Magnetic Resonance Imaging (MRI) or Nuclear Magnetic Resonance (NMR) ?

This will be a 4-5 part series covering physics, math and applications of the commonly used medical imaging technology Magnetic Resonance Imaging (MRI). The world 'nuclear' seem's to strike fear into many people. I hope that after reviewing this series the reader will be comfortable with 'nuclear' phenomena. The series will start with a discussion about light. Follow on Twitter: @MuzamilArshad18

Part 1: What is Light?

What is light? Humans have been asking this question for centuries now. The Greeks, Pythagoras, Euclid and others, described light as rays traveling in straight lines between objects, ultimately producing vision when they enter the eye. Hasan Ibn al-Haytham, considered by many as the "father of modern optics", made significant contributions to the geometric understanding of light. In the 17th century Christiaan Huygens published the first mathematical theory of light (1690) describing it as a "undulation" or oscillation of a substance that filled all of space, referred to as the 'ether' (debunked by the famous Michelson-Morley experiment in 1887). The wave theory of light was supported by data, namely the diffraction pattern observed by Thomas Young and gained further support when, in 1861-1862, the physicist James Clerk Maxwell published his famous Maxwell's Equations.

Maxwell's equations were a mathematical formulation of the many discoveries regarding electricity and magnetism (at that time considered to be separate entities). Maxwell was able to unify the numerous discoveries ( Gauss's Law, Faraday's Law, Ampere's Law) producing the 1st great unification in physics, namely that of electricity and magnetism into what we today call 'electromagnetism'. One of the most remarkable aspects of Maxwell's equations (one that blows my mind to this day) is that he was able to calculate the speed of light from two constants of the universe, namely the permeability of vacuum (measures the ability of a vacuum to support the formation of a magnetic field within itself) and the permittivity of vacuum (measures the ability of a vacuum to support the formation of an electric field within itself). Maxwell predicted that the speed of light would be 2.99792 x 10^8 m/s which is very close to the excepted speed of light (in meters/second) of 3 x 10^8 !!! Amazing.

So it would seem that the mystery of light is solved. Light is a electromagnetic wave. A traveling ripple in electromagnetic (EM) field that moves at a whopping speed of 186,272 miles/sec in a vacuum. In fact this explanation of light, as an EM field, explains the diffraction pattern of light (remember Huygens from above), refraction properties of light (the ability of light to bend in water or a prism) and why different colors of light bend more or less (a rainbow). Furthermore, EM theory of light also tells us exactly what is 'color'. What we perceive of as red, blue, yellow etc. is nothing more EM waves of different frequency or wavelength (and white light is just a collection of EM waves of different wavelengths) .

Figure 1 below demonstrates what an electromagnetic wave traveling along 1 dimension (1D) looks like. Of course EM waves can travel in 3D but its harder to visualize. Note in Figure 1 that the electric and magnetic fields are perpendicular to each other and the magnitude/amplitude (or strength of the field as represented by the length of the arrow) changes. The oscillation of the EM field is similar to the oscillations one sees in a water wave. At certain points in space the the height of the water wave is high (say 20 ft) and at other locations the height of the water wave is low (1 ft wave for example). Similarly the strength of the electric and magnetic fields vary in position. Waves can be described by a property known as the wavelength (in Figure 1 this is depicted by the greek letter lambda, λ) . This is the spatial distance between to corresponding points of a wave. Going back to water waves, the wavelength would be the distance, say in feet, between the 2 peaks of the water wave. If it takes say 10 feet to get from the peak of one wave to the next, we would say it has a wavelength of 10 feet. Similarly EM waves have a wavelength which describes the distance between two peaks of the electric or magnetic field. Not to complicate the picture, but sometimes people talk about the frequency (measured in Hertz, Hz) of a wave which simply measures how many oscillations occur per second. So 256 Hz means 256 oscillation in 1 second. For EM waves one can talk about either the wavelength or frequency because if you know one then you know the other. Using Figure 1 for example because we know the speed of light (which is a universal constant in a vacuum denoted as , c,) and we know the wavelength,the frequency is simply the speed of light divided by the wavelength. Note that frequency and wavelength have an 'inverse' relationship, that is as one goes up the other goes down. I will be using both wavelength (λ) and frequency (f) when discussing light so keep the inverse relationship in mind ( f = c/λ).

Figure 1. Light as Electromagnetic Wave

So what is red? Red is just an EM wave with a wavelength of around 700 nanometers (nm) or a frequency of 4.3 x 10^14 Hz. Blue light is just an EM wave with a wavelength around 490 nm or a frequency around 6.1 x 10^14 Hz. In fact what we Homo Sapiens call the 'visible light spectrum' is nothing more than EM waves in the range of 400-700 nm (with the color blue on the shorter side and red on the longer side). Bee's on the other hand, can 'see' EM waves in the ultraviolet range (10-400 nm). Your microwave uses EM waves with a wavelength of around 30 cm (or 3 x 10^8 nm so a much much longer wavelength that red). In fact microwaves fall within the range of what we call 'radiowaves' which have a wavelength range from 1 mm to 10,000 km! And of course radiowaves are used all around us. They are used by your cell phones, antennas, radar, broadcasting (TV or music -- in fact for those of you in the Chicagoland area the music station B96, broadcasts using radiowaves of frequency 96.3 MegaHertz which is a wavelength of 3.12 meters in case you were curious). If we could 'see' radiowaves we would find that no matter where we looked all we would see would be radiowaves, so effectively we couldn't 'see' anything else. Indeed we are in an ocean of radiowaves.

