Osmosis and the Kidneys

One textbook that covers much of the same material as the 4th edition of Intermediate Physics for Medicine and Biology—but at a somewhat lower level—is Physics of the Body, by John Cameron, James Skofronick and Roderick Grant. They have chapter titles such as “Physics of the Skeleton,” “Physics of the Ear and Hearing”, and “Physics of the Lungs and Breathing.” They apparently didn’t have the expertise among the three coauthors to write a chapter on the Physics of the Kidneys, so they recruited an outside author familiar with both physics and the renal system to write it for them. That author is none other than Russ Hobbie. In their preface they write

“Emeritus Professor Russell Hobbie of the University of Minnesota, the author of the more advanced text Intermediate Physics for Medicine and Biology, kindly contributed Chapter 6 [Osmosis and the Kidneys] on the physics of osmosis as it relates to fluid transport across membranes in the body. He also contributed to the revision of Chapter 9 [Electrical Signals from the Body]. His cooperation is greatly appreciated.”

Russ’s chapter covers some of the same topics as in Chapters 4 and 5 of IPMB, such as diffusion and osmotic pressure. However, his section 6.4 goes into more detail about the anatomy and physiology of the kidney that we do in IPMB. Here is an excerpt:

“The kidneys excrete much of the body’s metabolic waste products—except carbon dioxide and some water which leave through the lungs. They also regulate the concentration of most chemicals in the blood plasma. Each kidney contains over 1 million nephrons. Each nephron is a complete urine-forming unit. Figure 6.5 shows the kidneys and the ureters through which urine flows to the urinary bladder. Figure 6.6 shows a magnified view of a nephron.

Figure 6.7 shows the essential functioning parts of the nephron. Blood from the renal artery passes first by a membrane in the glomerulus, where a large amount of fluid—about 250 ml per minute (~1 cup)—passes through the basement membrane of the glomerulus. This process is called filtration. Careful measurements of dog kidneys using radioactively tagged solute molecules of different radii suggest that the filtration is by pores of 5 nm radius in the basement membrane. The filtration rate is controlled by valves which control the rate of blood flow through the glomerulus and the pressure drop across the glomerular basement membrane. Substances with a molecular weight of 5000 or less pass easily through the membrane with the water. Most proteins, which have a molecular weight of 69,000 or more, do not pass through the pores and remain in the blood. The filtrate then passes through the tubules, where 99% of it is reabsorbed (if it were not reabsorbed, we would void 360 liters of urine per day [!]). The other 1% passes into the collecting system as urine. Unwanted substances are not reabsorbed, so their concentration in the urine increases. Creatinine, a metabolic waste product, and sucrose are not reabsorbed at all. About half of the urea, a nitrogenous product of protein metabolism, is reabsorbed.”

One interesting appendix I found when thumbing through Physics of the Body is the “Standard Man”.

“In medical physics, where we are concerned with the anatomy and physiology of humans, it is convenient to define the physical characteristics of a ‘standard man.’ While the standard man is nonexistent, the following somewhat arbitrary values are useful for simulation and for computational purposes:

Age: 30 yr

Height: 1.72 m (5 ft 8 in)

Mass: 70 kg

Weight: 690 N (154 lb)

Surface area: 1.85 m²

Body core temperature: 37.0 C

Body skin temperature: 34.0 C

Heat capacity: 3.6 kJ/kg C (0.86 kcal/kg C)

Basal metabolism: 44 W/m² (38 kcal/m² hr, 70 kcal/hr, 1680 kcal/day)

Heart rate: 70 beats/min

Blood volume: 5.2 liters

Cardiac output: 5 liters/min

Blood pressure—systolic: 16 kPa (120 mm Hg)

Blood pressure—diastolic: 10.5 kPa (80 mm Hg)

Breathing rate: 15/min

O₂ consumption: 0.26 liter/min

CO₂ production: 0.21 liter/min

Total lung capacity: 6 liters

Tidal volume: 4.8 liters

Lung dead space: 0.15 liters” 

John Cameron, who passed away in 2005, was a giant in the field of medical physics. He was one of the founders of the well-known medical physics program at the University of Wisconsin. James Skofronick is emeritus professor in the department of physics at Florida State University. Roderick Grant is an emeritus professor in the department of physics and astronomy at Denison University.