How the Attenuation of Light Depends on Wavelength

Air and Water,
by Mark Denny.

In Chapter 14 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the absorption of light by water. Our Figure 14.14 shows that the absorption coefficient of water increases with the wavelength of light over the range from 600 to 750 nanometers, which is the red end of the visible spectrum.

To examine this behavior in more detail, let’s turn to Mark Denny’s book Air and Water: The Biology and Physics of Life’s Media. Denny has an entire section on the consequences of the attenuation of light. Below I present a modified version of his Figure 11.13B, plotting the attenuation coefficient as a function of wavelength. The most important point is that the attenuation of air is much less than that of water. The difference doesn’t look too striking in this figure, because the attenuation is plotted on a logarithmic scale, but the attenuation of water is at least a hundred times greater than the attenuation of air, and for large wavelengths (red light) the difference is far greater. On the right I added a scale for the penetration depth, which is just the reciprocal of the attenuation coefficient. For air, the penetration depth is at least ten kilometers, and often much more. This is good, because we definitely want sunlight to pass through the atmosphere and reach the earth’s surface. 

For water, the attenuation coefficient has a minimum around 470 nm, which is in the blue part of the visible spectrum. It then rises as the wavelength increases into the green, yellow, and red parts of the spectrum. Again, don’t let the logarithmic plot fool you. Between blue and red the attenuation coefficient increases by a factor of a hundred. Red light can only penetrate a few meters into water, but blue light reaches depths of hundreds of meters. Except very near the surface, aquatic animals live in a blue world. No sunlight reaches the bottom of the ocean, ten kilometers down.

I’ll let Denny describe more ramifications of the strong dependence of attenuation on color.

The attenuation coefficient of water varies with wavelength… Attenuation is high in the UV [ultraviolet] and IR [infrared], and is minimal for light at visible wavelengths. Given that life initially evolved in an aqueous medium, it may not be a coincidence that “visible” light corresponds to those wavelengths for which water is most transparent. The same argument can be applied to the pigments used by plants to capture light for photosynthesis. All of the major photosynthetic pigments (chlorophylls, carotenoids, and phycobilins) absorb light in the range of 400 to 700 nm, the range at which water is least attenuating…

Even within the visible range, the attenuation coefficient of water varies substantially (fig. 11.13B); red light is attenuated much more strongly than blue light. Again this effect is well known to SCUBA divers, who note that the apparent color of objects changes rapidly with depth. For instance, a camera case that is bright red at the surface appears gray at a depth of only a few meters because all of the available red light has been absorbed by water above… The rapid absorption of red light has had evolutionary consequences for plants. Because chlorophyll a (the most common photosynthetic pigment) absorbs strongly at a wavelength of 680 nm (red light), it is a relatively ineffective means for gathering light at depth. However, plants which live deep beneath the water’s surface have accessory pigments (carotenoids and phycobilins) that absorb at shorter wavelengths.

So Simple a Beginning

So Simple a Beginning,
by Raghuveer Parthasarathy.

My friend Raghuveer (Raghu) Parthasarathy (author of the blog The Eighteenth Elephant) recently published a biological physics book titled So Simple a Beginning: How Four Physical Principles Shape Our Living World. Here is an excerpt from his introduction.

I’ve already hinted at the view of nature… this book expands upon, which I identify as biophysical. The term implies a unification of biology and physics. It encapsulates the notion that the substances, shapes, and actions that constitute life are governed and constrained by the universal laws of physics, and that illuminating the connections between physical rules and biological manifestations reveals a framework upon which the dazzling variety of life is built. The notion of universality is central to the utility of physics, and to its appeal… Biophysics extends to the living world the quest for unity that lies at the heart of physics.

So, what are these four principles that Raghu says shape our living world?

• Self-Assembly: “the idea that the instructions for building with biological components—whether molecules, cells, or tissues—are encoded in the physical characteristics of the components themselves.”
• Regulatory Circuits: “The wet, squishy building blocks of life assemble into machines that can sense their environment, perform calculations, and make logical decisions.”
• Predictable Randomness: “The physical processes underlying the machinery of life are fundamentally random but, paradoxically, their average outcomes are reliably predictable.”
• Scaling: “Physical forces depend on the size and shape in ways that determine the forms accessible to living, growing, and evolving organisms.”

