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Sofia D, Zhou Q, Shahriyari L. Mathematical and Machine Learning Models of Renal Cell Carcinoma: A Review. Bioengineering (Basel) 2023; 10:1320. [PMID: 38002445 PMCID: PMC10669004 DOI: 10.3390/bioengineering10111320] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Revised: 11/08/2023] [Accepted: 11/13/2023] [Indexed: 11/26/2023] Open
Abstract
This review explores the multifaceted landscape of renal cell carcinoma (RCC) by delving into both mechanistic and machine learning models. While machine learning models leverage patients' gene expression and clinical data through a variety of techniques to predict patients' outcomes, mechanistic models focus on investigating cells' and molecules' interactions within RCC tumors. These interactions are notably centered around immune cells, cytokines, tumor cells, and the development of lung metastases. The insights gained from both machine learning and mechanistic models encompass critical aspects such as signature gene identification, sensitive interactions in the tumors' microenvironments, metastasis development in other organs, and the assessment of survival probabilities. By reviewing the models of RCC, this study aims to shed light on opportunities for the integration of machine learning and mechanistic modeling approaches for treatment optimization and the identification of specific targets, all of which are essential for enhancing patient outcomes.
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Affiliation(s)
| | | | - Leili Shahriyari
- Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA 01003, USA; (D.S.); (Q.Z.)
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2
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Yang L, Liu S, Meng T, Osher SJ. In-context operator learning with data prompts for differential equation problems. Proc Natl Acad Sci U S A 2023; 120:e2310142120. [PMID: 37725644 PMCID: PMC10523630 DOI: 10.1073/pnas.2310142120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2023] [Accepted: 08/12/2023] [Indexed: 09/21/2023] Open
Abstract
This paper introduces the paradigm of "in-context operator learning" and the corresponding model "In-Context Operator Networks" to simultaneously learn operators from the prompted data and apply it to new questions during the inference stage, without any weight update. Existing methods are limited to using a neural network to approximate a specific equation solution or a specific operator, requiring retraining when switching to a new problem with different equations. By training a single neural network as an operator learner, rather than a solution/operator approximator, we can not only get rid of retraining (even fine-tuning) the neural network for new problems but also leverage the commonalities shared across operators so that only a few examples in the prompt are needed when learning a new operator. Our numerical results show the capability of a single neural network as a few-shot operator learner for a diversified type of differential equation problems, including forward and inverse problems of ordinary differential equations, partial differential equations, and mean-field control problems, and also show that it can generalize its learning capability to operators beyond the training distribution.
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Affiliation(s)
- Liu Yang
- Department of Mathematics, University of California, Los Angeles, CA90095
| | - Siting Liu
- Department of Mathematics, University of California, Los Angeles, CA90095
| | - Tingwei Meng
- Department of Mathematics, University of California, Los Angeles, CA90095
| | - Stanley J. Osher
- Department of Mathematics, University of California, Los Angeles, CA90095
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3
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He J, Yao S, Zeng Q, Chen J, Sang T, Xie L, Pan Y, Feng Y. A unified global tractography framework for automatic visual pathway reconstruction. NMR Biomed 2023; 36:e4904. [PMID: 36633539 DOI: 10.1002/nbm.4904] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2022] [Revised: 01/05/2023] [Accepted: 01/10/2023] [Indexed: 06/15/2023]
Abstract
The human visual pathway starts from the retina, passes through the retinogeniculate visual pathway, the optic radiation, and finally connects to the primary visual cortex. Diffusion MRI tractography is the only technology that can noninvasively reconstruct the visual pathway. However, complete and accurate visual pathway reconstruction is challenging because of the skull base environment and complex fiber geometries. Specifically, the optic nerve within the complex skull base environment can cause abnormal diffusion signals. The crossing and fanning fibers at the optic chiasm, and a sharp turn of Meyer's loop at the optic radiation, contribute to complex fiber geometries of the visual pathway. A fiber trajectory distribution (FTD) function-based tractography method of our previous work and several high sensitivity tractography methods can reveal these complex fiber geometries, but are accompanied by false-positive fibers. Thus, the related studies of the visual pathway mostly applied the expert region of interest selection strategy. However, interobserver variability is an issue in reconstructing an accurate visual pathway. In this paper, we propose a unified global tractography framework to automatically reconstruct the visual pathway. We first extend the FTD function to a high-order streamline differential equation for global trajectory estimation. At the global level, the tractography process is simplified as the estimation of global trajectory distribution coefficients by minimizing the cost between trajectory distribution and the selected directions under the prior guidance by introducing the tractography template as anatomic priors. Furthermore, we use a deep learning-based method and tractography template prior information to automatically generate the mask for tractography. The experimental results demonstrate that our proposed method can successfully reconstruct the visual pathway with high accuracy.
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Affiliation(s)
- Jianzhong He
- Institution of Information Processing and Automation, Zhejiang University of Technology, Hangzhou, China
| | - Shun Yao
- Center for Pituitary Tumor Surgery, Department of Neurosurgery, The First Affiliated Hospital, Sun Yat-sen University, Guangzhou, China
- Department of Neurosurgery, Brigham and Women's Hospital, Harvard Medical School, Boston, Massachusetts, USA
| | - Qingrun Zeng
- Institution of Information Processing and Automation, Zhejiang University of Technology, Hangzhou, China
| | - Jinping Chen
- Center for Pituitary Tumor Surgery, Department of Neurosurgery, The First Affiliated Hospital, Sun Yat-sen University, Guangzhou, China
| | - Tian Sang
- Institution of Information Processing and Automation, Zhejiang University of Technology, Hangzhou, China
| | - Lei Xie
- Institution of Information Processing and Automation, Zhejiang University of Technology, Hangzhou, China
| | - Yiang Pan
- Institution of Information Processing and Automation, Zhejiang University of Technology, Hangzhou, China
| | - Yuanjing Feng
- Institution of Information Processing and Automation, Zhejiang University of Technology, Hangzhou, China
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4
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Lu K, Wang X, Gong H, Yang D, Ye M, Fang Q, Zhang XY, Wu R. The genetic architecture of trait covariation in Populus euphratica, a desert tree. Front Plant Sci 2023; 14:1149879. [PMID: 37089657 PMCID: PMC10113509 DOI: 10.3389/fpls.2023.1149879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Accepted: 03/20/2023] [Indexed: 05/03/2023]
Abstract
Introduction The cooperative strategy of phenotypic traits during the growth of plants reflects how plants allocate photosynthesis products, which is the most favorable decision for them to optimize growth, survival, and reproduction response to changing environment. Up to now, we still know little about why plants make such decision from the perspective of biological genetic mechanisms. Methods In this study, we construct an analytical mapping framework to explore the genetic mechanism regulating the interaction of two complex traits. The framework describes the dynamic growth of two traits and their interaction as Differential Interaction Regulatory Equations (DIRE), then DIRE is embedded into QTL mapping model to identify the key quantitative trait loci (QTLs) that regulate this interaction and clarify the genetic effect, genetic contribution and genetic network structure of these key QTLs. Computer simulation experiment proves the reliability and practicability of our framework. Results In order to verify that our framework is universal and flexible, we applied it to two sets of data from Populus euphratica, namely, aboveground stem length - underground taproot length, underground root number - underground root length, which represent relationships of phenotypic traits in two spatial dimensions of plant architecture. The analytical result shows that our model is well applicable to datasets of two dimensions. Discussion Our model helps to better illustrate the cooperation-competition patterns between phenotypic traits, and understand the decisions that plants make in a specific environment that are most conducive to their growth from the genetic perspective.
