June 2024
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1 Read
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Publications (80)
![Fig. 3 Physical implementation of a 4-element Windkessel afterload model (a) and its equivalent circuit model with the heart represented as power source w (b). Blood is pumped from the heart through the afterload made up of a resistive characteristic aortic impedance (R c ), inertance of the ejected blood (inductance) L, vascular compliance (capacitance) C, and peripheral vascular resistance R p . This results in aortic pressure p and flow φ. In the physical implementation, L is captured by the inherent inertance of the perfusate fluid. Circuit (b) modified from [22] with permission from the American Automatic Control Council](https://www.researchgate.net/publication/380158598/figure/fig2/AS:11431281239348594@1714309381604/Physical-implementation-of-a-4-element-Windkessel-afterload-model-a-and-its-equivalent_Q320.jpg)
![Fig. 6 Schematic of an actively controlled afterload device (above dashed line) connected to the heart (below). The afterload consists of a plunger actively controlled to position 0 < u ≤ d. The flow through the device consists of the aortic flow φ, and an auxiliary contribution ϕ, chosen to ensure φ + ϕ > 0. Plunger position control is based on measurements of aortic pressure p. (Reproduced from [36] with permission from the International Federation of Automatic Control)](https://www.researchgate.net/publication/380158598/figure/fig5/AS:11431281239348597@1714309382188/Schematic-of-an-actively-controlled-afterload-device-above-dashed-line-connected-to-the_Q320.jpg)
April 2024
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63 Reads
Methods in molecular biology (Clifton, N.J.)
Ex vivo working porcine heart models allow for the study of a heart’s function and physiology outside the living organism. These models are particularly useful due to the anatomical and physiological similarities between porcine and human hearts, providing an experimental platform to investigate cardiac disease or assess donor heart viability for transplantation. This chapter presents an in-depth discussion of the model’s components, including the perfusate, preload, and afterload. We explore the challenges of emulating cardiac afterload and present a historical perspective on afterload modeling, discussing various methodologies and their respective limitations. An actively controlled afterload device is introduced to enhance the model’s ability to rapidly adjust pressure in the large arteries, thereby providing a more accurate and dynamic experimental model. Finally, we provide a comprehensive experimental protocol for the ex vivo working porcine heart model.
March 2024
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4 Reads
IFAC Journal of Systems and Control
January 2024
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6 Reads
January 2024
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4 Reads
January 2024
January 2024
IFAC-PapersOnLine
January 2024
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1 Read
IFAC-PapersOnLine
![Mammillary three-compartment model example illustrating our novel method. The objective is to automatically learn the covariate model f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{f}}$$\end{document} that maps a known covariate vector φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\varphi }}$$\end{document} (comprising e.g., age, gender, or genetic factors) to the parameter vector θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\theta }}$$\end{document} (e.g. rate constant k··\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{\cdot \cdot }$$\end{document} and volumes V·\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V_\cdot$$\end{document}) of a fixed-structure pharmacometric (PK) model. The method is data-driven in that it uses drug administration profiles (time series data) u, and model-based in that it assumes a PK model of known structure. In this example, f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{f}}$$\end{document} is learned to minimize some error measure between observed (i.e. measured from samples) blood plasma concentrations and corresponding predictions Cpred\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_\text {pred}$$\end{document} by the model. Dots in the graphs show instances of dose changes and blood samples, respectively](https://www.researchgate.net/publication/374901184/figure/fig1/AS:11431281279462551@1726970566594/Mammillary-three-compartment-model-example-illustrating-our-novel-method-The-objective_Q320.jpg)
![Symbolic regression network with three layers, each marked by a gray box. The output of node zli\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_{li}$$\end{document} at layer l is the ith\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i ^{th}$$\end{document} component of zl=Wlxl+bl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{z}}_{l} = W_l {\varvec{x}}_l + {\varvec{b}}_l$$\end{document}, where xl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{x}}_l$$\end{document}, Wl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W_l$$\end{document} and bl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{b}}_l$$\end{document} are the input vector, weight matrix, and bias vector of that layer. The base expressions gli\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{li}$$\end{document} acting on zli\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_{li}$$\end{document} take on the role of activation functions used in ordinary ANNs. For example, the output of the first layer (and therefore input to the second layer) is x2=g1(W1x1+b1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{x}}_2 = {\varvec{g}}_1(W_1 {\varvec{x}}_1 + b_1)$$\end{document}. Input and output of the network is the covariate vector φ=x1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{\varphi }}= {\varvec{x}}_1$$\end{document} and the PK parameter θk=x4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta _k = {\varvec{x}}_4$$\end{document}, respectively](https://www.researchgate.net/publication/374901184/figure/fig2/AS:11431281279386692@1726970566747/Symbolic-regression-network-with-three-layers-each-marked-by-a-gray-box-The-output-of_Q320.jpg)
