Page 43 - Computational Modeling in Biomedical Engineering and Medical Physics

Physical, mathematical, and numerical modeling 29

For instance, fractals are applied in modeling the diabetic retinopathy, a very com-
mon complication of diabetes disease that produces changes in the morphology of blood
vessels in the diseased retina. The fractal properties of blood vessel patterns of the retina
involves manual segmentation of the blood vessel patterns and the analysis of the retinal
vasculature as a fractal (Cheng and Huang, 2003; Cheung et al., 2009; Uahabi and
Atounti, 2015), and singles out the fractal dimension and its lacunarity—fractals that
have the same fractal dimension but with different appearances—to probe of the disease
progression.
Fractal design tools may be utilized to mimic, to some degree of accuracy, naturally
made systems, for example, anatomic structures through fairly relevant presentations.
Even complex flow, tree-like structures such as the air passage of lungs (a flow system
for air), the capillaries (a flow system for blood), and the neuronal dendrites (a flow of
electrical signals) may be rendered using the fractal geometry (Bejan and Zane, 2012).
Although fractal geometry may render convincingly tree-like structures it neither relies
nor provides on the physical meaning of the system. Elaborated to represent a natural,
imperfect construction rather than the demiurgic perfect vision of the world, these
mathematical “monsters” are intensively and successfully used in computer rendering,
virtual reality nowadays. The apparent shape and structure of natural phenomena
(electrical discharges, river basins, vascular trees, etc.) may be quite convincingly ren-
dered but no clue on the underlying physics or the reasons of the shape is offered.
For instance, a current line of mathematical modeling in medicine assumes the tree
structures of the human body as “real” fractal objects, which allows the analysis of the
underlying physics fractal analysis (Uahabi and Atounti, 2015; Barnsley, 1988).
On the other hand, the Constructal law (Chapter 2: Shape and Structure
Morphing of Systems with Internal Flows) explains the design seen in nature, tree-
like, “monstrous,” structures including the anatomic entities (Bejan, 2000, 2012). This
law can be used to understand why design emerges and may predict how they will
evolve. After all, it is consistent with the Aristotele’s synthesis that “Nature makes all
things with a purpose” and “does nothing in vain” (D’Arcy, 1992). Constructal law
analyzes and explains that geometric complexity arises from the functions of the tree
structures in the human body—hemodynamic system, respiratory tract, renal system,
etc.
CAD-designed models are produced using mathematical algorithms implemented
in software tools that no have particular physical insights in the drawn object or its
functions. The shape, as close to reality as possible, is the objective and not the driving
forces (origins, constraints) that morph the system in the shape and form in which it
appears to the analyst. CAD made computational domains are used to modeling the
problems in Chapters 5 8(Morega et al., 2013a,b).
CAD, fractal, or hybrid CAD fractal constructions have to represent realistically
the natural systems that are subject to analysis: proper sizes, proportions, that is, realistic