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Affiliation(s)
- Kaiyan Lu
- College of Science, Beijing Forestry University, Beijing, China
| | - Xueshun Wang
- Department of Artificial Intelligence and Data Science, Guangzhou Xinhua University, Guangzhou, China
| | - Huiying Gong
- College of Biological Sciences and Technology, Center for Computational Biology, Beijing Forestry University, Beijing, China
| | - Dengcheng Yang
- College of Biological Sciences and Technology, Center for Computational Biology, Beijing Forestry University, Beijing, China
| | - Meixia Ye
- College of Biological Sciences and Technology, Center for Computational Biology, Beijing Forestry University, Beijing, China
| | - Qing Fang
- Faculty of Science, Yamagata University, Yamagata, Japan
| | - Xiao-Yu Zhang
- College of Science, Beijing Forestry University, Beijing, China
- *Correspondence: Xiao-Yu Zhang, ; Rongling Wu,
| | - Rongling Wu
- College of Biological Sciences and Technology, Center for Computational Biology, Beijing Forestry University, Beijing, China
- Yau Mathematical Sciences Center, Tsinghua University, Beijing, China
- *Correspondence: Xiao-Yu Zhang, ; Rongling Wu,
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Kuo CH, Chen JW, Yang Y, Lan YH, Lu SW, Wang CF, Lo YC, Lin CL, Lin SH, Chen PC, Chen YY. A Differentiable Dynamic Model for Musculoskeletal Simulation and Exoskeleton Control. Biosensors (Basel) 2022; 12:bios12050312. [PMID: 35624613 PMCID: PMC9138350 DOI: 10.3390/bios12050312] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Revised: 05/05/2022] [Accepted: 05/06/2022] [Indexed: 05/09/2023]
Abstract
An exoskeleton, a wearable device, was designed based on the user's physical and cognitive interactions. The control of the exoskeleton uses biomedical signals reflecting the user intention as input, and its algorithm is calculated as an output to make the movement smooth. However, the process of transforming the input of biomedical signals, such as electromyography (EMG), into the output of adjusting the torque and angle of the exoskeleton is limited by a finite time lag and precision of trajectory prediction, which result in a mismatch between the subject and exoskeleton. Here, we propose an EMG-based single-joint exoskeleton system by merging a differentiable continuous system with a dynamic musculoskeletal model. The parameters of each muscle contraction were calculated and applied to the rigid exoskeleton system to predict the precise trajectory. The results revealed accurate torque and angle prediction for the knee exoskeleton and good performance of assistance during movement. Our method outperformed other models regarding the rate of convergence and execution time. In conclusion, a differentiable continuous system merged with a dynamic musculoskeletal model supported the effective and accurate performance of an exoskeleton controlled by EMG signals.
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Affiliation(s)
- Chao-Hung Kuo
- Department of Biomedical Engineering, National Yang Ming Chiao Tung University, Taipei 11221, Taiwan; (C.-H.K.); (J.-W.C.); (Y.Y.); (Y.-H.L.); (S.-W.L.); (C.-F.W.)
- School of Medicine, National Yang Ming Chiao Tung University, Taipei 11221, Taiwan
- Department of Neurological Surgery, Neurological Institute, Taipei Veterans General Hospital, Taipei 11217, Taiwan
- Department of Neurological Surgery, University of Washington, Seattle, WA 98195-6470, USA
| | - Jia-Wei Chen
- Department of Biomedical Engineering, National Yang Ming Chiao Tung University, Taipei 11221, Taiwan; (C.-H.K.); (J.-W.C.); (Y.Y.); (Y.-H.L.); (S.-W.L.); (C.-F.W.)
| | - Yi Yang
- Department of Biomedical Engineering, National Yang Ming Chiao Tung University, Taipei 11221, Taiwan; (C.-H.K.); (J.-W.C.); (Y.Y.); (Y.-H.L.); (S.-W.L.); (C.-F.W.)
| | - Yu-Hao Lan
- Department of Biomedical Engineering, National Yang Ming Chiao Tung University, Taipei 11221, Taiwan; (C.-H.K.); (J.-W.C.); (Y.Y.); (Y.-H.L.); (S.-W.L.); (C.-F.W.)
| | - Shao-Wei Lu
- Department of Biomedical Engineering, National Yang Ming Chiao Tung University, Taipei 11221, Taiwan; (C.-H.K.); (J.-W.C.); (Y.Y.); (Y.-H.L.); (S.-W.L.); (C.-F.W.)
| | - Ching-Fu Wang
- Department of Biomedical Engineering, National Yang Ming Chiao Tung University, Taipei 11221, Taiwan; (C.-H.K.); (J.-W.C.); (Y.Y.); (Y.-H.L.); (S.-W.L.); (C.-F.W.)
- Biomedical Engineering Research and Development Center, National Yang Ming Chiao Tung University, Taipei 11221, Taiwan
| | - Yu-Chun Lo
- The Ph.D. Program for Neural Regenerative Medicine, College of Medical Science and Technology, Taipei Medical University, Taipei 11031, Taiwan;
| | - Chien-Lin Lin
- Department of Physical Medicine and Rehabilitation, China Medical University Hospital, Taichung 404332, Taiwan;
- School of Chinese Medicine, College of Chinese Medicine, China Medical University, Taichung 406040, Taiwan
| | - Sheng-Huang Lin
- Department of Neurology, Hualien Tzu Chi Hospital, Buddhist Tzu Chi Medical Foundation, Hualien 97002, Taiwan
- Department of Neurology, School of Medicine, Tzu Chi University, Hualien 97004, Taiwan
- Correspondence: (S.-H.L.); (Y.-Y.C.)
| | - Po-Chuan Chen
- School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;
| | - You-Yin Chen
- Department of Biomedical Engineering, National Yang Ming Chiao Tung University, Taipei 11221, Taiwan; (C.-H.K.); (J.-W.C.); (Y.Y.); (Y.-H.L.); (S.-W.L.); (C.-F.W.)
- The Ph.D. Program for Neural Regenerative Medicine, College of Medical Science and Technology, Taipei Medical University, Taipei 11031, Taiwan;
- Correspondence: (S.-H.L.); (Y.-Y.C.)
