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Question: 1—Echocardiography images Images were acquired from end of diastole to end of systole at different phases (7 phases) within a cardiac cycle by a Vivid 3 GE Health echocardiography machine. To obtain worthy images at denoted phases, it would be dependent to operator (for the best clinical examination). Of course, having assumed images not only were acquired from A4C and A2C but also from short-axis views. Short axis views have not been used at your papers, so some radial, circumferential and sample rotatory data would be missed. Response: It is simply possible for us to record and analyze images of short-axis views. However, according to American Society of Echocardiography (ASE) [1, 2], in the modified Simpson’s rule which is a method for LV volume computation from 2-D echocardiography images, it suffices to acquire apical two and four chamber views (A4C, A2C) for left ventricular (LV) volume computation. Question: 2—Observed data yi′ s Echocardiography images paly role of observed data and they are symbolized by yi′ s. there is a sequence of observed data y1, y2,…,yN. N is the number of obtained images. In fact we have made a chain of displacement, rotation and pure strain or nonrigid transformation (deformation) by these observed data that is started from y1 and is ended up to yN. This chain has some conceptual interpretations of the elasticity of the global left ventricular motion/function and the regional LV fiber arrangement/movement. Response: Yes, it is correct. Question: 3—Embed observed data to a high dimensional space Response: Yes, it is correct. Question: 4—Image processing on yi′ s and geodesic distance between yi′ s Observed data y1, y2,…,yN are embed to a meshed surface sized number of pixels of an image. Translation, rotation and pure deformation of y1, y2,…,yN are occurred/and studied at this surface utilizing the mathematical elasticity theory. A distance metric is defined that computes distances between observed points. Medical interpretations of observed points over the time should be checked/and stated clearly at your manuscripts. Images are not usual images but also are images from the left ventricle. Motion (displacement and velocity), deformation (strain and strain rate) and torsion of each myocardial sample have to be extracted during a cardiac cycle in the mentioned surface. These are used on the creation of graph G referred to their papers. Response: In this stage, we have just computed the distance between the two images in a cardiac cycle using non-rigid image registration regardless of relationship between images over the time. Therefore by this method, the motion and longitudinal deformation (short-axis views are needed to get for radial and circumferential deformations) of LV myocardium between all of two images in a cardiac cycle are extracted (for example, between end systole image and end diastole image, etc.). Then, in other stage of our method (calculation of the matrix of pairwise geodesic distance and apply multidimensional scaling on the resulting geodesic distance matrix to construct the low dimensional data points xi), motion and longitudinal deformation of LV myocardium during a cardiac cycle are extracted. Question: 5—An Isomap f The main tool at this method is the function “f” which is an isometric map [2, 3]. I will be interested to know the structure/formula or relationship of this isometric function which has most probably a lot of practical information of the left ventricular function and structure. I mean, how we can get a good representation of such a this function “f” for heart science study? Is it “f” known as an algebraic function? What information has been coded to fibers (f−1) of this isometric function “f”? Response: Isomap algorithm is one of the most popular sets of nonlinear dimensionality reduction (NLDR) algorithms. This algorithm attempts to extract low-dimensional data points from input points in a high-dimensional space in such a way that pairwise geodesic distances (the distance between two points measured over the manifold) are preserved. So that nearby and far points in high-dimensional space map to nearby and far points in low-dimensional space. This method is frequently used for visualization of medial image set. Detail of this method is described in Tenenbaum et al. and Borg et al. [3, 4]. It should be noted that we do not change the structure or formula of isomap algorithm. We only define a new image distance function based on image registration in calculation of geodesic distance between yi′ s in isomap algorithm. With this modification, Isomap algorithm is specified for assessment of the left ventricular function and structure. However, precise mathematical descriptions of f and (f−1) applied to echocardiography images and using the other NLDR algorithms need further researches in the following of this article. Question: 6—A reconstructed curve on a 2D manifold space & hidden data xi′ s; f(yi) = xi Isometric function results in a reconstructive curve crossing from hidden data (xi′ s) in a surface. It’s natural that some information (maybe clinical information) would betransferred to these hidden points like the curve of LV volume changes and so on and so on. A main question is: what are these new points xi′ s exactly (medically point of view)? What the other data has been come out from these hidden points? I think all of these questions back to gain a good understanding of isometric function “f”. Response: These points xi′ s will probably enable physicians to diagnose and follow up many cardiac structures and functions that also open doors to much more research at imaging cardiology in the future. References 1. AlizadehSani Z, Shalbaf A, Behnam H, Shalbaf R: Automatic computation of left ventricularvolume changes over a cardiac cycle from echocardiography images by nonlinear dimensionality reduction. J Digit Imaging : July, 2014 2. Tenenbaum JB, de Silva V, Langford JC: global geometric framework for nonlinear dimensionalityreduction. Science 290:2319–2323, 2000. Reprint available online: http://web.mit.edu/cocosci/Papers/sci_reprint.pdf 3. Ledesma-Carbayo MJ, Kybic J, Desco M, et al.: Spatio-temporal nonrigid registration for ultrasoundcardiac motion estimation. IEEE Trans Med Imaging 24:1113–1126, 2005.

