Chapter four: CARDIAC ULTRASOUND TUTORIAL SERIES

Terminlogy of the Physics of Ultrasound (continued)


by


Dr z. Gooding


Physics versus Mathematics:

This chapter is an extension of the previous, to stress the importance that a thorough mastery of the "Fundamentals of Physics", reenforced by a basic knowledge of Mathematics, will help understand the Physics of Ultrasound.

To illustrate the above statement, let's take a look at the following example and see how it can serve our purpose. If someone drops a ball from the top of Sears Tower, one can measure the "time" it takes the ball to hit the ground and also compute the "distance" covered, which is
basically the height of the Tower. With the knowledge that a basic law of physics known as Law of Gravity is involved, the height (h) of the tower can be expressed mathematically as follows:

h = 1/2 g t x t

where h is the height of the tower expressed in meters, g the local acceleration of gravity (9.8 meters per second x second) and t the time of fall in seconds.

Note that g and t are known, and t is squared (t x t).
Similar laws that mathematically describe the fundamental nature of ultrasound will be explained. But first a basic math review is necessary.

It is recommended that the candidates for the ultrasound boards should become familiar and understand each type of math problem reviewed below such as:

1. Fractions (addition, multiplication, and division);












2. Decimals;












3. Significant figures;












4. Scientific notations;












5. Rules of exponents;












6. Binary system;












7. Graphing;












8. Units of measurements.

Fractions:

By definition a fraction (x/y) has 2 members a "numerator" (x) and a "denominator (y).

Rule 1: both addition and subtraction of fractions require a common denominator.

1/5 + 3/4 =====> (1/5 x 4) + (3/4 x 5) = (4/20) + (15/20) = 19/2

3/4 - 1/5 =====> (3/4 x 5) - (1/5 x 4) = 15/20 - (4/20) = 11/20

Rule 2: in a multiplication , numerators are multiplied together and denominators together.

1/5 x 3/4 = 1 x 3/ 5 x 4 = 3/20

Rule3: in a division, invert the second term and then proceed as in multiplication;

3/4 divided by 1/5 =====> 3/4 x 5/1 = 15/4

Decimals:

Rule1: When the denominator of a fraction is a power of 10, that fraction can be readily
converted into decimals:

5/10 = 0.5

5/100 = 0.05

5/1000 = 0.005

Rule2: If the denominator is not a power of 10, the decimal can be obtained by
performing the division

5/9 = 0.55

Significant Figures:

Consider the entries below:

45.684 (3 decimals) + 7.7 (1 decimal) + 6.15 (2decimals) = 59.534 = 59.5

• In both addition and subtraction, the total must be rounded to the same number of digits as the entry with the least number of decimal places. Therefore the total is 59.5.
  



• In multiplication and division round to 2 digits.

45.68 x 7.7 = 351.736 =====> 351.74

45.8/7.7 = 5.93247 =====> 5.93

Algebra:

As a branch of Mathematics (exact science), the goal of Algebra is to solve for "unknown quantities" (aka variables) represented by alphabetic letters (x, y, z) in an equation.

An equation is defined by its "sides" or "members". In the following example: x = 2y, x is the first member and 2y is the second member.

Algebra also has rules, used to solve for the variables encountered in diagnostic ultrasound equations.

Rule1: when a variable is multiplied by a number, both members of the equation must be divided by that number.

6x = 12 =====> 6x/6 = 12/6 =====> x = 2

Rule2: when numbers are added to a variable, subtract that number from both members of the equation.

x + 6 = 20 =====> x + 6 - 6 = 20 - 6 =====> x = 14

Rule3: when the equation is in the form of a fration, cross multiply and solve for the variable.

y/5 = 10/25 =====> y x 25 = 5 x 10 =====> y = 2

At this point the candidates are invited to take a quiz in order to practice working with equations and hence solving for a variety of variables similar to the ones given in ultrasound board exams.

Chapter three : CARDIAC ULTRASOUND TUTORIAL SERIES

Terminology of the Physics of Ultrasound

by

Dr. Z. Gooding

One way of dealing with this chapter is to present it in the form of Q & A as follows:

1.What is ULTRASOUND exactly ?

To answer this question, one must realize that the term "ultrasound" contains in fact 2 words: "ultra" and "sound" . Physics teaches us that in order for a sound to be detected by the human ear, it has to occur with a certain "pitch" or "frequency" (proper terminology). In other words any sound occurring with a lower (infra) or higher (ultra) frequency is not going to be detected by the human ear. The frequency range for sound is known to be between 20 Hz and 20.000 Hz ( Hz being the abbreviation of Hertz, Physicist who gave his name as a the unit of frequency). Consequently, the frequency of ultrasound has got to be higher than 20.000 Hz and that of infrasound below 20 Hz as illustrated in the diagram below:



Infrasound---------SOUND--------ULTRASOUND

2. What's "frequency" ?

In the broad sense of the term, it is the "number-of-times", "how often" an event takes place. Therefore, it is relatively safe to assume that the "event" in question is potentially "repetitive".
In "Physics of Ultrasound" "frequency" is the number of "cycles" per "unit of time", which brings us to the very definition of "hertz" (e.g. the number of cycles per second). As we will see, in our particular context of "ultrasound", the "frequency" pertains to the number of cycles per second an ultrasound "pulse" is generated (transmitted).

