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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

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

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 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

Laser Micro-Printing of Dye-Molecules on Polymeric Surfaces

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Open Journal of Applied Sciences 2016年第7期6卷 416-421页

作者： wesley Sims Aschalew Kassu Carlton Farley Anup Sharma Department of Physics Chemistry and Mathematics Alabama A&M University Normal AL USA Department of Mechanical Engineering Civil Engineering and Construction Management Alabama A&M University Normal AL USA

We describe a technique for micro-patterning and immobilization of dyes on polymer substrates using a low-power visible laser for dye-excitation. Deposits from an aqueous medium containing the dye can be attached at any desired spot on the substrate simply by exposing the area to laser light. The area of the laser beam can control the spot-size of immobilized dye, in the range of 10 - 100 microns. The immobilization technique is characterized by micro-printing numerals, alphabets and patterns on polybutadiene substrates with Rhodamine (Rh6G) dye. Adsorption of laser-excited dye molecules within the polymer appears to be the mechanism for laser-printing technique.

关键词： Laser Micro-Printing Laser Immobilization of Molecules Micro-Patterning Reticle

Investigation on Adipose Mechanical Properties under Compression Loading for Improving Human Body Modelling

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Investigation on Adipose Mechanical Properties under Compres...

作者： wesley Chebii Rutto 湖南大学

学位级别：硕士

迄今为止,旨在减轻弹道和弹片攻击的军事级装甲材料在抵抗爆炸冲击方面效果较差。为了改善装甲的爆炸吸收特性,第一步是彻底了解爆炸对人体本身的影响。皮下脂肪组织与人体其他软组织一样,容易受到爆炸冲击和弹片穿透等影响。但是,目前... 详细信息

迄今为止,旨在减轻弹道和弹片攻击的军事级装甲材料在抵抗爆炸冲击方面效果较差。为了改善装甲的爆炸吸收特性,第一步是彻底了解爆炸对人体本身的影响。皮下脂肪组织与人体其他软组织一样,容易受到爆炸冲击和弹片穿透等影响。但是,目前尚缺乏表征脂肪对变化负荷条件的生物力学响应的研究。这为研究脂肪组织负荷的机理提供了充分的依据,这将是改善保护装置设计的关键一步。基于改进PPE的需要,当前的研究工作旨在通过研究在不同应变率下的准静态和动态压缩载荷下的力学性能,来研究脂肪组织的力学。主要目的是通过实验测试和数值模拟来了解组织的应变率响应,并确定最能预测皮下组织AT载荷-变形行为的模型。获得脂肪组织的力学特性,并与现有脂肪组织相结合,为今后生物力学领域的建模提供参考。取猪皮下脂肪组织作为标本。利用MTS万能试验机对试件进行单轴压缩试验,获得应力应变响应数据。试件被切割成10×10×10mm的立方体。分别在0.05%/s、0.5%/s和5%/s三个应变速率范围内进行了试验。选择三阶QLV和一阶Ogden的材料本构模型对皮下脂肪组织的被动行为进行建模。用python代码对实验数据进行数值模拟。超弹性的材料参数;α=8.41μ=16.4,C=-136.980,C=-225.60,C=3636.85。设计了一个有限元模型来模拟脂肪组织。为了得到准确的结果,对它进行了精细的网格划分。0.05%～5%应变率的平均弹性模量和剪切模量为:初始E≈12.71±10.93 k Pa,最终E≈1300±66.60 k Pa。初始刚度模量G≈4.23±2.30 k Pa,最终G≈433.30±22.20 k PaOgden和拟线性粘弹性模型的相关系数R=0.9809,R=0.9986。这些是模型与实验数据在0.5%应变率下的确定系数。实验和仿真结果的比较表明,该模型能够较准确地再现应力应变曲线。因此,所建议的材料参数能够较好地预测皮下脂肪组织的负荷和变形。皮下脂肪组织具有应变速率依赖性,在稳态载荷下表现出非线性的应力-应变响应。它在准静态载荷作用下表现出柔软、顺从的特性,在动态载荷作用下表现出刚性、回弹性的特性。

关键词：皮下脂肪组织应变率有限变形粘弹性单轴压缩