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Whiteley TD, Avitabile D, Siebers PO, Robinson D, Owen MR. Modelling the emergence of cities and urban patterning using coupled integro- differential equations. J R Soc Interface 2022; 19:20220176. [PMID: 35506210 PMCID: PMC9065963 DOI: 10.1098/rsif.2022.0176] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Human residential population distributions show patterns of higher density clustering around local services such as shops and places of employment, displaying characteristic length scales; Fourier transforms and spatial autocorrelation show the length scale between UK cities is around 45 km. We use integro-differential equations to model the spatio-temporal dynamics of population and service density under the assumption that they benefit from spatial proximity, captured via spatial weight kernels. The system tends towards a well-mixed homogeneous state or a spatial pattern. Linear stability analysis around the homogeneous steady state predicts a modelled length-scale consistent with that observed in the data. Moreover, we show that spatial instability occurs only for perturbations with a sufficiently long wavelength and only where there is a sufficiently strong dependence of service potential on population density. Within urban centres, competition for space may cause services and population to be out of phase with one another, occupying separate parcels of land. By introducing competition, along with a preference for population to be located near, but not too near, to high service density areas, secondary out-of-phase patterns occur within the model, at a higher density and with a shorter length scale than in phase patterning. Thus, we show that a small set of core behavioural ingredients can generate aggregations of populations and services, and pattern formation within cities, with length scales consistent with real-world data. The analysis and results are valid across a wide range of parameter values and functional forms in the model.
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Affiliation(s)
- Timothy D Whiteley
- School of Mathematical Sciences, University of Nottingham, Nottingham, UK
| | - Daniele Avitabile
- Department of Mathematics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
| | - Peer-Olaf Siebers
- School of Computer Science, University of Nottingham, Nottingham, UK
| | - Darren Robinson
- School of Architecture, University of Sheffield, Sheffield, UK
| | - Markus R Owen
- School of Mathematical Sciences, University of Nottingham, Nottingham, UK
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Wang Y, Wang Z. Inference on the structure of gene regulatory networks. J Theor Biol 2022;:111055. [PMID: 35150721 DOI: 10.1016/j.jtbi.2022.111055] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Revised: 01/29/2022] [Accepted: 02/03/2022] [Indexed: 11/20/2022]
Abstract
In this paper, we conduct theoretical analyses on inferring the structure of gene regulatory networks. Depending on the experimental method and data type, the inference problem is classified into 20 different scenarios. For each scenario, we discuss the problem that with enough data, under what assumptions, what can be inferred about the structure. For scenarios that have been covered in the literature, we provide a brief review. For scenarios that have not been covered in literature, if the structure can be inferred, we propose new mathematical inference methods and evaluate them on simulated data. Otherwise, we prove that the structure cannot be inferred.
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Zhang XY, Gong H, Fang Q, Zhu X, Jiang L, Wu R. A Holling Functional Response Model for Mapping QTLs Governing Interspecific Interactions. Front Genet 2021; 12:766372. [PMID: 34721549 PMCID: PMC8554200 DOI: 10.3389/fgene.2021.766372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2021] [Accepted: 09/30/2021] [Indexed: 11/13/2022] Open
Abstract
Genes play an important role in community ecology and evolution, but how to identify the genes that affect community dynamics at the whole genome level is very challenging. Here, we develop a Holling type II functional response model for mapping quantitative trait loci (QTLs) that govern interspecific interactions. The model, integrated with generalized Lotka-Volterra differential dynamic equations, shows a better capacity to reveal the dynamic complexity of inter-species interactions than classic competition models. By applying the new model to a published mapping data from a competition experiment of two microbial species, we identify a set of previously uncharacterized QTLs that are specifically responsible for microbial cooperation and competition. The model can not only characterize how these QTLs affect microbial interactions, but also address how change in ecological interactions activates the genetic effects of the QTLs. This model provides a quantitative means of predicting the genetic architecture that shapes the dynamic behavior of ecological communities.
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Affiliation(s)
- Xiao-Yu Zhang
- College of Science, Beijing Forestry University, Beijing, China
| | - Huiying Gong
- College of Science, Beijing Forestry University, Beijing, China
| | - Qing Fang
- Faculty of Science, Yamagata University, Yamagata, Japan
| | - Xuli Zhu
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, Center for Computational Biology, College of Biological Sciences and Technology, Beijing Forestry University, Beijing, China
| | - Libo Jiang
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, Center for Computational Biology, College of Biological Sciences and Technology, Beijing Forestry University, Beijing, China
| | - Rongling Wu
- Beijing Advanced Innovation Center for Tree Breeding by Molecular Design, Center for Computational Biology, College of Biological Sciences and Technology, Beijing Forestry University, Beijing, China
- Center for Statistical Genetics, The Pennsylvania State University, Hershey, PA, United States
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9
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Chen S, Chiaramonte R. In creatinine kinetics, the glomerular filtration rate always moves the serum creatinine in the opposite direction. Physiol Rep 2021; 9:e14957. [PMID: 34405576 PMCID: PMC8371355 DOI: 10.14814/phy2.14957] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2021] [Revised: 06/15/2021] [Accepted: 06/15/2021] [Indexed: 01/23/2023] Open
Abstract
INTRODUCTION When the serum [creatinine] is changing, creatinine kinetics can still gauge the kidney function, and knowing the kinetic glomerular filtration rate (GFR) helps doctors take care of patients with renal failure. We wondered how the serum [creatinine] would respond if the kinetic GFR were tweaked. In every scenario, if the kinetic GFR decreased, the [creatinine] would increase, and vice versa. This opposing relationship was hypothesized to be universal. METHODS Serum [creatinine] and kinetic GFR, along with other parameters, are described by a differential equation. We differentiated [creatinine] with respect to kinetic GFR to test if the two variables would change oppositely of each other, throughout the gamut of all allowable clinical values. To remove the discontinuities in the derivative, limits were solved. RESULTS The derivative and its limits were comprehensively analyzed and proved to have a sign that is always negative, meaning that [creatinine] and kinetic GFR must indeed move in opposite directions. The derivative is bigger in absolute value at the higher end of the [creatinine] scale, where a small drop in the kinetic GFR can cause the [creatinine] to shoot upward, making acute kidney injury similar to chronic kidney disease in that regard. CONCLUSIONS All else being equal, a change in the kinetic GFR obligates the [creatinine] to change in the opposite direction. This does not negate the fact that an increasing [creatinine] can be compatible with a rising kinetic GFR, due to differences in how the time variable is treated.