So Simple a Beginning is a very different book than Intermediate Physics for Medicine and Biology. SSaB is an introductory book for the general public; IPMB is an intermediate textbook for upper-level undergraduates in the sciences. SSaB examines life from the molecular scale to organs and organisms; IPMB focuses more on tissue-scale physiology and up, with only passing mention of molecular biology and biochemistry. SSaB has no math; IPMB has equations on nearly every page. SSaB has no end-of-chapter homework problems; one of IPMB’s strengths is its large collection of exercises for the reader. SSaB is elegantly and beautifully written; IPMB’s prose is workmanlike, nothing too graceful but adequate for the job. Finally, SSaB contains dozens of Raghu’s charming drawings and paintings; IPMB’s figures tend to be competent but not artistic. I’m gonna send out a strongly worded letter to whoever’s in charge of distributing talent. No one should have the ability to write well and draw skillfully. Raghu does both. That’s cheating.

I’ll end with the final paragraph of Raghu’s introduction. He quotes Darwin’s famous last paragraph of On the Origin of Species. He probably wanted to title his book This View of Life but Stephen Jay Gould already claimed that phrase for his series of essays about evolution. Instead, Raghu took So Simple a Beginning. Raghu’s writing reminds me of Gould, one of my favorite authors. He writes like Gould would have written had Gould been a physicist.

As interesting as these topics and examples may be, their cumulative effect is greater than the sum of their parts. Biophysics transforms the way we look at the world. At the end of On the Origin of Species, Darwin writes:

There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.

I hope to convince you that Nature has a grandeur even deeper than what Darwin discerned. Rather than a contrast between the fixed, clockwork laws of physics and the generation of endless and beautiful forms, the two are inextricably linked. We can identify the crucial “simple beginning” not as the origin of life, nor the formation of our planet, but as the primeval emergence of the physical laws that characterize our universe. The influence of these laws on life didn’t end billions of years ago, but rather shaped and continue to shape all the wonderful forms around us and within us. To discern simplicity amid complexity and to draw connections between life’s diverse phenomena and universal physical concepts gives us a deeper appreciation of ourselves, our fellow living creatures, and the natural world that we inhabit. I hope you’ll agree.

I agree. Read So Simple a Beginning. You’ll love it.

 

Raghuveer Parthasarathy describes So Simple a Beginning.

https://www.youtube.com/watch?v=fxnqq9Dv18o

Louis Harold Gray: A Founding Father of Radiobiology

Louis Harold Gray:
A Founding Father of Radiobiology,
by Sinclair Wynchank.

Only great scientists have units named after them: the newton, the joule, the watt. An important unit in medical physics is the gray. Chapter 15 of Intermediate Physics for Medicine and Biology states

The absorbed dose is the expectation value of the energy imparted per unit mass:

D = dE/dm .            (15.68)

It is measured in joules per kilogram or gray (Gy).

Is the gray named after a scientist or does it have something to do with the color? And if a scientist, then just who is Dr. Gray? The answer can be found in Sinclair Wynchank’s scientific biography Louis Harold Gray: A Founding Father of Radiobiology (Springer, 2007). My summary of Gray’s life is taken from Wynchank’s excellent book.

Gray—known to his friends as “Hal”—was an English radiobiologist born in London in 1905. His parents were poor, and he attended high school at Christ’s Hospital, a British public boarding school established to help boys who could not afford other institutions. The school was noted for its excellent teaching of science. Gray thrived and performed well enough in the sciences that in 1924 he was awarded a scholarship to Trinity College, part of the University of Cambridge.

