- PII
- S30345030S0374064125070042-1
- DOI
- 10.7868/S3034503025070042
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 61 / Issue number 7
- Pages
- 910-918
- Abstract
- We investigate windkessel blood flow model with fractional derivative. A cost-effective numerical ap- proximation of the model equation is considered, which allows calculations with high precision. The approximation is tested on the proposed special case with the existing analytical solution. We use pro- posed numerical approximation to test various methods to identify the fractional order from real blood pressure profiles. The obtained methods allow to determine the order of the fractional derivative with an accuracy not worse than 15 %.
- Keywords
- модель упругого резервуара дробная производная гемодинамика обратная задача
- Date of publication
- 07.12.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 32
References
- 1. Frank, O. The basic shape of the arterial pulse. First treatise: mathematical analysis / O. Frank // J. of Molecular and Cellular Cardiology. — 1990. — V. 22, № 3. — P. 255–277.
- 2. Estimating central blood pressure from aortic flow: development and assessment of algorithms / J. Mariscal-Harana, P.H. Charlton, S. Vennin [et al.] // Amer. J. Physiol. Heart Circ. Physiol. — 2021. — V. 320, № 2 — P. H494–H510.
- 3. Bahloul, M.A. Human hypertension blood flow model using fractional calculus / M.A. Bahloul, Y. Aboelkassem, T.M. Laleg-Kirati // Front Physiol. — 2022. — V. 13. — Art. 838593.
- 4. Adhikary, A. Realization of Foster structure-based ladder fractor with phase band specification / A. Adhikary, A. Shil, A. Biswas // Circuits Syst. Signal Process. — 2020. — V. 39. — P. 2272–2292.
- 5. Gamilov, T. Fractional-order windkessel boundary conditions in a one-dimensional blood flow model for fractional flow reserve (FFR) estimation / T. Gamilov, R. Yanbarisov // Fractal Fract. — 2023. — V. 7, № 5. — Art. 373.
- 6. Resmi, V.L. Study on fractional order arterial windkessel model using optimization method / V.L. Resmi, N. Selvaganesan // IETE J. of Education. — 2023. — V. 64, № 2. — P. 103–111.
- 7. Vabishchevich, P.N. Approximate solution of the Cauchy problem for a first-order integrodifferential equation with solution derivative memory / P.N. Vabishchevich // J. Comp. Appl. Math. — 2023. — V. 422. — Art. 114887.
- 8. Algorithms for the fractional calculus: a selection of numerical methods / K. Diethelm, N.J. Ford, A.D. Freed, Yu. Luchko // Comp. Meth. in Appl. Mech. and Eng. — 2005. — V. 194, № 6–8. — P. 743–773.
- 9. Exact results for a fractional derivative of elementary functions / G. Shchedrin, N.C. Smith, A. Gladkina, L.D. Carr // SciPost Phys. — 2018. — V. 4. — Art. 029.
- 10. Stevens, S.A. A differentiable, periodic function for pulsatile cardiac output based on heart rate and stroke volume / S.A. Stevens, W.D. Lakin, W. Goetz // Math. Biosciences. — 2003. — V. 128, № 2. — P. 201–211.
- 11. Hancock, J.T. CatBoost for big data: an interdisciplinary review / J.T. Hancock, T.M. Khoshgoftaar // J. Big Data. — 2020. — V. 7. — Art. 94.