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Affiliation(s)
- Sheldon Chen
- Section of NephrologyMD Anderson Cancer CenterHoustonTXUSA
| | - Robert Chiaramonte
- Internal MedicineThe State University of New York Downstate Health Sciences UniversityBrooklynNYUSA
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Mongin D, Caparros AU, Gateau J, Gencer B, Alvero-Cruz JR, Cheval B, Cullati S, Courvoisier DS. Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach. Multivariate Behav Res 2021; 56:649-668. [PMID: 32363935 DOI: 10.1080/00273171.2020.1754155] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated homeostatic systems experiencing multiple excitations. It focuses on the evolution of a signal (e.g., heart rate) before, during, and after excitations taking the system out of its equilibrium (e.g., physical effort during cardiac stress testing). Such approach can be applied to a broad range of outcomes such as physiological processes in medicine and psychosocial processes in social sciences, and it allows to extract simple characteristics of the signal studied. The model is based on a first order linear differential equation with constant coefficients defined by three main parameters corresponding to the initial equilibrium value, the dynamic characteristic time, and the reaction to the excitation. Assuming the presence of interindividual variability (random effects) on these three parameters, we propose a two-step procedure to estimate them. We then compare the results of this analysis to several other estimation procedures in a simulation study that clarifies under which conditions parameters are accurately estimated. Finally, applications of this model are illustrated using cardiology data recorded during effort tests.
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Affiliation(s)
- Denis Mongin
- Quality of Care Division, Geneva University Hospitals
- Department of General Internal Medicine, Rehabilitation and Geriatrics, University of Geneva
| | - Adriana Uribe Caparros
- Department of General Internal Medicine, Rehabilitation and Geriatrics, University of Geneva
| | | | - Baris Gencer
- Cardiology Division, Geneva University Hospitals
| | - Jose Ramon Alvero-Cruz
- Department of Human physiology, histology, pathological anatomy and physical education, Malaga University, Andalucía Tech
| | - Boris Cheval
- Quality of Care Division, Geneva University Hospitals
- Department of General Internal Medicine, Rehabilitation and Geriatrics, University of Geneva
| | - Stéphane Cullati
- Quality of Care Division, Geneva University Hospitals
- Department of General Internal Medicine, Rehabilitation and Geriatrics, University of Geneva
- Swiss NCCR "Lives: Overcoming Vulnerability: Life Course Perspectives", University of Geneva
| | - Delphine S Courvoisier
- Quality of Care Division, Geneva University Hospitals
- Department of General Internal Medicine, Rehabilitation and Geriatrics, University of Geneva
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Salas-Eljatib C. An approach to quantify climate-productivity relationships: an example from a widespread Nothofagus forest. Ecol Appl 2021; 31:e02285. [PMID: 33423354 DOI: 10.1002/eap.2285] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2020] [Revised: 09/14/2020] [Accepted: 10/06/2020] [Indexed: 06/12/2023]
Abstract
Unique combinations of geographic and environmental conditions make quantifying the importance of factors that influence forest productivity difficult. I aimed to model the height growth of dominant Nothofagus alpina trees in temperate forests of Chile, as a proxy for forest productivity, by building a dynamic model that accounts for topography, habitat type, and climate conditions. Using stem analysis data of 169 dominant trees sampled throughout south-central Chile (35°50' and 41°30' S), I estimated growth model parameters using a nonlinear mixed-effects framework that takes into account the hierarchical structure of the data. Based on the proposed model, I used a system-dynamics approach to analyze growth rates as a function of topographic, habitat type, and climatic variability. I found that the interaction between aspect, slope, and elevation, as well as the effect of habitat type, play an essential role in determining tree height growth rates of N. alpina. Furthermore, the precipitation in the warmest quarter, precipitation seasonality, and annual mean temperature are critical climatic drivers of forest productivity. Given a forecasted climate condition for the region by 2100, where precipitation seasonality and mean annual temperature increase by 10% and 1°C, respectively, and precipitation in the warmest quarter decreases by 10 mm, I predict a reduction of 1.4 m in height growth of 100-yr-old dominant trees. This study shows that the sensitivity of N. alpina-dominated forests to precipitation and temperature patterns could lead to a reduction of tree height growth rates as a result of climate change, suggesting a decrease in carbon sequestration too. By implementing a system dynamics approach, I provide a new perspective on climate-productivity relationships, bettering the quantitative understanding of forest ecosystem dynamics under climate change. The results highlight that while temperature rising might favor forest growth, the decreasing in both amount and distribution within a year of precipitation can be even more critical to reduce forest productivity.
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Affiliation(s)
- Christian Salas-Eljatib
- Centro de Modelación y Monitoreo de Ecosistemas, Facultad de Ciencias, Escuela de Ingeniería Forestal, Universidad Mayor, Santiago, Chile
- Vicerrectoría de Investigación y Postgrado, Universidad de La Frontera, Temuco, Chile
- Departamento de Silvicultura y Conservación de la Naturaleza, Universidad de Chile, Santiago, Chile
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Mühlbauer LK, Schulze M, Harpole WS, Clark AT. gauseR: Simple methods for fitting Lotka-Volterra models describing Gause's "Struggle for Existence". Ecol Evol 2020; 10:13275-13283. [PMID: 33304536 PMCID: PMC7713957 DOI: 10.1002/ece3.6926] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2020] [Revised: 08/07/2020] [Accepted: 08/26/2020] [Indexed: 11/13/2022] Open
Abstract
Point 1: The ecological models of Alfred J. Lotka and Vito Volterra have had an enormous impact on ecology over the past century. Some of the earliest-and clearest-experimental tests of these models were famously conducted by Georgy Gause in the 1930s. Although well known, the data from these experiments are not widely available and are often difficult to analyze using standard statistical and computational tools. Point 2: Here, we introduce the gauseR package, a collection of tools for fitting Lotka-Volterra models to time series data of one or more species. The package includes several methods for parameter estimation and optimization, and includes 42 datasets from Gause's species interaction experiments and related work. Additionally, we include with this paper a short blog post discussing the historical importance of these data and models, and an R vignette with a walk-through introducing the package methods. The package is available for download at github.com/adamtclark/gauseR. Point 3: To demonstrate the package, we apply it to several classic experimental studies from Gause, as well as two other well-known datasets on multi-trophic dynamics on Isle Royale, and in spatially structured mite populations. In almost all cases, models fit observations closely and fitted parameter values make ecological sense. Point 4: Taken together, we hope that the methods, data, and analyses that we present here provide a simple and user-friendly way to interact with complex ecological data. We are optimistic that these methods will be especially useful to students and educators who are studying ecological dynamics, as well as researchers who would like a fast tool for basic analyses.