This article highlights some numerical challenges when implementing the bounded integer model for composite score modeling and suggests an improved implementation. The improvement is based on an approximation of the logarithm of the error function. After presenting the derivation of the improved implementation, the article compares the performance of the algorithm to a naive implementation of the log-likelihood using both simulations and a real data example. In the simulation setting, the improved algorithm yielded more precise and less biased parameter estimates when the within-subject variability was small and estimation was performed using the Laplace algorithm. The estimation results did not differ between implementations when the SAEM algorithm was used. For the real data example, bootstrap results differed between implementations with the improved implementation producing identical or better objective function values. Based on the findings in this article, the improved implementation is suggested as the new default log-likelihood implementation for the bounded integer model. Electronic supplementary material The online version of this article (10.1007/s10928-020-09727-8) contains supplementary material, which is available to authorized users.

To inform targeted HIV testing, we developed and externally validated a risk-score algorithm that incorporated behavioral characteristics. Outpatient data from five health facilities in western Kenya, comprising 19,458 adults ≥ 15 years tested for HIV from September 2017 to May 2018, were included in univariable and multivariable analyses used for algorithm development. Data for 11,330 adults attending one high-volume facility were used for validation. Using the final algorithm, patients were grouped into four risk-score categories: ≤ 9, 10–15, 16–29 and ≥ 30, with increasing HIV prevalence of 0.6% [95% confidence interval (CI) 0.46–0.75], 1.35% (95% CI 0.85–1.84), 2.65% (95% CI 1.8–3.51), and 15.15% (95% CI 9.03–21.27), respectively. The algorithm’s discrimination performance was modest, with an area under the receiver-operating-curve of 0.69 (95% CI 0.53–0.84). In settings where universal testing is not feasible, a risk-score algorithm can identify sub-populations with higher HIV-risk to be prioritized for HIV testing. Electronic supplementary material The online version of this article (10.1007/s10461-020-02962-7) contains supplementary material, which is available to authorized users.

Input estimation is employed in cases where it is desirable to recover the form of an input function which cannot be directly observed and for which there is no model for the generating process. In pharmacokinetic and pharmacodynamic modelling, input estimation in linear systems (deconvolution) is well established, while the nonlinear case is largely unexplored. In this paper, a rigorous definition of the input-estimation problem is given, and the choices involved in terms of modelling assumptions and estimation algorithms are discussed. In particular, the paper covers Maximum a Posteriori estimates using techniques from optimal control theory, and full Bayesian estimation using Markov Chain Monte Carlo (MCMC) approaches. These techniques are implemented using the optimisation software CasADi, and applied to two example problems: one where the oral absorption rate and bioavailability of the drug eflornithine are estimated using pharmacokinetic data from rats, and one where energy intake is estimated from body-mass measurements of mice exposed to monoclonal antibodies targeting the fibroblast growth factor receptor (FGFR) 1c. The results from the analysis are used to highlight the strengths and weaknesses of the methods used when applied to sparsely sampled data. The presented methods for optimal control are fast and robust, and can be recommended for use in drug discovery. The MCMC-based methods can have long running times and require more expertise from the user. The rigorous definition together with the illustrative examples and suggestions for software serve as a highly promising starting point for application of input-estimation methods to problems in drug discovery. Electronic supplementary material The online version of this article (doi:10.1007/s10928-016-9467-z) contains supplementary material, which is available to authorized users.

