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Effect of Depth-Dependent Nociceptor Density on the Heat-Induced Withdrawal Reflex

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Applied Mathematics 2020年第8期11卷 788-824页

Previously we introduced a concise dose-response model for the heat-induced withdrawal reflex caused by millimeter wave radiation. The model predicts the occurrence of withdrawal reflex from the given spatial temperature profile. It was formulated on the assumption that the density of nociceptors in skin is uniform, independent of the depth. The model has only two parameters: the activation temperature of heat-sensitive nociceptors and the critical threshold on the activated volume for triggering withdrawal reflex. In this study, we consider the case of depth-dependent nociceptor density in skin. We use a general parametric form with a scaling parameter in the depth direction to represent the nociceptor density. We analyze system behaviors for four density types of this form. Based on the theoretical results, we develop a methodology for 1) identifying from test data the density form of nociceptors distribution, 2) finding from test data the scaling parameter in the density form, and 3) determining from test data the activation temperature of nociceptors.

关键词： High-Energy Millimeter Wave Radiation Heat-Induced Pain Depth-Dependent Nociceptor Density In Skin

Asymptotics and Well-Posedness of the Derived Distribution Density in a Study of Biovariability

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Applied Mathematics 2018年第6期9卷 672-690页

作者： Hongyun Wang wesley A. Burgei Hong Zhou Department of Applied Mathematics and Statistics University of California Santa Cruz CA USA US Department of Defense Joint Non-Lethal Weapons Directorate Quantico VA USA Department of Applied Mathematics Naval Postgraduate School Monterey CA USA

In our recent work (Wang, Burgei, and Zhou, 2018) we studied the hearing loss injury among subjects in a crowd with a wide spectrum of heterogeneous individual injury susceptibility due to biovariability. The injury risk of a crowd is defined as the average fraction of injured. We examined mathematically the injury risk of a crowd vs the number of acoustic impulses the crowd is exposed to, under the assumption that all impulses act independently in causing injury regardless of whether one is preceded by another. We concluded that the observed dose-response relation can be explained solely on the basis of biovariability in the form of heterogeneous susceptibility. We derived an analytical solution for the distribution density of injury susceptibility, as a power series expansion in terms of scaled log individual non-injury probability. While theoretically the power series converges for all argument values, in practical computations with IEEE double precision, at large argument values, the numerical accuracy of the power series summation is completely wiped out by the accumulation of round-off errors. In this study, we derive a general asymptotic approximation at large argument values, for the distribution density. The combination of the power series and the asymptotics provides a practical numerical tool for computing the distribution density. We then use this tool to verify numerically that the distribution obtained in our previous theoretical study is indeed a proper density. In addition, we will also develop a very efficient and accurate Pade approximation for the distribution density.

关键词： Distribution of Individual Injury Susceptibility in a Crowd Biovariability Asymptotic Approximation Pade Approximation

Interpreting Dose-Response Relation for Exposure to Multiple Sound Impulses in the Framework of Immunity

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Health 2017年第13期9卷 1817-1842页

Hearing loss is a common military health problem and it is closely related to exposures to impulse noises from blast explosions and weapon firings. In a study based on test data of chinchillas and scaled to humans (Military Medicine, 181: 59-69), an empirical injury model was constructed for exposure to multiple sound impulses of equal intensity. Building upon the empirical injury model, we conduct a mathematical study of the hearing loss injury caused by multiple impulses of non-uniform intensities. We adopt the theoretical framework of viewing individual sound exposures as separate injury causing events, and in that framework, we examine synergy for causing injury (fatigue) or negative synergy (immunity) or independence among a sequence of doses. Starting with the empirical logistic dose-response relation and the empirical dose combination rule, we show that for causing injury, a sequence of sound exposure events are not independent of each other. The phenomenological effect of a preceding event on the subsequent event is always immunity. We extend the empirical dose combination rule, which is applicable only in the case of homogeneous impulses of equal intensity, to accommodate the general case of multiple heterogeneous sound exposures with non-uniform intensities. In addition to studying and extending the empirical dose combination rule, we also explore the dose combination rule for the hypothetical case of independent events, and compare it with the empirical one. We measure the effect of immunity quantitatively using the immunity factor defined as the percentage of decrease in injury probability attributed to the sound exposure in the preceding event. Our main findings on the immunity factor are: 1) the immunity factor is primarily a function of the difference in SELA (A- weighted sound exposure level) between the two sound exposure events;it is virtually independent of the magnitude of the two SELA values as long as the difference is fixed;2) the immunity fac

关键词： Risk of Significant Injury Logistic Dose-Response Relation SELA (A-Weighted Sound Exposure Level) Effective SELA for Multiple Heterogeneous Sound Impulses Fatigue and Immunity

Opportunities and Challenges for Inverse Design of Nanostructures with Sequence Defined Macromolecules

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Accounts of Materials Research 2021年第9期2卷 697-700页

作者： wesley F.Reinhart Antonia Statt Materials Science and Engineering Pennsylvania State UniversityUniversity ParkPennsylvania 16802United States Institute for Computational and Data Sciences Pennsylvania State UniversityUniversity ParkPennsylvania 16802United States Materials Science and Engineering Grainger College of EngineeringUniversity of IllinoisUrbanaChampaignIllinois 61801United States