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Affiliation(s)
| | | | - W. Stanley Harpole
- Institute of BiologyMartin Luther UniversityHalleGermany
- Department of Physiological DiversityHelmholtz Centre for Environmental Research (UFZ)LeipzigGermany
- German Centre for Integrative Biodiversity Research (iDiv) Halle‐Jena‐LeipzigLeipzigGermany
| | - Adam T. Clark
- Department of Physiological DiversityHelmholtz Centre for Environmental Research (UFZ)LeipzigGermany
- German Centre for Integrative Biodiversity Research (iDiv) Halle‐Jena‐LeipzigLeipzigGermany
- Synthesis Centre for Biodiversity Sciences (sDiv)LeipzigGermany
- Institute of BiologyKarl‐Franzens‐University of GrazHolteigasse 6, Graz, 8010Austria
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13
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Abstract
Creatinine clearance is a tenet of nephrology practice. However, with just a single creatinine concentration included in the denominator of the creatinine clearance equation, the resulting value seems to apply only in the steady state. Does the basic clearance formula work in the nonsteady state, and can it recapitulate the kinetic glomerular filtration rate (GFR) equation? In the kinetic state, a nonlinear creatinine trajectory is reducible into a “true average” value that can be found using calculus, proceeding from a differential equation based on the mass balance principle. Using the fundamental theorem of calculus, we prove definitively that the true average is the correct creatinine to divide by, even as the mathematical model accommodates clinical complexities such as volume change and other factors that affect creatinine kinetics. The true average of a creatinine versus time function between 2 measured creatinine values is found by a definite integral. To use the true average to compute kinetic GFR, 2 techniques are demonstrated, a graphical one and a numerical one. We apply this concept to a clinical case of an individual with acute kidney injury requiring dialysis; despite the effects of hemodialysis on serum creatinine concentration, kinetic GFR was able to track the underlying kidney function and provided critical information regarding kidney function recovery. Finally, a prior concept of the maximum increase in creatinine per day is made more clinically objective. Thus, the clearance paradigm applies to the nonsteady state as well when the true average creatinine is used, providing a fundamentally valid strategy to deduce kinetic GFRs from serum creatinine trends occurring in real-life acute kidney injury and kidney recovery.
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Affiliation(s)
- Sheldon Chen
- Section of Nephrology, MD Anderson Cancer Center, Houston, TX
- Address for Correspondence: Sheldon Chen, MD, MD Anderson Cancer Center, 1515 Holcombe Blvd, Unit 1468, Houston, TX 77230-1402.
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14
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Wang H, Tian Z, Wang H, Yan Q. Optimization and reaction kinetics analysis for phosphorus removal in struvite precipitation process. Water Environ Res 2020; 92:1162-1172. [PMID: 32072707 DOI: 10.1002/wer.1311] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2020] [Revised: 02/12/2020] [Accepted: 02/13/2020] [Indexed: 06/10/2023]
Abstract
As a promising strategy to remove and recover phosphorus from wastewater, optimization of the struvite (MgNH4 PO4 .6H2 O) precipitation parameters is required to achieve desirable phosphorus removal efficiency. To tackle the challenges upon the precipitation optimization methods as three-level full factorial designs, and central composite design as well, Box-Behnken design was implemented to optimize different reaction parameters for phosphorus removal and recovery during struvite precipitation in the current study. Moreover, the reaction orders and the rate equation were all determined to reveal the reaction kinetics parameters of struvite precipitation. The results showed that the optimal operating parameters of pH, Mg/P ratio and N/P ratio were 9.82, 1.45, and 4.00, respectively, by which more than 95% of phosphorus removal efficiency could be achieved. In addition, it was found that pH and pH/(N/P) had the most influence on phosphorus removal efficiency among different individual factors and interactive items, respectively. The partial orders of PO4 -P, Mg2+ , and NH 4 + in kinetic rate equation were determined as 1.586, 0.930, and 1.236 while the rate constant k was 0.0167 ± 0.0014 mM-2.752 per minute by differential method. PRACTITIONER POINTS: Different reaction parameters were optimized by Box-Behnken design. pH and pH/(N/P) had the most influence on phosphorus removal efficiency among different individual factors and interactive items. The reaction orders and the rate equation were all determined to reveal the reaction kinetics parameters.
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Affiliation(s)
- Han Wang
- School of Environmental and Civil Engineering, Jiangnan University, Wuxi, China
- Jiangsu Key Laboratory of Anaerobic Biotechnology, Wuxi, China
| | - Zeyuan Tian
- China Shanghai Architectural Design & Research Institute, Shanghai, China
| | - He Wang
- School of Environmental and Civil Engineering, Jiangnan University, Wuxi, China
| | - Qun Yan
- School of Environmental and Civil Engineering, Jiangnan University, Wuxi, China
- Jiangsu Key Laboratory of Anaerobic Biotechnology, Wuxi, China
- Jiangsu Collaborative Innovation Center of Technology and Material of Water Treatment, Suzhou, China
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15
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Abstract
Biological systems are inherently complex, and the increasing level of detail with which we are able to experimentally probe such systems continually reveals new complexity. Fortunately, mathematical models are uniquely positioned to provide a tool suitable for rigorous analysis, hypothesis generation, and connecting results from isolated in vitro experiments with results from in vivo and whole-organism studies. However, developing useful mathematical models is challenging because of the often different domains of knowledge required in both math and biology. In this work, we endeavor to provide a useful guide for researchers interested in incorporating mathematical modeling into their scientific process. We advocate for the use of conceptual diagrams as a starting place to anchor researchers from both domains. These diagrams are useful for simplifying the biological process in question and distinguishing the essential components. Not only do they serve as the basis for developing a variety of mathematical models, but they ensure that any mathematical formulation of the biological system is led primarily by scientific questions. We provide a specific example of this process from our own work in studying prion aggregation to show the power of mathematical models to synergistically interact with experiments and push forward biological understanding. Choosing the most suitable model also depends on many different factors, and we consider how to make these choices based on different scales of biological organization and available data. We close by discussing the many opportunities that abound for both experimentalists and modelers to take advantage of collaborative work in this field.
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Affiliation(s)
- Mikahl Banwarth-Kuhn
- Department of Applied Mathematics, School of Natural Sciences, University of California, Merced, California 95343
| | - Suzanne Sindi
- Department of Applied Mathematics, School of Natural Sciences, University of California, Merced, California 95343
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16
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Leake C, Johnston H, Smith L, Mortari D. Analytically Embedding Differential Equation Constraints into Least Squares Support Vector Machines Using the Theory of Functional Connections. Mach Learn Knowl Extr 2019; 1:1058-1083. [PMID: 32478282 PMCID: PMC7259481 DOI: 10.3390/make1040060] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Differential equations (DEs) are used as numerical models to describe physical phenomena throughout the field of engineering and science, including heat and fluid flow, structural bending, and systems dynamics. While there are many other techniques for finding approximate solutions to these equations, this paper looks to compare the application of the Theory of Functional Connections (TFC) with one based on least-squares support vector machines (LS-SVM). The TFC method uses a constrained expression, an expression that always satisfies the DE constraints, which transforms the process of solving a DE into solving an unconstrained optimization problem that is ultimately solved via least-squares (LS). In addition to individual analysis, the two methods are merged into a new methodology, called constrained SVMs (CSVM), by incorporating the LS-SVM method into the TFC framework to solve unconstrained problems. Numerical tests are conducted on four sample problems: One first order linear ordinary differential equation (ODE), one first order nonlinear ODE, one second order linear ODE, and one two-dimensional linear partial differential equation (PDE). Using the LS-SVM method as a benchmark, a speed comparison is made for all the problems by timing the training period, and an accuracy comparison is made using the maximum error and mean squared error on the training and test sets. In general, TFC is shown to be slightly faster (by an order of magnitude or less) and more accurate (by multiple orders of magnitude) than the LS-SVM and CSVM approaches.