Pearls : now putting together the above information, it is fairly safe to state that ultrasound consists of sound waves that occur (cyclically) with a frequency above 20.000 Hz (upper limit of human hearing range).

3. Using the above terminology (however "small" it might seem), how do we go to the next step and tie "things" up in such a way that makes these two terms more meaningful to our review of the "Physics of Ultrasound" ?

As a general "rule" (mine), in "Physics" all terms are somehow "tied" together, that is "interrelated" in essence through "mathematical" equations, that allow for even more meaningful "expression" and explanation of natural phenomena, such as "ultrasound". In other words, if "ultrasound" is not a "tangible" entity per se, it nevertheless lends itself to one that can be "characterized" by "variables" that can explain it in a more "concrete" , realistic way, which brings us to the following statement that should "sum" things up for us at this point:

"Ultrasound waves" are defined by their "physical" "characteristics", having to do with "how-often" ("frequency") they occur, and "how-they-can-be" represented "graphically" in a way that sonographers can "visually" understand, and also apply to develop and improve their diagnostic skills. This statement leads us to a new and meaningful definition of "ultrasound" that hopefully should "tie" things up for sonographers (see pearl below).

Pearls:

As ultrasound waves " deploy" in a "medium"(body organs), they are characterized by their :

1. Frequency (expressed in hertz or number of cycles per second);

2. Wavelength (distance, represented by the greek letter "lambda" between 2 consecutive peaks on the sound wave "profile") (see graph below);

3. Intensity (strength of the ultrasound);

4. Velocity (speed of propagation or distance covered by ultrasound per second);

The above characteristics are all represented by symbols (more of that later) as well as "mathematically" interrelated. To this end, velocity for instance is equal to the product of "frequency" and "wavelenth" (v=frequency x wavelength).

At this point, the next best "move" would be to place the above characteristics within the context of "General Physics" itself , and see how they can apply to "ultrasound" (chapter four).

Chapter two : CARDIAC ULTRASOUND TUTORIAL SERIES

Physics of Ultrasound

by

Dr. Z. Gooding


It is to the advantage of the ARDMS candidates to approach the study of PHYSICS in the context of ULTRASOUND bearing in mind the following points:

1. Physics is simply a BASIC SCIENCE, which unlike MATHEMATICS is not an EXACT SCIENCE. However, as a science, PHYSICS borrows mathematical TERMS to explain and quantify the occurrence of natural PHENOMENA (pl. of phenomenon);

2. Physics, as a science, has its own "language" (TERMINOLOGY), that ARDMS candidates need to be acquainted with, in order to understand the way ULTRASOUND works;

3. Physics also obeys some well-known natural (universal) LAWS and therefore can be "put" into EQUATIONS that are easily "quantifiable";

4. Physics explains the inherent CHARACTERISTICS of ultrasound and hence the "behavior" of SOUND WAVES in a given "environment" (MEDIUM) (body organs);

5. Once acquainted with the PHYSICS of SOUND WAVES, ARDMS candidates will be able to comprehend how these WAVES can be used as a DIAGNOSTIC tool.

6. Finally ARDMS candidates must keep in mind that a clear definition of each term used in this review is the key to understanding the PHYSICS of ULTRASOUND and passing the ARDMS BOARDS, which brings us to the next chapter devoted to the TERMINOLOGY per se.

Chapter one: CARDIAC ULTRASOUND TUTORIAL SERIES

INTRODUCTION


by


Dr z. gooding


The following article and the many more to come in the " Cardiac Ultrasound Tutorial Series " target Echocardiographers seeking ARDMS or ASE Certification, as well as Cardiac Sonographers pursuing RDCS Registration.

This tutorial will focus first on the Physics of Ultrasound, then on the other modalities of Echocardiography.

Understanding the essence of Physics in general, and that of Ultrasound in particular is paramount to passing and hence getting certified in the field of Cardiac Ultrsound.

Most applicants find the ARDMS Examination difficult, to say the least. The main reason has to do with the "way" the majority of them came into working in the field.

"Cardiac Ultrasound Tutorial" is dedicated to helping ARDMS
candidates overcome the many "difficulties" that stand between them and success
in the field.

To this end, a step-by-step TUTORIAL will be implemented to help you retain what you will have just learned and preserve
that information till you have the entire picture under control !

No more confusion or loss of previously acquired knowledge is to be expected.

What you get from the Cardiac Ultrasound Series is clear explanation of the basic concepts in Physics that will ultimately and literally "pave" the road of learning and earning for you, hence enabling you to move on with your career and your life.
Two birds with one stone as the old adage goes !