Cambridge was famous for being the home of the Cavendish Laboratory, headed by Ernest Rutherford. When Gray graduated with a bachelors degree in physics he joined the Cavendish as a graduate student. His thesis advisor was James Chadwick, who discovered the neutron and was Rutherford’s right-hand-man. As a graduate student, Gray derived the Bragg-Gray relationship (see Equation 16.35 in IPMB). Wynchank writes

Hal’s first scientific publication was in 1929 and it provided a method of calculating the dose of X-rays that were used to irradiate someone (the cavity ionisation principle). This was a most important piece of work, for it allows someone to have an X-ray picture taken and then for it to be known what X-ray dosage had been given. Excessive use of X-rays is very dangerous and in the early days of X-ray applications, some doctors and patients died because they had received excessive doses of this radiation… every reader of these words, who has had a chest, or any other X-ray, has benefited from this work of Hal. It is now known as the Bragg-Gray principle, since both Hal and Professor W. H. Bragg, a friend of Rutherford, a Nobelist, former exhibitioner of Trinity College and professor of physics at Leeds, had both independently described the principle. But Bragg had not realised its importance and its long range implications.

After obtaining his PhD in 1931, Gray remained at Cambridge but changed his research direction to study the interaction of radiation with biological materials. After Chadwick discovered the neutron in 1932, Gray became interested how neutrons interacted with tissue. In that same year, Gray married Frieda (Freye) Marjorie Picot, an English Literature major at Girton College, Cambridge.

Wynchank continues:

Hal’s work at Cambridge ended in 1933 when he took up a post of hospital physicist at the Mount Vernon Hospital in Northwood, on the northern edge of London... Hal’s principal reason for the move was to be able to do full time research in his newly chosen field, the study of ionising radiation to aid cancer treatment... [In February 1938, Hal built] the world’s first accelerator neutron source for biological research... Hal’s insight with regard to this crucial function of energy deposition in tissue irradiation led finally to the unit of absorbed dose of radiation being re-defined in terms of energy and being adopted internationally in 1953. Later the unit was posthumously named after him, being officially termed the “Gray”... In 2 years of slog and improvising most creatively, [Hal and his collaborator] built the neutron generator and then studied the relative effectiveness of various radiations: neutrons, alphas, X-rays and gammas, when they cause cellular damage... Hal found that his neutrons when irradiating mouse tumours were 17 times more effective than gammas.

Gray and Freye had two sons, born in 1939 and 1943. Gray was a firm pacifist. During World War II his work was considered so important that he was exempted from military duty.

At the start of 1946, Hal was appointed senior physicist in the Radiotherapy Research Unit (RRU) of the Medical Research Council (MRC), located at the large and very prestigious postgraduate Hammersmith Hospital in West London... Hal was the first to explain the oxygen enhancement effect, although others had previously suggested that some parts of a tumour might lack oxygen and so be able to resist destruction by ionising radiation... Radioactive atoms (radioisotopes) were also investigated at the RRU. Their valuable clinical applications resulted from collaborative studies at the Hammersmith Hospital and elsewhere. This was the beginning of a new medical speciality, nuclear medicine.

In 1953, after a dispute with his supervisor about the relative priority of clinical versus basic research, Gray abruptly left the RRU and accepted a new position in a London laboratory funded by the charity known as the British Empire Cancer Campaign (BECC).

Hal’s life work after Cambridge can be summed up as relating radiobiology to radiotherapy, so that more effective treatment of cancer would result. Almost single-handedly he was the initiator of the relevance of oxygen, stressing its potential importance to the treatment of patients. This oxygen effect (that is its presence) increased radiation’s destructive power. He made many radiotherapists appreciate the importance, where it was appropriate, of experimental results to the better understanding of how to manage their patients… Free radicals’ effects on the DNA molecule, a crucial component of life, were also studied by Hal and his colleagues… Ways of improving the action of radiation were studied and the findings allowed more effective treatment. One successful such approach was to find pharmaceuticals which, if located in the region to be irradiated, cause the radiation to kill more cancer cells. These pharmaceutical products are radiosensitisers and Hal was one of the first to investigate them.

Gray received many prestigious awards, including election as a Fellow of the Royal Society of London. He died in July 1965, at the age of 59, from a stroke. Had Gray not died so young, he might have eventually been awarded a Nobel Prize.

I’ll end with a tribute to Gray that readers of IPMB will appreciate. Gray was

“the first—and quite possibly the last—scientist to have had a thorough appreciation in all four sectors of radiation research: physics, chemistry, biology and medicine.”

 ____________________________________________

A personal note: Academically speaking I am descended from James Chadwick, so Louis Harold Gray is my academic great-great-great uncle. It’s good to know you better, Uncle Hal!

