HPC Tier Module
Pennes Bioheat Equation (Ablation / Hyperthermia)
March transient tissue heating with the Pennes bioheat equation and a cited thermal dose - exact, in-browser.
This tool runs inside GDBS HPC. What it computes and the authorities it applies are below.
The problem
Thermal-therapy modeling and engineering verification need a bioheat solver that reports temperature and thermal dose against exact benchmarks, flags numerical instability, and surfaces every tissue constant rather than hiding them.
The local-first solution
This plugin integrates the cited Pennes bioheat PDE by explicit or implicit finite differences in exact f64, computes the Sapareto-Dewey CEM43 dose, and checks the solution against two closed-form benchmarks - all deterministic and in your browser with no upload.
What it does
Centred 2nd-order Laplacian with FTCS explicit or backward-Euler implicit time marching
Pennes perfusion heat-sink term in both the explicit update and implicit diagonal
Von Neumann stability number computed and hard-flagged when violated
Sapareto-Dewey CEM43 cumulative-equivalent-minutes thermal dose by trapezoidal integration
Steady-state perfusion benchmark with the exact penetration depth sqrt(k/(w_b c_b))
Pure-diffusion sine-mode decay benchmark when perfusion and sources are off
Honest scope
Exact: the Laplacian stencil, the explicit and implicit updates, the Thomas solve, the stability number, the trapezoidal CEM43 integral, and the two closed-form benchmarks. The Pennes perfusion term is an approximate model treating blood as a uniform, instantly-equilibrating sink at fixed arterial temperature, with temperature-independent properties; it does not model discrete-vessel cooling, nonlinear perfusion, the Arrhenius damage integral, phase change, or 3D anatomy, and CEM43 is an isoeffect dose reported, not a clinical determination. Research, education, and engineering verification only - not a medical device and not for clinical or treatment-planning decisions.
Authorities cited
- Pennes, H. H. (1948). Analysis of tissue and arterial blood temperatures in the resting human forearm. Journal of Applied Physiology 1(2), 93-122. - The bioheat equation rho c dT/dt = k lap T + w_b c_b (T_a - T) + Q_met and the perfusion heat-sink term. DOI 10.1152/jappl.1948.1.2.93.
- Sapareto, S. A., & Dewey, W. C. (1984). Thermal dose determination in cancer therapy. International Journal of Radiation Oncology, Biology, Physics 10(6), 787-800. - The CEM43 = integral R^(43-T) dt cumulative-equivalent-minutes thermal-dose model (R=0.5 above, 0.25 below 43 C). DOI 10.1016/0360-3016(84)90379-1.
- Carslaw, H. S., & Jaeger, J. C. (1959). Conduction of Heat in Solids, 2nd ed. Oxford. - Separable sine-mode solutions and their exponential decay for the heat equation (the w_b=0 pure-diffusion benchmark).
- LeVeque, R. J. (2007). Finite Difference Methods for Ordinary and Partial Differential Equations. SIAM. - Centred 2nd-order Laplacian (sec 3.2), forward/backward Euler time stepping, Dirichlet BCs. DOI 10.1137/1.9780898717839.
- Strikwerda, J. C. (1989/2004). Finite Difference Schemes and Partial Differential Equations, 2nd ed. SIAM. - von Neumann stability of explicit reaction-diffusion schemes (the perfusion term tightens the FTCS limit). DOI 10.1137/1.9780898717938.
- Press, W. H., et al. (2007). Numerical Recipes, 3rd ed. CUP, sec 2.4. - The Thomas algorithm for tridiagonal systems (the exact backward-Euler line solve).
- Hasgall, P. A., et al. (2022). IT'IS Database for thermal and electromagnetic parameters of biological tissues, v4.1. IT'IS Foundation. DOI 10.13099/VIP21000-04-1. - Cited default tissue/blood properties (k, rho, c, w_b, c_b, Q_met).
- Duck, F. A. (1990). Physical Properties of Tissue: A Comprehensive Reference Book. Academic Press. - Thermal conductivity, perfusion, and metabolic-heat ranges used for the cited defaults.
- Weinbaum, S., & Jiji, L. M. (1985). A new simplified bioheat equation for the effect of blood flow on local average tissue temperature. ASME J. Biomech. Eng. 107(2), 131-139. - The countercurrent correction that Pennes omits (cited as a NOT-MODELED limitation). DOI 10.1115/1.3138533.
Get an email when tools like this one change
Leave your email and we will tell you when we add or update Healthcare & Biomedical tools like this one, at most once a month.
We email you once to confirm. After that, unsubscribe from any issue in one click. Your address goes to VaultSync only (privacy).
Run the bioheat solve
Compute the temperature field and thermal dose in your browser, with nothing uploaded to anyone's cloud. Save the run to Sandbox, attach it to a Worklog case, or share parameters through a Gate portal.