Purpose This work describes a staged approach to the application of pharmacokinetic-pharmacodynamic (PK-PD) modeling in the voltage-gated sodium ion channel (NaV1.7) inhibitor drug discovery effort to address strategic questions regarding in vitro to in vivo translation of target modulation. Methods PK-PD analysis was applied to data from a functional magnetic resonance imaging (fMRI) technique to non-invasively measure treatment mediated inhibition of olfaction signaling in non-human primates (NHPs). Initial exposure-response was evaluated using single time point data pooled across 27 compounds to inform on in vitro to in vivo correlation (IVIVC). More robust effect compartment PK-PD modeling was conducted for a subset of 10 compounds with additional PD and PK data to characterize hysteresis. Results The pooled compound exposure-response facilitated an early exploration of IVIVC with a limited dataset for each individual compound, and it suggested a 2.4-fold in vitro to in vivo scaling factor for the NaV1.7 target. Accounting for hysteresis with an effect compartment PK-PD model as compounds advanced towards preclinical development provided a more robust determination of in vivo potency values, which resulted in a statistically significant positive IVIVC with a slope of 1.057 ± 0.210, R-squared of 0.7831, and p value of 0.006. Subsequent simulations with the PK-PD model informed the design of anti-nociception efficacy studies in NHPs. Conclusions A staged approach to PK-PD modeling and simulation enabled integration of in vitro NaV1.7 potency, plasma protein binding, and pharmacokinetics to describe the exposure-response profile and inform future study design as the NaV1.7 inhibitor effort progressed through drug discovery.

The purpose of this study was to assess the pharmacokinetics of dexmedetomidine in the ICU settings during the prolonged infusion and to compare it with the existing literature data using the Bayesian population modeling with literature-based informative priors. Thirty-eight patients were included in the analysis with concentration measurements obtained at two occasions: first from 0 to 24 h after infusion initiation and second from 0 to 8 h after infusion end. Data analysis was conducted using WinBUGS software. The prior information on dexmedetomidine pharmacokinetics was elicited from the literature study pooling results from a relatively large group of 95 children. A two compartment PK model, with allometrically scaled parameters, maturation of clearance and t-student residual distribution on a log-scale was used to describe the data. The incorporation of time-dependent (different between two occasions) PK parameters improved the model. It was observed that volume of distribution is 1.5-fold higher during the second occasion. There was also an evidence of increased (1.3-fold) clearance for the second occasion with posterior probability equal to 62 %. This work demonstrated the usefulness of Bayesian modeling with informative priors in analyzing pharmacokinetic data and comparing it with existing literature knowledge. Electronic supplementary material The online version of this article (doi:10.1007/s10928-016-9474-0) contains supplementary material, which is available to authorized users.

Purpose Currently, the FDA allows biowaivers for Class I (high solubility and high permeability) and Class III (high solubility and low permeability) compounds of the Biopharmaceutics Classification System (BCS). Scientific evidence should be provided to support biowaivers for BCS Class I and Class III (high solubility and low permeability) compounds. Methods Data on the effects of excipients on drug permeability are needed to demonstrate that commonly used excipients do not affect the permeability of BCS Class III compounds, which would support the application of biowaivers to Class III compounds. This study was designed to generate such data by assessing the permeability of four BCS Class III compounds and one Class I compound in the presence and absence of five commonly used excipients. Results The permeability of each of the compounds was assessed, at three to five concentrations, with each excipient in two different models: Caco-2 cell monolayers, and in situ rat intestinal perfusion. No substantial increases in the permeability of any of the compounds were observed in the presence of any of the tested excipients in either of the models, with the exception of disruption of Caco-2 cell monolayer integrity by sodium lauryl sulfate at 0.1 mg/ml and higher. Conclusion The results suggest that the absorption of these four BCS Class III compounds would not be greatly affected by the tested excipients. This may have implications in supporting biowaivers for BCS Class III compounds in general.