Self-assembly of block copolymers has a rich history and has been shown to be a versatile and robust strategy for the bottom-up fabrication of nanostructured functional materials,1 with especially exciting applications in medicine.2 This is due in part to the fact that even blocky sequences composed of a few monomers exhibit rich phase behavior which can be tuned to achieve exotic structures.3,4 However,these simple patterns represent only a tiny fraction of all sequences that can be synthesized in a modern chemistry *** instance,biological proteins which may be composed of dozens of amino acids in arbitrary(and lengthy)sequences can be readily *** it is presently impossible to predict how these complex chemistries lead to structures without experimental or computational trial and error.

关键词： sequences versatile readily

Risk of Hearing Loss Caused by Multiple Acoustic Impulses in the Framework of Biovariability

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Health 2018年第5期10卷 604-628页

We consider the hearing loss injury among subjects in a crowd with a wide spectrum of individual intrinsic injury probabilities due to biovariability. For multiple acoustic impulses, the observed injury risk of a crowd vs the effective combined dose follows the logistic dose-response relation. The injury risk of a crowd is the average fraction of injured. The injury risk was measured in experiments as follows: each subject is individually exposed to a sequence of acoustic impulses of a given intensity and the injury is recorded;results of multiple individual subjects were assembled into data sets to mimic the response of a crowd. The effective combined dose was adjusted by varying the number of impulses in the sequence. The most prominent feature observed in experiments is that the injury risk of the crowd caused by multiple impulses is significantly less than the value predicted based on assumption that all impulses act independently in causing injury and all subjects in the crowd are statistically identical. Previously, in the case where all subjects are statistically identical (i.e., no biovariability), we interpreted the observed injury risk caused by multiple impulses in terms of the immunity effects of preceding impulses on subsequent impulses. In this study, we focus on the case where all sound exposure events act independently in causing injury regardless of whether one is preceded by another (i.e., no immunity effect). Instead, we explore the possibility of interpreting the observed logistic dose-response relation in the framework of biovariability of the crowd. Here biovariability means that subjects in the crowd have their own individual injury probabilities. That is, some subjects are biologically less or more susceptible to hearing loss injury than others. We derive analytically the distribution of individual injury probability that produces the observed logistic dose-response relation. For several parameter values, we prove that the derived distributio

关键词： Risk of Significant Hearing Loss Injury Dose-Response Relation for Multiple Acoustic Impulses Biovariability A Crowd With Heterogeneous Individual Injury Probabilities

Fragility of statistically significant findings from randomized clinical trials of surgical treatment of humeral shaft fractures:A systematic review

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World Journal of Orthopedics 2022年第9期13卷 825-836页

作者： Stephen Craig Morris Anirudh K Gowd Avinesh Agarwalla wesley P Phipatanakul Nirav H Amin Joseph N Liu Department of Orthopaedic Surgery Loma Linda UniversityLoma LindaCA 92354United States Department of Orthopaedic Surgery Wake Forest University Baptist Medical CenterWinston-SalemNC 27157United States Department of Orthopaedic Surgery Westchester Medical CenterValhallaNY 10595United States Department of Orthopaedic Surgery Premier Orthopaedic and Trauma SpecialistsPomonaCA 91767United States Department of Orthopedic Surgery USC Epstein Family Center for Sports MedicineLos AngelesCA 90089United States

BACKGROUND Despite recent meta-analyses of randomized controlled trials(RCTs),there remains no consensus regarding the preferred surgical treatment for humeral shaft *** fragility index(FI)is an emerging tool used to evaluate the robustness of RCTs by quantifying the number of participants in a study group that would need to switch outcomes in order to reverse the study *** To investigate the fragility index of randomized control trials assessing outcomes of operative fixation in proximal humerus *** We completed a systematic review of RCTs evaluating the surgical treatment of humeral shaft *** criteria included:articles published in English;patients randomized and allotted in 1:1 ratio to 2 parallel arms;and dichotomous outcome *** FI was calculated for total complications,each complication individually,and secondary surgeries using the Fisher exact test,as previously *** Fifteen RCTs were included in the analysis comparing open reduction plate osteosynthesis with dynamic compression plate or locking compression plate,intramedullary nail,and minimally invasive plate *** median FI was 0 for all parameters *** individual outcomes,the FI was 0 for 81/91(89%)of *** FI exceeded the number lost to follow up in only 2/91(2%)*** The FI shows that data from RCTs regarding operative treatment of humeral shaft fractures are fragile and does not demonstrate superiority of any particular surgical technique.