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Affiliation(s)
- Carl Leake
- Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
| | - Hunter Johnston
- Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
| | - Lidia Smith
- Mathematics Department, Blinn College, Bryan, TX 77802, USA
| | - Daniele Mortari
- Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
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17
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Baller D, Thomas DM, Cummiskey K, Bredlau C, Schwartz N, Orzechowski K, Miller RC, Odibo A, Shah R, Salafia CM. Gestational growth trajectories derived from a dynamic fetal-placental scaling law. J R Soc Interface 2019; 16:20190417. [PMID: 31662073 DOI: 10.1098/rsif.2019.0417] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
Fetal trajectories characterizing growth rates in utero have relied primarily on goodness of fit rather than mechanistic properties exhibited in utero. Here, we use a validated fetal-placental allometric scaling law and a first principles differential equations model of placental volume growth to generate biologically meaningful fetal-placental growth curves. The growth curves form the foundation for understanding healthy versus at-risk fetal growth and for identifying the timing of key events in utero.
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Affiliation(s)
- Daniel Baller
- Department of Mathematical Sciences, United States Military Academy, West Point, NY 10996, USA
| | - Diana M Thomas
- Department of Mathematical Sciences, United States Military Academy, West Point, NY 10996, USA
| | - Kevin Cummiskey
- Department of Mathematical Sciences, United States Military Academy, West Point, NY 10996, USA
| | - Carl Bredlau
- Department of Computer Science, Montclair State University, Montclair, NJ 07043, USA
| | - Nadav Schwartz
- Division of Maternal Fetal Medicine, 3400 Spruce Street, Philadelphia, PA 19104, USA
| | | | - Richard C Miller
- Department of Obstetrics and Gynecology, St Barnabas Medical Center, Livingston, NJ 07039, USA
| | - Anthony Odibo
- Division of Maternal Fetal Medicine, University of South Florida, Tampa, FL 33620, USA
| | - Ruchit Shah
- Placental Analytics, New Rochelle, NY 10538, USA
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18
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Li Z, Shao T. An Improved Ecological Services Valuation Model in Land Use Project. Int J Environ Res Public Health 2019; 16:ijerph16081474. [PMID: 31027282 PMCID: PMC6518053 DOI: 10.3390/ijerph16081474] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/03/2019] [Revised: 04/21/2019] [Accepted: 04/22/2019] [Indexed: 12/05/2022]
Abstract
Natural ecosystems benefit human lives via providing fundamental life-support services and goods upon which human civilization depends. However, as nature provides those for free, many people believe that they are of little or no value and they exploit the land greedily and unreasonably, which makes serious ecological degradation. Concerning this issue, we present the ecological services valuation model (ESVM) to measure the cost of environmental degradation of land use cost, which is an evaluation model of environmental degradation cost. Environmental degradation cost refer to the cost of deterioration or compromise of natural environment through natural processes or human activities, which consists of opportunity cost and environmental damage cost. Land area is an important variable in the ESVM. Based on Osmotic system, we put forward the effective land area, which combines the scale factor and the impact of external environment. What is more, the Cobb–Douglas production function is modified to establish the model. Finally, we propose the calculation formula of the economic cost of land use projects. Analysis of effectiveness and sensitivity prove that ESVM was a relatively stable model.
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Affiliation(s)
- Zhichao Li
- School of Political Science and Public Administration, East China University of Political Science and Law, Shanghai 201620, China.
| | - Tianqu Shao
- School of Public Administration, University of Electronic Science and Technology of China, Chengdu 611731, China.
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19
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Wen X, Chen G, Lu G, Liu Z, Yan P. Differential Equation-Based Prediction Model for Early Change Detection in Transient Running Status. Sensors (Basel) 2019; 19:E412. [PMID: 30669535 DOI: 10.3390/s19020412] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/23/2018] [Revised: 01/16/2019] [Accepted: 01/18/2019] [Indexed: 11/21/2022]
Abstract
Early detection of changes in transient running status from sensor signals attracts increasing attention in modern industries. To achieve this end, this paper presents a new differential equation-based prediction model that can realize one-step-ahead prediction of machine status. Together with this model, an analysis of continuous monitoring of condition signal by means of a null hypothesis testing is presented to inspect/diagnose whether an abnormal status change occurs or not during successive machine operations. The detection operation is executed periodically and continuously, such that the machine running status can be monitored with an online and real-time manner. The effectiveness of the proposed method is demonstrated using three representative real-engineering applications: external loading status monitoring, bearing health status monitoring and speed condition monitoring. The method is also compared with those benchmark methods reported in the literature. From the results, the proposed method demonstrates significant improvements over others, which suggests its superiority and great potentials in real applications.
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20
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Abstract
Dynamic system consisting of ordinary differential equations (ODEs) is a well-known tool for describing dynamic nature of gene regulatory networks (GRNs), and the dynamic features of GRNs are usually captured through time-course gene expression data. Owing to high-throughput technologies, time-course gene expression data have complex structures such as heteroscedasticity, correlations between genes, and time dependence. Since gene experiments typically yield highly noisy data with small sample size, for a more accurate prediction of the dynamics, the complex structures should be taken into account in ODE models. Hence, this study proposes an ODE model considering such data structures and a fast and stable estimation method for the ODE parameters based on the generalized profiling approach with data smoothing techniques. The proposed method also provides statistical inference for the ODE estimator and it is applied to a zebrafish retina cell network.
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Affiliation(s)
- Yoonji Kim
- Department of Statistics, Sungkyunkwan University , Seoul, Korea
| | - Jaejik Kim
- Department of Statistics, Sungkyunkwan University , Seoul, Korea
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21
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Chow SM, Ou L, Ciptadi A, Prince EB, You D, Hunter MD, Rehg JM, Rozga A, Messinger DS. Representing Sudden Shifts in Intensive Dyadic Interaction Data Using Differential Equation Models with Regime Switching. Psychometrika 2018; 83:476-510. [PMID: 29557080 PMCID: PMC7370947 DOI: 10.1007/s11336-018-9605-1] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2016] [Revised: 12/26/2017] [Indexed: 05/25/2023]
Abstract
A growing number of social scientists have turned to differential equations as a tool for capturing the dynamic interdependence among a system of variables. Current tools for fitting differential equation models do not provide a straightforward mechanism for diagnosing evidence for qualitative shifts in dynamics, nor do they provide ways of identifying the timing and possible determinants of such shifts. In this paper, we discuss regime-switching differential equation models, a novel modeling framework for representing abrupt changes in a system of differential equation models. Estimation was performed by combining the Kim filter (Kim and Nelson State-space models with regime switching: classical and Gibbs-sampling approaches with applications, MIT Press, Cambridge, 1999) and a numerical differential equation solver that can handle both ordinary and stochastic differential equations. The proposed approach was motivated by the need to represent discrete shifts in the movement dynamics of [Formula: see text] mother-infant dyads during the Strange Situation Procedure (SSP), a behavioral assessment where the infant is separated from and reunited with the mother twice. We illustrate the utility of a novel regime-switching differential equation model in representing children's tendency to exhibit shifts between the goal of staying close to their mothers and intermittent interest in moving away from their mothers to explore the room during the SSP. Results from empirical model fitting were supplemented with a Monte Carlo simulation study to evaluate the use of information criterion measures to diagnose sudden shifts in dynamics.
