by

Wilson C. Chin and Jamie A. Chin

Stratamagnetic Software, LLC

Houston and Beijing

2020 was our defining year – Our year of living dangerously. Very dangerously. No sooner had we packed our belongings, anticipating a return to the United States after visiting Grandma, 85, who underwent knee surgery, and Grandpa, 89, who had just finished his fourth hospital stay for heart abnormalities and stroke, would the Covid-19 pandemic unexpectedly strike. Flights were cancelled. Borders were shut. Lives were turned upside-down. Unpredictability became the only predictable norm. And just when all returned to normal in 2021, the Delta-variant, and then Omicron, would rear their pointed and unrelenting heads. We would spend more than three unexpected but fruitful years in Beijing.

Photos of patients connected to breathing machines proliferated. Others less fortunate gasped their final breaths. For the lucky few, intubation allowed air to pass freely, ventilating lungs and supporting artificial respiration. We never knew that fluid mechanics could be so relevant. And we would find ourselves in and out of hospitals. The first author, after long, long flights, would find himself immobile from "DVT" or "Deep Vein Thrombosis." Not just in one leg, but blood clots in both. As if that were not enough, add a poorly timed case of gout that left physicians in three well-known hospitals confused and bewildered.

But through this cloud would appear a silver lining. The authors, a petroleum scientist and a biologist, were witness to close-up diagnoses by dedicated and cooperative doctors and nurses administering shots, shots and more shots. We were curious over "shots," which are normally rather mundane. Many are daunting and simply hurt. But why were syringes of contrasting sizes and shapes used? At different angles? We observed how some medicines were "thick" while others were "thin." What factors determined optimal injection points? Where did injected fluids really travel? How did blood – not the "simple red fluid" many think – actually flow through complicated systems of arteries and veins? Was there a means to predict porous tissue properties and flows using geoscience methods that probe rock properties deep in the earth? Can we perform "whole body simulations" that support diagnostic efforts?

In conduit, as opposed to porous media flows, we learned that blood was a heterogeneous rather than the homogeneous liquid most take for granted. That it was mostly a non-Newtonian fluid rather than a simple ideal liquid. Was the "viscosity" measured in lab tests really meaningful? Is it possible to describe flows accurately in bifurcated systems? What of flows in blood vessels with clogged and deformed cross-sections as opposed to perfect circles? Or those involving square stents? And what of flows marked by significant curvature, for instance, those near the heart or through varicose veins? These problems are addressed mathematically in Chapters 1-6. Our quest to answer these questions began in humble surroundings. And our answers, developed over much conjecture and debate, would hopefully produce models of value to clinicians and medical researchers.

We began by exploiting similarities between complicated systems of oil wells and arterial flows in the body. Studying pressure drop and flow rate relations driven by positive displacement pumps, like the mud pumps used in drilling and those powering the human heart. We explored Darcy flow analogies behind fluid motions in heterogeneous and anisotropic oil reservoirs, and connected these to porous flow events that proliferate within body tissue. And when needed, we exploited electrical analogies to model blood flow and organ interactions. But how would these analogies and their extensions benefit medical research and ultimately clinical practice? This question led to interesting answers.

From what we understood about anatomic pathology, detailed diagnostic information is available from samples based on characteristics like visual appearance, location, texture, smell, patient history, and so on. Often, conventional imaging methods like ultrasound, MRI, Catscan and X-ray supplement basic examinations. However, these are also qualitative and based on subjective interpretation depending on physician expertise and experience, and patient sex, age, health and ethnicity; moreover, the methods are expensive, inconvenient and impractical for routine use. We asked, "Can we provide quantitative local information on tissue compressibility, permeability, anisotropy, porosity and background pressure in real-time conveniently and inexpensively?" This led to the development of minimally invasive sensors whose transient measurements could be unambiguously interpreted using validated analysis methods – these new models are based on rigorous Darcy flow math formulations and their analytical solutions. This new approach, applied to recent animal and patient data, is addressed in Chapter 7.

What new problems and researches can we address with newly available tissue properties? Research efforts are presently segregated according to simple "conduit versus porous media" classifications. Their rationales and justifications are easily summarized: flows along arteries and veins are mainly longitudinal. Because vessel walls are largely impermeable to flow, the recipient tissues receiving oxygen and nutrients "see" only isolated entry and exit points. This approach delineates the analysis boundary separating what initially appears to be two different disciplines. But this need not be. It is important to understand how blood flows actually interact with tissues and organs. Damaged vessels, for example, do interact with tissue and are no longer invisible to it. This subject is relevant in light of recent work showing how certain proteins can cause blood vessel damage in Covid-19 patients and lead to strokes and heart attacks. Covid, now primarily viewed as a respiratory disease, may be linked to other afflictions by way of transverse blood flow communication – a circuitous mechanism that is numerically modeled in Chapters 8 and 9 focusing on blood vessel and tissue interactions.

In the prior three years, our biofluids methods were motivated and driven by similarities between porous media flows in the human body and those in the geosciences and petroleum exploration. This overall approach has proven beneficial. Over the past centuries, science has advanced rapidly through developments of physical analogies. Experience teaches us that where analogies exist, understanding will follow, and that analysis methods can be intelligently mirrored and generalized to develop new perspectives. This approach to learning, we have followed and plan to communicate in this book.

But even more challenging was the daunting task requiring us to present our biofluids ideas to a broad audience, from undergraduates, to clinicians, to medical researchers, and to engineers and scientists, interested in understanding an expanding and evolving discipline. That is, to deliver our ideas and results assuming only a basic academic preparation, between the covers of a four-hundred page volume, and within the constraints of a year’s worth of study time, at most. To achieve this objective, the authors have adopted a rapidly paced tutorial style that is rigorous yet understandable, focused yet encompassing, and academically oriented yet interesting.

Wilson Chin, Houston