American Institute of Mathematical Sciences

Advanced
2009, 6(1): 93-115. doi: 10.3934/mbe.2009.6.93

Estimation and identification of parameters in a lumped cerebrovascular model

Scott R. Pope 1, , Laura M. Ellwein 2, , Cheryl L. Zapata 3, , Vera Novak 4, , C. T. Kelley 1, and  Mette S. Olufsen 1,

1. 

Department of Mathematics, North Carolina State University, Campus Box 8205, Raleigh, NC 27695, United States, United States, United States
2. 

Olin Engineering Center, Marquette University, 1515 West Wisconsin Ave, Room 206, Milwaukee, WI 53233, United States
3. 

Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, United States
4. 

Harvard Medical School and Beth Israel Deaconess Medical Center Division of Gerontology, 110 Francis Street LM0B Suite 1b, Boston, MA 02215, United States

Received  July 2008 Revised  September 2008 Published  December 2008

This study shows how sensitivity analysis and subset selection can be employed in a cardiovascular model to estimate total systemic resistance, cerebrovascular resistance, arterial compliance, and time for peak systolic ventricular pressure for healthy young and elderly subjects. These quantities are parameters in a simple lumped parameter model that predicts pressure and flow in the systemic circulation. The model is combined with experimental measurements of blood flow velocity from the middle cerebral artery and arterial finger blood pressure. To estimate the model parameters we use nonlinear optimization combined with sensitivity analysis and subset selection. Sensitivity analysis allows us to rank model parameters from the most to the least sensitive with respect to the output states (cerebral blood flow velocity and arterial blood pressure). Subset selection allows us to identify a set of independent candidate parameters that can be estimated given limited data. Analyses of output from both methods allow us to identify five independent sensitive parameters that can be estimated given the data. Results show that with the advance of age total systemic and cerebral resistances increase, that time for peak systolic ventricular pressure is increases, and that arterial compliance is reduced. Thus, the method discussed in this study provides a new methodology to extract clinical markers that cannot easily be assessed noninvasively.
Keywords: cerebrovascular resistance, subset selection, systemic resistance, parameter estimation, sensitivity analysis, cardiovascular modeling.
Mathematics Subject Classification: Primary: 92C30, 92C35, 92C50, 65L09; Secondary: 93B40.
Citation: Scott R. Pope, Laura M. Ellwein, Cheryl L. Zapata, Vera Novak, C. T. Kelley, Mette S. Olufsen. Estimation and identification of parameters in a lumped cerebrovascular model. Mathematical Biosciences & Engineering, 2009, 6 (1) : 93-115. doi: 10.3934/mbe.2009.6.93
[1]

Sebastian Bonhoeffer, Pia Abel zur Wiesch, Roger D. Kouyos. Rotating antibiotics does not minimize selection for resistance. Mathematical Biosciences & Engineering, 2010, 7 (4) : 919-922. doi: 10.3934/mbe.2010.7.919
[2]

Krzysztof Fujarewicz, Krzysztof Łakomiec. Parameter estimation of systems with delays via structural sensitivity analysis. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : 2521-2533. doi: 10.3934/dcdsb.2014.19.2521
[3]

Cristian Tomasetti, Doron Levy. An elementary approach to modeling drug resistance in cancer. Mathematical Biosciences & Engineering, 2010, 7 (4) : 905-918. doi: 10.3934/mbe.2010.7.905
[4]

Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences & Engineering, 2005, 2 (2) : 227-238. doi: 10.3934/mbe.2005.2.227
[5]

Urszula Ledzewicz, Shuo Wang, Heinz Schättler, Nicolas André, Marie Amélie Heng, Eddy Pasquier. On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach. Mathematical Biosciences & Engineering, 2017, 14 (1) : 217-235. doi: 10.3934/mbe.2017014
[6]

Qi Deng, Zhipeng Qiu, Ting Guo, Libin Rong. Modeling within-host viral dynamics: The role of CTL immune responses in the evolution of drug resistance. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3543-3562. doi: 10.3934/dcdsb.2020245
[7]

Timothy C. Reluga, Jan Medlock. Resistance mechanisms matter in SIR models. Mathematical Biosciences & Engineering, 2007, 4 (3) : 553-563. doi: 10.3934/mbe.2007.4.553
[8]

Ross Callister, Duc-Son Pham, Mihai Lazarescu. Using distribution analysis for parameter selection in repstream. Mathematical Foundations of Computing, 2019, 2 (3) : 215-250. doi: 10.3934/mfc.2019015
[9]

Piotr Bajger, Mariusz Bodzioch, Urszula Foryś. Singularity of controls in a simple model of acquired chemotherapy resistance. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2039-2052. doi: 10.3934/dcdsb.2019083
[10]

Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 129-150. doi: 10.3934/dcdsb.2006.6.129
[11]

Donato Patrizia, Andrey Piatnitski. On the effective interfacial resistance through rough surfaces. Communications on Pure and Applied Analysis, 2010, 9 (5) : 1295-1310. doi: 10.3934/cpaa.2010.9.1295
[12]

Avner Friedman, Najat Ziyadi, Khalid Boushaba. A model of drug resistance with infection by health care workers. Mathematical Biosciences & Engineering, 2010, 7 (4) : 779-792. doi: 10.3934/mbe.2010.7.779
[13]

Hamed Azizollahi, Marion Darbas, Mohamadou M. Diallo, Abdellatif El Badia, Stephanie Lohrengel. EEG in neonates: Forward modeling and sensitivity analysis with respect to variations of the conductivity. Mathematical Biosciences & Engineering, 2018, 15 (4) : 905-932. doi: 10.3934/mbe.2018041
[14]

Hengki Tasman, Edy Soewono, Kuntjoro Adji Sidarto, Din Syafruddin, William Oscar Rogers. A model for transmission of partial resistance to anti-malarial drugs. Mathematical Biosciences & Engineering, 2009, 6 (3) : 649-661. doi: 10.3934/mbe.2009.6.649
[15]

Zhenzhen Chen, Sze-Bi Hsu, Ya-Tang Yang. The continuous morbidostat: A chemostat with controlled drug application to select for drug resistance mutants. Communications on Pure and Applied Analysis, 2020, 19 (1) : 203-220. doi: 10.3934/cpaa.2020011
[16]

Piotr Bajger, Mariusz Bodzioch, Urszula Foryś. Corrigendum to "Singularity of controls in a simple model of acquired chemotherapy resistance". Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 2021-2021. doi: 10.3934/dcdsb.2020105
[17]

Robert E. Beardmore, Rafael Peña-Miller. Rotating antibiotics selects optimally against antibiotic resistance, in theory. Mathematical Biosciences & Engineering, 2010, 7 (3) : 527-552. doi: 10.3934/mbe.2010.7.527
[18]

Ami B. Shah, Katarzyna A. Rejniak, Jana L. Gevertz. Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1185-1206. doi: 10.3934/mbe.2016038
[19]

H.T. Banks, S. Dediu, H.K. Nguyen. Sensitivity of dynamical systems to parameters in a convex subset of a topological vector space. Mathematical Biosciences & Engineering, 2007, 4 (3) : 403-430. doi: 10.3934/mbe.2007.4.403
[20]

Sebastian Springer, Heikki Haario, Vladimir Shemyakin, Leonid Kalachev, Denis Shchepakin. Robust parameter estimation of chaotic systems. Inverse Problems and Imaging, 2019, 13 (6) : 1189-1212. doi: 10.3934/ipi.2019053

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (86)
  • HTML views (0)
  • Cited by (45)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy