Thermo-electrical equivalents for simulating the electro-mechanical behavior of biological tissue
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1 Ilaria Cinelli Thermo-electrical equivalents for simulating the electro-mechanical behavior of biological tissue
2 Cao, H., Migliazza, J., Liu, X. C., & Dominick, D. (2012). Elia, S., Lamberti, P., & Tucci, V. (2009).
3 Cao, H., Migliazza, J., Liu, X. C., & Dominick, D. (2012). Elia, S., Lamberti, P., & Tucci, V. (2009).
4 Cao, H., Migliazza, J., Liu, X. C., & Dominick, D. (2012) Elia, S., Lamberti, P., & Tucci, V. (2009).
5 [7] B.-J. Wang, (1995). [4] Nagel, J. R. (2011).
6 [7] B.-J. Wang, (1995). [4] Nagel, J. R. (2011).
7 [7] B.-J. Wang, (1995). [4] Nagel, J. R. (2011).
8 [Watt] [Ampere] [7] B.-J. Wang, (1995). [4] Nagel, J. R. (2011).
![6.13-3 [Watt] [1],[4],[7]* [Ampere] * Quasi-static theory [7] B.](/docs-images/83/87267546/images/9-6.jpg "-J. Wang, (1995). [1]Bedard C., (2004). [4] Nagel, J. R. (2011).")
9 [Watt] [1],[4],[7]* [Ampere] * Quasi-static theory [7] B.-J. Wang, (1995). [1]Bedard C., (2004). [4] Nagel, J. R. (2011).
10 [Watt] [1],[4],[7]* [Ampere] Temperature [ C] Voltage [V] Joule [J] Coulomb [C] [7] B.-J. Wang, (1995). [1]Bedard C., (2004). [4] Nagel, J. R. (2011).
11 [Watt] [1],[4],[7]* [Ampere] Temperature [ C] Voltage [V] Joule [J] Coulomb [C] [7] B.-J. Wang, (1995). [1]Bedard C., (2004). [4] Nagel, J. R. (2011).
12 Steady State k T + Q = 0 [ W m 3] σ V + ρ σ ε = 0 [ A m 3] [7] B.-J. Wang, (1995). [1]Bedard C., (2004). [4] Nagel, J. R. (2011). [5] Halassy, S. (2012).
13 Steady State k T + Q = 0 [ W m 3] σ V + ρ σ ε = 0 [ A m 3] Transient ρc p T t k T Q = 0 [ W m 3] C m S v V m t 1 R i 2 V m + S v I = 0 [ A m 3] [5] [7] B.-J. Wang, (1995). [1]Bedard C., (2004). [4] Nagel, J. R. (2011). [5] Halassy, S. (2012).
14 Steady State k T + Q = 0 [ W m 3] σ V + ρ σ ε = 0 [ A m 3] Transient ρc p T t k T Q = 0 [ W m 3] C m S v V m t 1 R i 2 V m + S v I = 0 [ A m 3] [5] [7] B.-J. Wang, (1995). [1]Bedard C., (2004). [4] Nagel, J. R. (2011). [5] Halassy, S. (2012).
15 [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
16 [8] [8] [8] [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
17 [8] Material Properties Units Conductivity Specific Heat S um 1 F um 2 [8] Density kg um 3 [8] [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
18 Isotropic 3D cylindrical model ; Number of nodes: ; Number of elements: ; Element Types: DC3D6,DCC3D8. [8] [8] [8] [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
19 Boundary Conditions [3],[8] [8] V x x 0, t = 0 V x L, t = 0 V x y 0, t = 0 V x y L, t = 0 [8] Load [8] V x m, t = DISP [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
20 [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
21 [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
22 V m > V Th [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
23 V m > V Th [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
24 Na + Na + Na + K + K + Na + V m = V rest V m > V Th K + K + K + Na + Na + K + [3] Elia S, Lamberti P, Tucci, (2009). [8] Meffin, H., (2012).
25 DISP USDFLD Introduction Method (CAE/code) Validation Conclusion Transferring of ions cross the membrane g Na, g K, g l [2] Subcellular Ionic Currents Na, K, l [2] K + K+ Na + Cellular The nonlinear Cable Equation [5] Na + Na + K + Trans-membrane voltage [6] Tissue [2] Hodgkin, A. L., & Huxley, A. F. (1952). [5] Halassy, S. (2012). [6] Plonsey, R., & Malmivuo, J. (1995).
26 DISP USDFLD Introduction Method (CAE/code) Validation Conclusion Transferring of ions cross the membrane g Na, g K, g l [2] Subcellular Ionic Currents Na, K, l [2] K + K+ Na + Cellular The nonlinear Cable Equation [5] Na + Na + K + Trans-membrane voltage [6] Tissue [2] Hodgkin, A. L., & Huxley, A. F. (1952). [5] Halassy, S. (2012). [6] Plonsey, R., & Malmivuo, J. (1995).
![DISP USDFLD Introduction Method (CAE/code) Validation Conclusion Transferring of ions cross the membrane g Na, g K, g l [2] Subcellular Ionic Currents Na, K, l [2] K + K+ Na + Cellular](/docs-images/83/87267546/images/27-4.jpg "The nonlinear Cable Equation [5] Na + Na + K + Trans-membrane voltage [6] Tissue [2] Hodgkin, A. L., & Huxley, A. F. (1952). [5] Halassy, S. (2012). [6] Plonsey, R., & Malmivuo, J.")
27 DISP USDFLD Introduction Method (CAE/code) Validation Conclusion Transferring of ions cross the membrane g Na, g K, g l [2] Subcellular Ionic Currents Na, K, l [2] K + K+ Na + Cellular The nonlinear Cable Equation [5] Na + Na + K + Trans-membrane voltage [6] Tissue [2] Hodgkin, A. L., & Huxley, A. F. (1952). [5] Halassy, S. (2012). [6] Plonsey, R., & Malmivuo, J. (1995).
28 Data [8],[9] n = 0,1,2. n = 1. Analytical Solution with voltage boundary condition [8],[9] [9] Tahayori, B., (2012). [8] Meffin, H., (2012).
29 Data [8],[9] n = 1. µa J 1 = 5000 m σ = 10µm Analytical Solution with voltage boundary condition [8],[9] g z = 1 2π e z2 2σ 2 V input z, θ, t = V n g z cos nθ cos(ωt) [9] Tahayori, B., (2012). [8] Meffin, H., (2012).
30 Data [8],[9] n = 1. µa J 1 = 5000 m σ = 10µm Analytical Solution with voltage boundary condition [8],[9] g z = 1 2π e z2 2σ 2 V input z, θ, t = V n g z cos nθ cos(ωt) V M (z, θ, t) V input z, θ, t [8],[9] [9] Tahayori, B., (2012). [8] Meffin, H., (2012).
![[9] Tahayori, B., (2012).](/docs-images/83/87267546/images/31-4.jpg "[8] Meffin, H., (2012).")
31 [9] Tahayori, B., (2012). [8] Meffin, H., (2012).
32 Na + Na + Na + V m = V rest K + K + K + [6] Plonsey, R., & Malmivuo, J. (1995).
33 Voltage/TEMP [mv] Introduction Method (CAE/code) Validation Conclusion Na + Na + Na + V m = V rest K + K + K + K + K + Na E-02 V m > V Th 2.00E-02 DVM (mv) [Clamp 5 mv] DVM (mv) [Clamp 10 mv] DVM (mv) [Clamp 40 mv] [2] Hodgkin, A. L., & Huxley, A. F. (1952). [3] Plonsey, R., & Malmivuo, J. (1995). 0.00E+00 Na E E E-02 Na + K + Time [sec]
![Voltage/TEMP [mv] Introduction Method (CAE/code) Validation Conclusion Na + Na + Na + V m = V rest K + K + K + K + K + Na + 4.00E-02 V m > V Th 2.](/docs-images/83/87267546/images/34-3.jpg "00E-02 DVM (mv) [Clamp 5 mv] DVM (mv) [Clamp 10 mv] DVM (mv) [Clamp 40 mv] [2] Hodgkin, A. L., & Huxley, A. F. (1952). [3] Plonsey, R., & Malmivuo, J. (1995). 0.00E+00 Na + Na + 0.")
34 Voltage/TEMP [mv] Introduction Method (CAE/code) Validation Conclusion Na + Na + Na + V m = V rest K + K + K + K + K + Na E-02 V m > V Th 2.00E-02 DVM (mv) [Clamp 5 mv] DVM (mv) [Clamp 10 mv] DVM (mv) [Clamp 40 mv] [2] Hodgkin, A. L., & Huxley, A. F. (1952). [3] Plonsey, R., & Malmivuo, J. (1995). 0.00E+00 Na + Na E E E-02 K + Time [sec]
35 Thermo-electrical equivalents Cable Equation Heat Equation
36 Thermo-electrical equivalents Cable Equation Heat Equation Nerve cell in FEA The non-linear Hodgkin-Huxley model with gating activation
37 Thermo-electrical equivalents Cable Equation Heat Equation Nerve cell in FEA The non-linear Hodgkin-Huxley model with gating activation Validation with analytical solutions In space and time
38 Applications Cardiac cells; General diffusion processes; Piezoelectric materials; Diffusive solitary wave or soliton in excitable media [10]. [10] Vargas E. V., (2011).
39 Acknowledgements McHugh Group Dr. Maeve Duffy Dr. Caoimhe Sweeney Anna Bobel Reyhaneh Shirazi Donnacha McGrath Enda Boland Mary O Shea Brían O Reilly Rosa Shine
40 References 1. Bédard C, Kröger H, Destexhe A. Modeling extracellular field potentials and the frequency-filtering properties of extracellular space. Biophys J. 2004;86(3): doi: /s (04) Hodgkin AL, Huxley AF. A Quantitative Description Of Membrane Current And Its Application To Conduction And Excitation In Nerve. J Physiol. 1952;117: Elia S, Lamberti P, Tucci V. A Finite Element Model for The Axon of Nervous Cells. 2009: Nagel JR. Solving the Generalized Poisson Equation Using the Finite-Difference Method ( FDM ) The Five-Point Star S. Halassy, Modelling of Nerve Impulses, McMaster University Hamilton, Ontario, Canada, R. Plonsey and J. Malmivuo, Bioelectromagnetism - Principles and Applications of Bioelectric and Biomagnetic Fields. New York, 1995, p Wang, B.-J. (1995). Electrico-thermal modelling in Abaqus. Abaqus User Conference. 8. Meffin, H., Tahayori, B., Grayden, D. B., & Burkitt, A. N. (2012). Modeling extracellular electrical stimulation: I. Derivation and interpretation of neurite equations. Journal of Neural Engineering, 9(6), doi: / /9/6/ B. Tahayori, H. Meffin, S. Dokos, A. N. Burkitt, and D. B. Grayden, Modeling extracellular electrical stimulation: II. Computational validation and numerical results., J. Neural Eng., vol. 9, no. 6, p , Dec E. V. Vargas, A. Ludu, R. Hustert, P. Gumrich, A. D. Jackson, and T. Heimburg, Periodic solutions and refractory periods in the soliton theory for nerves and the locust femoral nerve., Biophys. Chem., vol. 153, no. 2 3, pp , Jan
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