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Affiliation(s)
- Sy-Miin Chow
- Pennsylvania State University, 413 Biobehavioral Health Building, University Park, PA, 16802, USA.
| | - Lu Ou
- Pennsylvania State University, 413 Biobehavioral Health Building, University Park, PA, 16802, USA
| | | | | | - Dongjun You
- Pennsylvania State University, 413 Biobehavioral Health Building, University Park, PA, 16802, USA
| | - Michael D Hunter
- University of Oklahoma Health Sciences Center, 940 NE 13th Street, Suite 4900, Oklahoma City, OK, 73104, USA
| | - James M Rehg
- Georgia Institute of Technology, Atlanta, GA, USA
| | - Agata Rozga
- Georgia Institute of Technology, Atlanta, GA, USA
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22
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McDargh ZA, Deserno M. Dynamin's helical geometry does not destabilize membranes during fission. Traffic 2018; 19:328-335. [PMID: 29437294 DOI: 10.1111/tra.12555] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2017] [Revised: 02/02/2018] [Accepted: 02/04/2018] [Indexed: 11/29/2022]
Abstract
It is now widely accepted that dynamin-mediated fission is a fundamentally mechanical process: dynamin undergoes a GTP-dependent conformational change, constricting the neck between two compartments, somehow inducing their fission. However, the exact connection between dynamin's conformational change and the scission of the neck is still unclear. In this paper, we re-evaluate the suggestion that a change in the pitch or radius of dynamin's helical geometry drives the lipid bilayer through a mechanical instability, similar to a well-known phenomenon occurring in soap films. We find that, contrary to previous claims, there is no such instability. This lends credence to an alternative model, in which dynamin drives the membrane up an energy barrier, allowing thermal fluctuations to take it into the hemifission state.
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Affiliation(s)
- Zachary A McDargh
- Chemical Engineering Department, Columbia University, New York, New York
| | - Markus Deserno
- Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania
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23
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Sweeney DC, Douglas TA, Davalos RV. Characterization of Cell Membrane Permeability In Vitro Part II: Computational Model of Electroporation-Mediated Membrane Transport. Technol Cancer Res Treat 2018; 17:1533033818792490. [PMID: 30231776 PMCID: PMC6149036 DOI: 10.1177/1533033818792490] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2018] [Revised: 06/18/2018] [Accepted: 07/03/2018] [Indexed: 12/22/2022] Open
Abstract
Electroporation is the process by which applied electric fields generate nanoscale defects in biological membranes to more efficiently deliver drugs and other small molecules into the cells. Due to the complexity of the process, computational models of cellular electroporation are difficult to validate against quantitative molecular uptake data. In part I of this two-part report, we describe a novel method for quantitatively determining cell membrane permeability and molecular membrane transport using fluorescence microscopy. Here, in part II, we use the data from part I to develop a two-stage ordinary differential equation model of cellular electroporation. We fit our model using experimental data from cells immersed in three buffer solutions and exposed to electric field strengths of 170 to 400 kV/m and pulse durations of 1 to 1000 μs. We report that a low-conductivity 4-(2-hydroxyethyl)-1 piperazineethanesulfonic acid buffer enables molecular transport into the cell to increase more rapidly than with phosphate-buffered saline or culture medium-based buffer. For multipulse schemes, our model suggests that the interpulse delay between two opposite polarity electric field pulses does not play an appreciable role in the resultant molecular uptake for delays up to 100 μs. Our model also predicts the per-pulse permeability enhancement decreases as a function of the pulse number. This is the first report of an ordinary differential equation model of electroporation to be validated with quantitative molecular uptake data and consider both membrane permeability and charging.
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Affiliation(s)
- Daniel C. Sweeney
- Department of Biomedical Engineering and Mechanics, Virginia Tech,
Blacksburg, VA, USA
| | - Temple A. Douglas
- Department of Biomedical Engineering and Mechanics, Virginia Tech,
Blacksburg, VA, USA
| | - Rafael V. Davalos
- Department of Biomedical Engineering and Mechanics, Virginia Tech,
Blacksburg, VA, USA
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24
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Abstract
Cell division is a key biological process in which cells divide forming new daughter cells. In the present study, we investigate continuously how a Coleochaete cell divides by introducing a modified differential equation model in parametric equation form. We discuss both the influence of "dead" cells and the effects of various end-points on the formation of the new cells' boundaries. We find that the boundary condition on the free end-point is different from that on the fixed end-point; the former has a direction perpendicular to the surface. It is also shown that the outer boundaries of new cells are arc-shaped. The numerical experiments and theoretical analyses for this model to construct the outer boundary are given.
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Affiliation(s)
- Yuandi Wang
- Department of Mathematics, Shanghai University , Shanghai, China
| | - Jinyu Cong
- Department of Mathematics, Shanghai University , Shanghai, China
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25
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Chow SM, Lu Z, Sherwood A, Zhu H. Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm. Psychometrika 2016; 81:102-34. [PMID: 25416456 PMCID: PMC4441616 DOI: 10.1007/s11336-014-9431-z] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2013] [Indexed: 05/25/2023]
Abstract
The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.
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Affiliation(s)
- Sy-Miin Chow
- The Pennsylvania State University, 413 Biobehavioral Health Building, University Park, PA, 16802 , USA.
| | - Zhaohua Lu
- University of North Carolina at Chapel Hill, Chapel Hill, USA
| | | | - Hongtu Zhu
- University of North Carolina at Chapel Hill, Chapel Hill, USA
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26
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Abstract
Catastrophe theory (Thom, 1972, 1993) is the study of the many ways in which continuous changes in a system's parameters can result in discontinuous changes in 1 or several outcome variables of interest. Catastrophe theory-inspired models have been used to represent a variety of change phenomena in the realm of social and behavioral sciences. Despite their promise, widespread applications of catastrophe models have been impeded, in part, by difficulties in performing model fitting and model comparison procedures. We propose a new modeling framework for testing 1 kind of catastrophe model-the cusp catastrophe model-as a mixture structural equation model (MSEM) when cross-sectional data are available; or alternatively, as an MSEM with regime-switching (MSEM-RS) when longitudinal panel data are available. The proposed models and the advantages offered by this alternative modeling framework are illustrated using 2 empirical examples and a simulation study.
