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Abstract Cortical bone is characterized by a dense solid matrix permeated by fluid-filled pores. Ultrasound scattering has potential for the non-invasive evaluation of changes in bone porosity. However, there is an incomplete understanding of the impact of ultrasonic absorption in the solid matrix on ultrasound scattering. In this study, maps were derived from scanning acoustic microscopy images of human femur cross-sections. Finite-difference time domain ultrasound scatter simulations were conducted on these maps. Pore density, diameter distribution of the pores, and nominal absorption values in the solid and fluid matrices were controlled. Ultrasound pulses with a central frequency of 8.2 MHz were propagated, both in through-transmission and backscattering configurations. From these data, the scattering, bone matrix absorption, and attenuation extinction lengths were calculated. The results demonstrated that as absorption in the solid matrix was varied, the scattering, absorption, and attenuation extinction lengths were significantly impacted. It was shown that for lower values of absorption in the solid matrix (less than 2 dB mm⁻¹), attenuation due to scattering dominates, whereas at higher values of absorption (more than 2 dB mm⁻¹), attenuation due to absorption dominates. This will impact how ultrasound attenuation and scattering parameters can be used to extract quantitative information on bone microstructure. 

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reason-able may lead to significantly different conclusions. We develop a computational approach to understand the impact of the hyperparameters defining the prior on the posterior statistics of the quantities of interest. Our approach relies on global sensitivity analysis (GSA) of Bayesian inverse problems with respect to the prior hyperparameters. This, however, is a challenging problem-a naive double loop sampling approach would require running a prohibitive number of Markov chain Monte Carlo (MCMC) sampling procedures. The present work takes a foundational step in making such a sensitivity analysis practical by combining efficient surrogate models and a tailored importance sampling approach. In particular, we can perform accurate GSA of posterior statistics of quantities of interest with respect to prior hyperparameters without the need to repeat MCMC runs. We demonstrate the effectiveness of the approach on a simple Bayesian linear inverse problem and a nonlinear inverse problem governed by an epidemiological model. 

Physiologically-based pharmacokinetic (PBPK) modeling is important for studying drug delivery in the central nervous system, including determining antibody exposure, predicting chemical concentrations at target locations, and ensuring accurate dosages. The complexity of PBPK models, involving many variables and parameters, requires a consideration of parameter identifiability; i.e., which parameters can be uniquely determined from data for a specified set of concentrations. We introduce the use of a local sensitivity-based parameter subset selection algorithm in the context of a minimal PBPK (mPBPK) model of the brain for antibody therapeutics. This algorithm is augmented by verification techniques, based on response distributions and energy statistics, to provide a systematic and robust technique to determine identifiable parameter subsets in a PBPK model across a specified time domain of interest. The accuracy of our approach is evaluated for three key concentrations in the mPBPK model for plasma, brain interstitial fluid and brain cerebrospinal fluid. The determination of accurate identifiable parameter subsets is important for model reduction and uncertainty quantification for PBPK models. 

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models.A well-known Achilles' heel of this approach is its computational cost, which often renders it unfeasible in practice. An appealing alternative is to instead analyze the sensitivity of a surrogate model with the goal of lowering computational costs while maintaining sufficient accuracy. Should a surrogate be simple enough to be amenable to the analytical calculations of its Sobol' indices, the cost of GSA is essentially reduced to the construction of the surrogate.We propose a new class of sparse-weight extreme learning machines (ELMs), which, when considered as surrogates in the context of GSA, admit analytical formulas for their Sobol' indices and, unlike the standard ELMs, yield accurate approximations of these indices. The effectiveness of this approach is illustrated through both traditional benchmarks in the field and on a chemical reaction network. 

We consider hyper-differential sensitivity analysis (HDSA) of nonlinear Bayesian inverse problems governed by partialdifferential equations (PDEs) with infinite-dimensional parameters. In previous works, HDSA has been used to assessthe sensitivity of the solution of deterministic inverse problems to additional model uncertainties and also different types of measurement data. In the present work, we extend HDSA to the class of Bayesian inverse problems governed by PDEs. The focus is on assessing the sensitivity of certain key quantities derived from the posterior distribution. Specifically, we focus on analyzing the sensitivity of the MAP point and the Bayes risk and make full use of the information embedded in the Bayesian inverse problem. After establishing our mathematical framework for HDSA of Bayesian inverse problems, we present a detailed computational approach for computing the proposed HDSA indices. We examine the effectiveness of the proposed approach on an inverse problem governed by a PDE modeling heat conduction.