Where Pennes Falls Short and How Modellers Compensate

There have been many contributions to improve bioheat models over the years, focused on the shortfalls of Pennes and how to address them. Wulff introduced explicit blood flow convection, while Weinbaum-Jiji accounted for countercurrent heat exchange between arteries and veins, improving physiological realism especially in highly vascular tissues like muscle. Non-Fourier models addressed the fact that heat propagation isn’t instantaneous, which is critical for ultrafast heating like laser pulses.

Modern approaches combine, when appropriate, image-derived anatomy, tissue-level bioheat (often still Pennes-based), coupled simulations (e.g., EM, acoustic, fluid), and explicit vessel geometries. These hybrid approaches blend physics across scales: vessel-level details matter for local effects when explicitly modelled, but pressure propagation through tissue from pulsatile flow rarely affects surrounding tissue.

Figure 1 – Pennes Bioheat Domain (source: Alzubaidi et al, Thermography Quantification of Human Perfusion Thermal Signature, Preprints.org, 2018, CC BY 4.0)

More Complex Models Rarely Change the Answer

In theory, these models provide a more accurate picture of tissue reality. In practice, the payoff is heavily context-dependent. They introduce real challenges: parameter uncertainty across perfusion, vessel flow, and tissue properties; high computational cost; difficult validation; and regulatory opacity.

Even when working through these challenges is feasible, the output rarely moves the needle enough to matter. In many cases, device problems have uncertainties dominated by boundary conditions (contact, convection, geometry), device power variability, and patient variability, not those addressed by detailed models such as microvascular heat transfer or arterial effects.

Bioheat Modelling Across Device Categories

Thermal therapies (ablation and hyperthermia). In laser therapies, RF ablation, microwave ablation, and focused ultrasound applications, bioheat modelling can predict a temperature gradient field, lesion size, and tissue thermal dose. One case where Pennes needs augmentation is at higher temperatures (above 50-60°C), where perfusion collapses. A temperature-dependent or damage-dependent perfusion term accounts for this.

Implantable devices. Deep brain stimulators, stents, bone plates, and insulin pumps (the latter subject to heating from absorbed imaging radiation such as MRI) all require bioheat assessment of surrounding tissue temperature rise and compliance with safety limits such as IEC 60601. These are typically low delta-T, steady-state problems, which lend credibility to Pennes with conservative assumptions. Boundary conditions dominate uncertainty, and the higher accuracy from more complex models rarely changes design decisions.

Skin-contact devices and wearables. Monitors (ECG, CGM, BPM), smartwatches, and remote ecosystems for implantables such as pacemakers introduce layered tissue (skin, fat, muscle) and a strong environmental coupling at the boundary. Key challenges include transient heating, contact resistance, and thermoregulation (sweating, vasodilation). Counterintuitively, fat tissue often matters more than perfusion because it acts as thermal insulation and can isolate the effects of heat to more superficial tissues closer to the heat source.

Drug delivery and aerosols. Heated aerosol generation, airway modelling, and temperature-dependent deposition present more complex modelling requirements due to aerosol generation and propagation mechanics and shear-induced recombination and separation of aerosols. These affect aerosol size metrics, which then couple to mass transport dynamics. Phase change is also important, especially with hydrophilic aerosols. Bioheat enters where these phenomena affect tissue: a heated aerosol that impacts the throat, for example, brings thermal energy through deposition, creating a risk that must be assessed.

A Tiered Approach to Bioheat Modelling

Bioheat models are increasingly embedded in model-informed engineering decisions, providing concrete benefits across the product development cycle: early feasibility for bounding thermal risk, design iteration for optimizing geometry and power, verification to support test reduction, and submission evidence with risk-informed credibility assessments including targeted benchtop experimental validation.

As modelling becomes more central, the question is how to use it well. For bioheat in particular, a hierarchy-approach considers accuracy without going for the most complex models first:

• Baseline – Pennes with constant perfusion and conservative boundary conditions
• Enhanced – Pennes with temperature-dependent perfusion and damage models (Arrhenius or CEM43)
• Targeted Complexity – Explicit vessels and multiscale models (if inclusion is clinically relevant or justified)

All of these are decisions for the analyst to make, while weighing the trade-offs of effort against meaningful gains in accuracy for the decision at hand. ASME V&V 40 and the credibility assessments provided by it allow for these decisions to be justified for regulatory submissions.