![Pruning sequence of a symbolic regression network with output pharmacokinetic parameter θ2=k12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta _2 = k_{12}$$\end{document}. Input covariates are age, weight, gender, and arterial or venous sampling (AV). The nominal network has three dense layers, each followed by base expressions such as 1 (feedforward), multiplication, power function, division and absolute value. A black line represents a connection between two nodes, and a gray line represents a pruned (removed) connection. The final network represents the covariate expression of Eq. 10b](https://www.researchgate.net/publication/374901184/figure/fig3/AS:11431281279425026@1726970566922/Pruning-sequence-of-a-symbolic-regression-network-with-output-pharmacokinetic-parameter_Q320.jpg)
![Predicted versus observed propofol concentrations of our covariate model (Symreg, red) compared to the Eleveld covariate model in [4] (Eleveld, blue) in logarithmic scale. The identity function, representing a perfect model fit, is shown in black](https://www.researchgate.net/publication/374901184/figure/fig4/AS:11431281279371192@1726970567128/Predicted-versus-observed-propofol-concentrations-of-our-covariate-model-Symreg-red_Q320.jpg)
![Comparison of prediction error MdALE Eq. 5 between predicted and observed propofol concentrations for pharmacokinetic models. Our covariate model is denoted Symreg and the Eleveld covariate model is described in [4]. The constant model represents one parameter set over the population and individual represents individual set of model parameters. The lower whisker for the individual models goes to zero](https://www.researchgate.net/publication/374901184/figure/fig5/AS:11431281279371193@1726970567333/Comparison-of-prediction-error-MdALE-Eq-5-between-predicted-and-observed-propofol_Q320.jpg)
October 2023
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41 Reads
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5 Citations
Journal of Pharmacokinetics and Pharmacodynamics
Efficiently finding covariate model structures that minimize the need for random effects to describe pharmacological data is challenging. The standard approach focuses on identification of relevant covariates, and present methodology lacks tools for automatic identification of covariate model structures. Although neural networks could potentially be used to approximate covariate-parameter relationships, such approximations are not human-readable and come at the risk of poor generalizability due to high model complexity.In the present study, a novel methodology for the simultaneous selection of covariate model structure and optimization of its parameters is proposed. It is based on symbolic regression, posed as an optimization problem with a smooth loss function. This enables training of the model through back-propagation using efficient gradient computations.Feasibility and effectiveness are demonstrated by application to a clinical pharmacokinetic data set for propofol, containing infusion and blood sample time series from 1031 individuals. The resulting model is compared to a published state-of-the-art model for the same data set. Our methodology finds a covariate model structure and corresponding parameter values with a slightly better fit, while relying on notably fewer covariates than the state-of-the-art model. Unlike contemporary practice, finding the covariate model structure is achieved without an iterative procedure involving manual interactions.
June 2023
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26 Reads
Efficiently finding covariate model structures that minimize the need for random effects to describe pharmacological data is challenging. The standard approach focuses on identification of relevant covariates, and present methodology lacks tools for automatic identification of covariate model structures. Although neural networks could potentially be used to approximate covariate-parameter relationships, such approximations are not human-readable and come at the risk of poor generalizability due to high model complexity. In the present study, a novel methodology for simultaneous selection of covariate model structure and optimization of its parameters is proposed. It is based on symbolic regression, posed as an optimization problem with smooth loss function. This enables training the model through back-propagation using efficient gradient computations. Feasibility and effectiveness is demonstrated by application to a clinical pharmacokinetic data set for propofol, containing infusion and blood sample time series from 1,031 individuals. The resulting model is compared to a published state-of-the-art model for the same data set. Our methodology finds a covariate model structure and corresponding parameter values with a slightly better fit, while relying on notably fewer covariates than the state-of the-art model. Unlike contemporary practice, finding the covariate model structure is achieved without an iterative procedure involving manual interactions.
