Page 59 - Computational Modeling in Biomedical Engineering and Medical Physics

46 Computational Modeling in Biomedical Engineering and Medical Physics

conversion in electronics. On its venue, biophysics aims to solve problems of biology
using the laws, theory, and technology of the physical sciences.
But these theories and technologies do not purpose to explain the shape of a sys-
tem as its outcome, manifestation, and struggle to adapt to constraints either embodied
as optimization criteria in engineered systems, or as result of interactions with the
environment, in natural animated and inanimate systems—shapes of systems with pur-
pose and under certain constraints.
Heat transfer principles (Chapter 1: Physical, Mathematical, and Numerical
Modeling) explain the geometric structure of systems, their spatial arrangement, and
the amounts of their parts. If a system is purposed to convert, as well as possible, heat
crossing it into work, subjected to constraints (the available heat input, the size, and
costs), then the factors responsible to reducing the pending irreversibility are optimiza-
tion degrees of freedom. The heat flows through the system, from the input (hot
source) to the output (cold source, the ambient) and to the ambient (leaked heat), are
driven by temperature gradients across thermal conductance paths (power plant parts),
which are related to the entropy that is generated (Bejan, 1996). The first law analysis
shows off that when the power plant is subject to size constraint, the irreversibility
(entropy generation) of its functioning may be minimized by adjusting the sizes, or
optimally allocating and morphing these conductances, the spatial conveyors of heat
fluxes: in essence, provide good conductivity paths (“paving” materials) to “ease”,
facilitate the currents flows.
Spatial allotment comes with shaping the system and its parts. This, geographically
means allocation of hardware is such a way that imperfection (resistance to flow) is dis-
tributed around, and its constituent parts all “work” under same stress. This holds for
engineered systems, which, subjected to optimization, progressively resemble to (shape
like), and function like natural systems. For instance, the animals’ structures are pre-
sented through accurate power laws that relate their body sizes and other flow and
performance parameters (Murray, 1926a,b; Schmidt-Nielsen, 1972); Peters, 1983;
4
Bejan, 2000a,b). The unifying feature is that the metabolism rate (the exergy con-
sumption rate) is fairly, parsimoniuously shared between organs (system parts) in pro-
portions that are reasonably insensible to animal size.
From the perspective of the constructal theory, which means to treat the living sys-
tems as energy systems (power plants) with flows, constraints, shaped with purpose and
capable of evolution, the forecast of the metabolic rate for the body and its parts
equates the prediction of the body structure and shape, its parts, their sizes, and irre-
versibly in relation with each other.

4
The exergy (maximum available energy) of a closed system equals the maximum possible useful work
that brings the system into equilibrium with a heat reservoir, reaching maximum entropy.