively; p < 0.05 for both monitors compared with control). No difference was measured in the mean pulse readings between the comparisons (p = 0.72). The absolute difference in systolic and diastolic blood pressure readings from control varied the least wih the arm monitor. Compared with the mercury sphygmomanometer, the arm monitor was the most accurate in measuring blood pressure. The wrist and finger monitors resulted in statistically significant mean systolic and diastolic differences compared with the mercury sphygmomanometer.