Citations (51)
... A simple construction using a variable flow conductance and pump is combined with feedback control principles to allow the user to program the desired pressure-flow dynamics. A drawing of such a device is shown in Fig. 5, and described in detail in [36]. The basic operating principle is akin to the previously mentioned pump-based afterloads, with the key difference that pressure in the large arteries can be rapidly adjusted. ...
Reference:
Ex Vivo Working Porcine Heart Model
- Citing Article
January 2023
IFAC-PapersOnLine
... We have chosen to implement our method using the parameterization in Eq. 1 due to numeric benefits. These are further explained in [13], where we developed a fast and natively differentiable simulator for the three-order mammillary model. ...
- Citing Article
January 2023
IFAC-PapersOnLine
... There were only two articles in this category, and both introduced a novel method [33,34]. [34], a particular type of neural network. ...
- Citing Article
- Full-text available
October 2023
Journal of Pharmacokinetics and Pharmacodynamics
... In the physical implementation, L is captured by the inherent inertance of the perfusate fluid. Circuit (b) modified from [22] with permission from the American Automatic Control Council Another afterload implementation uses a pump to force perfusate toward the aortic root during working mode, generally in combination with a resistive element and sometimes a compliant chamber. The resistor shunts excess flow away from the aortic root. ...
Reference:
Ex Vivo Working Porcine Heart Model
- Citing Conference Paper
June 2022
... Our group has investigated an alternative afterload approach using an adjustable pneumatic system based on Starling's original design wherein the pressure surrounding a flexible tube through which the perfusate flows is modulated to control afterload [35]. The afterload demonstrated physiological loading conditions in multiple porcine working heart experiments. ...
Reference:
Ex Vivo Working Porcine Heart Model
- Citing Article
- Full-text available
May 2022
Artificial Organs
... Among emergencies, the impact of hypothetical interventions, such as social distancing during pandemics, could be simulated using realistic population data and tools for capacity and needs analyses [26]. Before epidemic seasons or when the pandemic alert was issued by the WHO, local outbreak prediction algorithms could be calibrated using the most recent information about the infectious agent and local circumstances [27][28][29]. ...
- Citing Article
- Full-text available
March 2022
Emerging Infectious Diseases
... [2]- [6]. We have previously shown [7]- [9] how the combination of a short asymmetric relay experiment and optimization techniques outperform the original relay autotuner [1]. However, such improvements have not yet made it into the product lines of major vendors. ...
- Citing Conference Paper
August 2021
... Another limitation that relates to generalizability is the definition and registration of cases and deaths. The number of reported cases is, as discussed earlier, related to testing capacity and this changed over time during the study period 24 . Moreover, the registration of deaths during the first year of the pandemic differed between countries regarding mainly two aspects; (1) if deaths at all were registered and, (2) if deaths were registered as deceased "caused by" COVID-19 (i.e. as the underlying cause of death) or deceased "associated with" COVID-19. ...
- Citing Article
- Full-text available
December 2021
... An advantage of these Windkessel afterloads is that, with correctly adjusted elements, they can produce near-physiological pressure waveforms in the large arteries [19]. However, identifying valid parameter values and adjusting the elements accordingly is nontrivial [26]. Since the mid 1980s, the ability of these models to adjust aortic pressure in working heart models has been explored. ...
Reference:
Ex Vivo Working Porcine Heart Model
- Citing Article
January 2021
IFAC-PapersOnLine
... with τ 2 = 1/k e0 and one may have a theoretical transfer function model of the simplified structure from Fig. 5 as series connection of (5) and (6) and extract the parameters τ 1 , τ 2 and K, respectively. However, in [16] it has been shown that the model parameters from (6) are underestimated and data based identification is suggested to update this model. In this simplified model, there is no need to use the complex and nonlinear gains from (3) and (4) as they reduce to a constant K captured within the model (6). ...
- Citing Article
- Full-text available
January 2021
IFAC-PapersOnLine