关键词： Humerus fracture Open reduction internal fixation Intramedullary nail Fragility index Complications Fragility index

Risk of Hearing Loss Injury Caused by Multiple Flash Bangs on a Crowd

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American Journal of Operations Research 2018年第4期8卷 239-265页

A flash bang is a non-lethal explosive device that delivers intensely loud bangs and bright lights to suppress potentially dangerous targets. It is usually used in crowd control, hostage rescue and numerous other missions. We construct a model for assessing quantitatively the risk of hearing loss injury caused by multiple flash bangs. The model provides a computational framework for incorporating the effects of the key factors defining the situation and for testing various sub-models for these factors. The proposed model includes 1) uncertainty in the burst point of flash bang mortar, 2) randomness in the dispersion of multiple submunitions after the flash bang mortar burst, 3) decay of acoustic impulse from a single submunition to an individual subject along the ground surface, 4) the effective combined sound exposure level on an individual subject caused by multiple submunitions at various distances from the subject, and 5) randomness in the spatial distribution of subjects in the crowd. With the mathematical model formulated, we seek to characterize the overall effect of flash bang mortar in the form of an effective injury area. We carry out simulations to study the effects of uncertainty and randomness on the risk of hearing loss injury of the crowd. The proposed framework serves as a starting point for a comprehensive assessment of hearing loss injury risk, taking into consideration all realistic and relevant features of flash bang mortar. It also provides a platform for testing and updating component models.

关键词： Risk of Significant Hearing Loss Mathematical Framework for Assessing Injury Risk Effective Injury Area Decay of Acoustic Impulse along Ground Surface Dose-Response Relation Fluctuations in Actual Injury Numbers

Dose-Injury Relation as a Model for Uncertainty Propagation from Input Dose to Target Dose

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American Journal of Operations Research 2018年第5期8卷 360-385页

作者： Hongyun Wang wesley A. Burgei Hong Zhou Department of Applied Mathematics University of California Santa Cruz CA USA U.S. Department of Defense Joint Non-Lethal Weapons Directorate Quantico VA USA Department of Applied Mathematics Naval Postgraduate School Monterey CA USA

We study a general framework for assessing the injury probability corresponding to an input dose quantity. In many applications, the true value of input dose may not be directly measurable. Instead, the input dose is estimated from measurable/controllable quantities via numerical simulations using assumed representative parameter values. We aim at developing a simple modeling framework for accommodating all uncertainties, including the discrepancy between the estimated input dose and the true input dose. We first interpret the widely used logistic dose-injury model as the result of dose propagation uncertainty from input dose to target dose at the active site for injury where the binary outcome is completely determined by the target dose. We specify the symmetric logistic dose-injury function using two shape parameters: the median injury dose and the 10 - 90 percentile width. We relate the two shape parameters of injury function to the mean and standard deviation of the dose propagation uncertainty. We find 1) a larger total uncertainty will spread more the dose-response function, increasing the 10 - 90 percentile width and 2) a systematic over-estimate of the input dose will shift the injury probability toward the right along the estimated input dose. This framework provides a way of revising an established injury model for a particular test population to predict the injury model for a new population with different distributions of parameters that affect the dose propagation and dose estimation. In addition to modeling dose propagation uncertainty, we propose a new 3-parameter model to include the skewness of injury function. The proposed 3-parameter function form is based on shifted log-normal distribution of dose propagation uncertainty and is approximately invariant when other uncertainties are added. The proposed 3-parameter function form provides a framework for extending skewed injury model from a test population to a target population in application.

关键词： Dose Injury Relation Dose Propagation Uncertainty Median Injury Dose 10 - 90 Percentile Width Skewness Mapping Injury Model from One Population to Another

A Concise Model and Analysis for Heat-Induced Withdrawal Reflex Caused by Millimeter Wave Radiation

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American Journal of Operations Research 2020年第2期10卷 31-81页

作者： Hongyun Wang wesley A. Burgei Hong Zhou Department of Applied Mathematics University of California Santa Cruz USA U.S. Department of Defense Joint Non-Lethal Weapons Directorate Quantico USA Department of Applied Mathematics Naval Postgraduate School Monterey CA USA

In this study, we consider the heat-induced withdrawal reflex caused by exposure to an electromagnetic beam. We propose a concise dose-response relation for predicting the occurrence of withdrawal reflex from a given spatial temperature profile. Our model is distilled from sub-step components in the ADT CHEETEH-E model developed at the Institute for Defense Analyses. Our model has only two parameters: the activation temperature of nociceptors and the critical threshold on the activated volume. When the spatial temperature profile is measurable, the two parameters can be determined from test data. We connect this dose-response relation to a temperature evolution model for electromagnetic heating. The resulting composite model governs the process from the electromagnetic beam deposited on the skin to the binary outcome of subject’s reflex response. We carry out non-dimensionalization in the time evolution model. The temperature solution of the non-dimensional system is the product of the applied power density and a parameter-free function. The effects of physical parameters are contained in non-dimensional time and depth. Scaling the physical temperature distribution into a parameter-free function greatly simplifies the analytical solution, and helps to pinpoint the effects of beam spot area and applied power density. With this formulation, we study the theoretical behaviors of the system, including the time of reflex, effect of heat conduction, biological latency in observed reflex, energy consumption by the time of reflex, and the strategy of selecting test conditions in experiments for the purpose of inferring model parameters from test data.

关键词： Millimeter Wave Radiation Heat-Induced Pain Withdrawal Reflex Dose-Response Model Biological Latency Non-Dimensionalization Effect of Heat Conduction