So it seems that the story of the light is complete. Unfortunately, this is not the case. While there is ample evidence of the wave properties of light, there are certain phenomena which the wave theory cannot account for. Next we explore the 'other side' of light.

The 'corpuscular theory of light' proposed by Rene Descartes (1637) and further developed by the great Sir Isaac Newton (1672) theorized that light was composed of tiny 'corpuscles', what we would today call particles or quanta. In this theory, light consists of tiny particles (imagine very smalls balls) which can bounce of objects and enter the eye producing vision. The diffraction pattern data and the success of Maxwell's equations, among other things, tipped the balance in favor of the wave theory of light ,therefore, the corpuscular theory was 'set aside'. Then, near the end of the 19th century, a 'catastrophe' occurred in physics which would ultimately end the wave only view of light. To this day it is referred to as 'the ultraviolet catastrophe'.

In brief, the ultraviolet catastrophe refers to a very severe mismatch between the predicted radiance spectrum of light (energy emitted by a hot object at different wavelengths/frequency) using Maxwell's theory and the measured spectrum. Figure 2 demonstrates the ultraviolet catastrophe. At a temperature of 5000 K (thats 4726 Celsius or 8540 Fahrenheit. FYI surface temperature of the Sun is 5778 K!) the black solid curve demonstrates the prediction using Maxwell's wave theory of light. The x-axis is wavelength in micrometers (10^-6 m) and the y-axis is the radiance (basically how much energy measured in kiloWatts is being emitted. The energy a light bulb emits is measured in Watts typically). The solid blue curve is the actual data of measured radiance at 5000 K. Note in the dashed red line, that at larger wavelength's (>2 microns) the mismatch between prediction and measurement is "small" and gets smaller as the wavelength increases. At the purple dashed line (< 1.5 microns) the mismatch is "large" and only gets larger as the wavelength gets shorter. This mismatch is the ultraviolet catastrophe, and solving it would usher in a revolution in physics/science which, I consider, as revolutionary as Charles Darwin's theory of evolution.

Figure 2. Ultraviolet Catastrophe

Somewhere between 1899-1901 Max Planck solved the ultraviolet catastrophe (winning the 1918 Nobel Prize in Physics) and ushering in the era of Quantum Mechanics! His solution to the ultraviolet catastrophe was to modify how the energy in an EM wave is calculated in Maxwell's theory. Figure 3 demonstrates how energy in an EM wave is calculated both using Maxwell's wave theory (which caused the ultraviolet catastrophe) and according to Max Planck's quantization scheme. The graph on the left demonstrates that according to the wave theory of light the energy in the EM wave is proportional to the square of the maximum value of the electric or magnetic field. The blue graph has a maximum magnitude of 1, the red graph of 2, and the green graph of 4. According to the wave theory then the energy of the EM wave is proportional to the square of the maximum magnitude. Max Planck, however, proposed that the energy of the EM wave should depend NOT on the magnitude of the EM wave, but rather on its frequency or wavelength (remember these two quantities are related as f = c/λ ). In Planck's equation the energy of the EM wave was related to its frequency/wavelength by a new universal constant that we call Planck's constant (h). As demonstrated in Figure 3 on the right, the energy of the EM wave is proportional to its frequency (the number of cycles/per second). This "simple" proposal had far reaching consequences that even Max Planck could not have imagined at the time.

Figure 3. Energy in EM wave

The last piece to this story of light ends with Albert Einstein who in 1905 used Max Planck's new formula for the energy in an EM wave to hypothesize that light was composed of particles (or quanta as we say) with discrete energy values given by Planck's formula. He used this to explain what we today call the photoelectric effect, and in doing so won the physics Nobel Prize in 1921 (interestingly he did not get the Nobel Prize for his work on Special and General Relativity)!

The works of Max Planck, Albert Einstein and other scientists (eg: Arthur Compton) strongly established the corpuscular nature of the EM wave. Today we describe light and EM waves in general using both wave and particle theories.

The take home point is that light is just one sliver of the electromagnetic spectrum which contains EM waves of various wavelengths/frequencies. The larger the wavelength (or the smaller the frequency) the lower the energy of the EM wave. Thus radiowaves, with their long wavelength and low frequency are the least amount of energy , while x-rays and gamma rays are EM waves with a great deal of energy due to their small wavelength and high frequencies.

In the next section we will explore the effects of EM waves on biological tissue!

-Stay tuned and Thank You for reading. I'd appreciate any questions, comments etc.