Intergovernmental Panel on Climate Change Sixth Assessment Report

IPCC Sixth Assessment Report

This week, the Intergovernmental Panel on Climate Change (IPCC) released the full version of its Sixth Assessment Report. A news article posted by the Union of Concerned Scientists begins with the headline

New IPCC Report Finds Sharp Cuts in Fossil Fuels and Emissions Urgently Needed, Policymakers’ Failures Putting Climate Goals at Risk

What, you may ask, does the IPCC report have to do with physics applied to medicine and biology? Everything. The medical and biological consequences of ignoring the physics of climate change will be catastrophic. The advances in medical physics and biological physics that Russ Hobbie and I outline in Intermediate Physics for Medicine and Biology are insignificant compared to the disastrous health risks that could result from unchecked global warming.

Fighting the climate crisis is not new. Below are excerpts from a 1999 position statement published in the American Journal of Physics (my favorite journal).

Climate Change and Greenhouse Gases

The following position statement was released on 28 January 1999 by the American Geophysical Union. The Executive Board of the American Association of Physics Teachers endorsed this statement at its meeting on 20 March 1999. 

Atmospheric concentrations of carbon dioxide and other greenhouse gases have substantially increased as a consequence of fossil fuel combustion and other human activities. These elevated concentrations of greenhouse gases are predicted to persist in the atmosphere for times ranging to thousands of years. Increasing concentrations of carbon dioxide and other greenhouse gases affect the Earth-atmosphere energy balance, enhancing the natural greenhouse effect and thereby exerting a warming influence at the Earth’s surface…

The world may already be committed to some degree of human-caused climate change, and further buildup of greenhouse gas concentrations may be expected to cause further change. Some of these changes may be beneficial and others damaging for different parts of the world. However, the rapidity and uneven geographic distribution of these changes could be very disruptive. AGU recommends the development and evaluation of strategies such as emissions reduction, carbon sequestration, and adaptation to the impacts of climate change. AGU believes that the present level of scientific uncertainty does not justify inaction in the mitigation of human-induced climate change and/or the adaptation to it.

Alas, this statement was followed by two decades of inaction. The IPCC Sixth Assessment Report describes the danger we now face. We know the science; now we must act. I urge readers of IPMB to study the IPCC Report and to consider the issue of climate change when deciding who to vote for in future elections. 

Act Now on Climate Change

https://www.youtube.com/watch?v=hakqRofpMFs&t=44s

Diffusion with a Buffer

The Mathematics of Diffusion,
by John Crank.

Homework Problem 27 in Chapter 4 of Intermediate Physics for Medicine and Biology examines diffusion in the presence of a buffer. The problem shows that the buffer slows diffusion and introduces the idea of an effective diffusion constant. I like this problem but I admit it’s rather long-winded. Recently, when thumbing through John Crank’s book The Mathematics of Diffusion (doesn’t everyone thumb through The Mathematics of Diffusion on occasion?), I found an easier way to present the same basic idea. Below is a simplified version of Problem 27.

Section 4.8

Problem 27½. Calcium ions with concentration C diffuse inside cells. Assume that this free calcium is in instantaneous local equilibrium with calcium of concentration S that is bound to an immobile buffer, such that

S = RC ,          (1)

where R is a dimensionless constant. Calcium released from the buffer acts as a source term in the diffusion equation

   ∂C/∂t = D ∂²C/∂x² − ∂S/∂t .        (2)

(a) Explain in words why ∂S/∂t is the correct source term. Be sure to address why there is a minus sign.

(b) Substitute Eq. (1) into Eq. (2), derive an equation of the form

∂C/∂t = D_eff ∂²C/∂x² ,         (3)

and obtain an expression for the effective diffusion constant D_eff.

(c) If R is much greater than one, describe the physical affect the buffer has on diffusion.

(d) Show that this problem corresponds to the case of Problem 27 when [B] is much greater than [CaB]. Explain physically what this means.

To do part (d), you will need to look at the problem in IPMB. 

The bottom line: an immobile buffer hinders diffusion. The stronger the buffer (the larger the value of R), the slower the calcium diffuses. The beauty of the homework problem is that it illustrates this property with only a little mathematics.

Enjoy!