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27
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Thomas DM, Weedermann M, Fuemmeler BF, Martin CK, Dhurandhar NV, Bredlau C, Heymsfield SB, Ravussin E, Bouchard C. Dynamic model predicting overweight, obesity, and extreme obesity prevalence trends. Obesity (Silver Spring) 2014; 22:590-7. [PMID: 23804487 PMCID: PMC3842399 DOI: 10.1002/oby.20520] [Citation(s) in RCA: 39] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/01/2013] [Accepted: 05/27/2013] [Indexed: 12/04/2022]
Abstract
OBJECTIVE Obesity prevalence in the United States appears to be leveling, but the reasons behind the plateau remain unknown. Mechanistic insights can be provided from a mathematical model. The objective of this study is to model known multiple population parameters associated with changes in body mass index (BMI) classes and to establish conditions under which obesity prevalence will plateau. DESIGN AND METHODS A differential equation system was developed that predicts population-wide obesity prevalence trends. The model considers both social and nonsocial influences on weight gain, incorporates other known parameters affecting obesity trends, and allows for country specific population growth. RESULTS The dynamic model predicts that: obesity prevalence is a function of birthrate and the probability of being born in an obesogenic environment; obesity prevalence will plateau independent of current prevention strategies; and the US prevalence of overweight, obesity, and extreme obesity will plateau by about 2030 at 28%, 32%, and 9% respectively. CONCLUSIONS The US prevalence of obesity is stabilizing and will plateau, independent of current preventative strategies. This trend has important implications in accurately evaluating the impact of various anti-obesity strategies aimed at reducing obesity prevalence.
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Affiliation(s)
- Diana M. Thomas
- Center for Quantitative Obesity Research, Montclair State University, Montclair, NJ
| | | | | | - Corby K. Martin
- Pennington Biomedical Research Center, Louisiana State University System, Baton Rouge, LA
| | - Nikhil V. Dhurandhar
- Pennington Biomedical Research Center, Louisiana State University System, Baton Rouge, LA
| | - Carl Bredlau
- Center for Quantitative Obesity Research, Montclair State University, Montclair, NJ
| | - Steven B. Heymsfield
- Pennington Biomedical Research Center, Louisiana State University System, Baton Rouge, LA
| | - Eric Ravussin
- Pennington Biomedical Research Center, Louisiana State University System, Baton Rouge, LA
| | - Claude Bouchard
- Pennington Biomedical Research Center, Louisiana State University System, Baton Rouge, LA
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28
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Wang Z, Liu J, Wang J, Wang Y, Wang N, Li Y, Li R, Wu R. Dynamic modeling of genes controlling cancer stem cell proliferation. Front Genet 2012; 3:84. [PMID: 22661984 PMCID: PMC3357477 DOI: 10.3389/fgene.2012.00084] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2012] [Accepted: 04/26/2012] [Indexed: 12/18/2022] Open
Abstract
The growing evidence that cancer originates from stem cells (SC) holds a great promise to eliminate this disease by designing specific drug therapies for removing cancer SC. Translation of this knowledge into predictive tests for the clinic is hampered due to the lack of methods to discriminate cancer SC from non-cancer SC. Here, we address this issue by describing a conceptual strategy for identifying the genetic origins of cancer SC. The strategy incorporates a high-dimensional group of differential equations that characterizes the proliferation, differentiation, and reprogramming of cancer SC in a dynamic cellular and molecular system. The deployment of robust mathematical models will help uncover and explain many still unknown aspects of cell behavior, tissue function, and network organization related to the formation and division of cancer SC. The statistical method developed allows biologically meaningful hypotheses about the genetic control mechanisms of carcinogenesis and metastasis to be tested in a quantitative manner.
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Affiliation(s)
- Zhong Wang
- Center for Statistical Genetics, The Pennsylvania State University Hershey, PA, USA
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29
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Abstract
Why does a single fire ant Solenopsis invicta struggle in water, whereas a group can float effortlessly for days? We use time-lapse photography to investigate how fire ants S. invicta link their bodies together to build waterproof rafts. Although water repellency in nature has been previously viewed as a static material property of plant leaves and insect cuticles, we here demonstrate a self-assembled hydrophobic surface. We find that ants can considerably enhance their water repellency by linking their bodies together, a process analogous to the weaving of a waterproof fabric. We present a model for the rate of raft construction based on observations of ant trajectories atop the raft. Central to the construction process is the trapping of ants at the raft edge by their neighbors, suggesting that some "cooperative" behaviors may rely upon coercion.
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Affiliation(s)
| | | | - David L. Hu
- Schools of Mechanical Engineering
- Biology, Georgia Institute of Technology, Atlanta, GA 30318
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30
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Abstract
Mathematical and computational models have become indispensable tools for integrating and interpreting heterogeneous biological data, understanding fundamental principles of biological system functions, genera-ting reliable testable hypotheses, and identifying potential diagnostic markers and therapeutic targets. Thus, such tools are now routinely used in the theoretical and experimental systematic investigation of biological system dynamics. Here, we discuss model building as an essential part of the theoretical and experimental analysis of biomolecular network dynamics. Specifically, we describe a procedure for defining kinetic equations and parameters of biomolecular processes, and we illustrate the use of fractional activity functions for modeling gene expression regulation by single and multiple regulators. We further discuss the evaluation of model complexity and the selection of an optimal model based on information criteria. Finally, we discuss the critical roles of sensitivity, robustness analysis, and optimal experiment design in the model building cycle.
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Dullens HF, Van der Tol MW, De Weger RA, Den Otter W. A survey of some formal models in tumor immunology. Cancer Immunol Immunother 1986; 23:159-64. [PMID: 3491679 PMCID: PMC11038894 DOI: 10.1007/bf00205644] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/06/1986] [Accepted: 07/29/1986] [Indexed: 01/06/2023]
Abstract
Computer technology has acquired an important role in structuring a variety of biological systems. The availability of modern powerful computers has stimulated the development of good and accurate models of biological systems. Biological systems, such as the immune response against cancer, are complex and it is difficult to experimentally control all the interacting elements constituting the immune response of a host to cancer. Complex biosystems do not always behave or act as expected during experimental investigation. In these cases computer models can be helpful in understanding the behavior of such complex systems. The purpose of this review is to consider the use of mathematical models to study the immune response against cancer. The logic and design of some operable models relevant for tumor immunology will be discussed. Special attention is given to the conceptualization of a model based upon a new hypothesis of tumor rejection presented by De Weger et al. [10]. Technical details concerning the mathematical aspects, differential equations, details on hardware and software package etc. are not included in this survey. These details are contained to in the original papers.
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