Transcription
Hello and welcome back. We've now looked at the speed of sound as it travels through various tissues, and we've looked at the properties of the tissue that will determine the speed in which sound travels through that tissue. I now want to look at a couple of parameters that I've grouped together that all relate to the ultrasound beam's intensity. And you'll see as this course goes on, beam intensity is a critically important factor when it comes to making an ultrasound image. We're also going to discuss the attenuation of that beam as it travels through tissue and how we can go about thinking and calculating that intensity loss.
Now, when we look at an ultrasound beam or a sound wave traveling through tissue, we can see there are localized pressure changes. We get regions of compression and regions of rarefaction. Now, if we think of this dotted line as the pressure in the tissue without a sound wave going through, positive deflections in that local pressure being regions of compression, and negative deflections being regions of rarefaction.
Now, these local pressure changes can be measured in units known as pascals, a pressure measurement here. And these pascals, these local changes in pressure, are the amplitude of our sound wave, the deflection of the baseline pressure within the tissue. This amplitude is really important when calculating the power and the intensity of our ultrasound beam.
Now, the amplitude is related to the power of our beam. Now, we measure power in what? What's our joules per second? It's energy per second. How much work is done in a tissue by those local pressure changes? When we look at a joule, it's the work done by a Newton of force over a distance, and that over a period of time is what's known as the power, the wattage of the ultrasound beam that we're putting out.
Now, we can see that the power is proportional to the pressure squared. Now, this pressure is the amplitude of our wave, that localized pressure change. So we can see that if we double our amplitude, we double the local pressure change, we quadruple the power. As pressure increases, our power increases to the power of two.
Now, if we think about an ultrasound probe, it covers a set amount of real estate. It has a certain area to our ultrasound probe. Now, the intensity is the measure of power that is put into the tissues over the area that that power is being released. We can see that as power increases, intensity increases. So it goes without saying that intensity is also related to pressure changes, to the amplitude of our wave. As the amplitude doubles, our intensity quadruples if the area remains the same. As we spread that ultrasound power over a larger area, our intensities will decrease. If the area gets smaller, that intensity increases.
Now, it's very difficult to actually calculate the specific intensity at a region within our tissues. And what we generally do is use what's known as the decibel scale, a relative intensity scale. We're looking at the intensity of the wave in one region and comparing it to the intensity of the wave in another region. Now, this could be sound waves traveling through a tissue and losing intensity. So as our sound wave starts off with one intensity, it loses some intensity through absorption, through scattering, and it becomes another intensity. We can now determine the relationship between these two intensities by using the decibel scale. Another way we could do this is if we have set our ultrasound machine to a specific power, to a specific gain, and we increase that power and we change the intensity, we can use decibels to describe that change in intensity.
Now, we saw that change in intensity, change in amplitude, it was an exponential process. These processes aren't linear, and ultrasound attenuation is also not a linear process. It's an exponential decrease. So using a logarithmic scale will allow us to use smaller decibel values while describing great changes in intensity.
The term decibel actually comes from Alexander Graham Bell. They were looking at the intensity lost in phone lines. That's where this value comes from. And a decibel is the log scale of the second intensity that we are comparing to the first intensity, and it's a 10 log scale. So if our intensity in I2 here was the same as i1, our intensity ratio is one here. We get a decibel change of zero. There is no change. Decibels describe the change in intensity.
Now, a change in three decibels refers to a doubling of the intensity. Our first intensity is half as much as our second intensity. As intensity doubles, our decibel scale goes up by three. A 10 decibel increase in intensity results in a 10-fold increase in intensity. If this had an intensity of 10, at 10 decibel increase would result in this being an intensity of 100.
Now, this is where people get confused. A 10 decibel increase results in a 10-fold increase. We're talking about a logarithmic scale here. So adding a further 10 decibels is not a linear increase, it's another 10-fold increase in intensity. So an increase in 20 decibels results in a 100-fold increase, a 10 decibel plus 10 decibel, a 10-fold increase and then another 10-fold increase. You need to get your mind around that. So we can see that a small decibel increase drastically leads to a really big decibel increase. We're dealing with an exponential scale here.
The reverse is also true with a negative decibel value. A negative three decibel or three decibel decrease in intensity results in a halving of the intensity. A 10 decibel decrease results in a 10-fold decrease in intensity, and a 20 decibel decrease results in a hundredfold decrease in intensity.
Now, when we are looking at attenuation through tissues, we are getting a decrease in intensity. And we've dedicated a whole talk looking specifically at attenuation of ultrasound beams as they travel through tissue. But I wanted to mention this here while we're talking about intensities. We'll see later that we can calculate soft tissue attenuation, importantly, this is specifically for soft tissue, by multiplying the frequency of the sound, the frequency of the probe that we're using, by 0.5 decibels per centimeter of tissue traveled per megahertz. So in this example, let's take a two megahertz ultrasound beam. We've got two megahertz times by 0.5, that equals a one decibel per centimeter decrease in intensity. So in our first centimeter here, we'll get one decibel decrease in intensity. After three centimeters here, we'll have a one to three decibel decrease in intensity.
Now, we saw that a three decibel decrease in intensity is a halving of that intensity. So for a two megahertz ultrasound beam at three centimeters depth, we have lost half of that beam's intensity. If we were then to take a four megahertz ultrasound beam, four times 0.5 is a two decibel per centimeter decrease. So in the first centimeter, we have lost two decibels. In 1.5 centimeters, we have lost three decibels, we've halved our intensity. And you can see that as frequency increases, our attenuation gets more and more and more. So attenuation is proportional to the amount of frequency. The higher the frequency, the quicker the intensity drop off, the quicker the attenuation of that beam.
Now, when we're thinking of an ultrasound beam traveling through tissue, we think of these local pressure changes. Now, we can have multiple ultrasound beams traveling through a tissue at any given point. And we can see that if we have two ultrasound beams that are in phase with one another, the regions of compression and rarefaction match up. We can get what's known as constructive interference. We get addition of these amplitudes here. Our amplitude of our wave increases, our intensity increases to the power of two. This amplitude change results in an increased intensity of our ultrasound beam. The same is true when they are out of phase. We get what's known as destructive interference. The amplitudes cancel one another out, and we get reduction in the intensity of our ultrasound beam.
Now, why is this important? Well, we're going to look at ultrasound beams being produced within a transducer, and there are multiple transducer elements within that ultrasound beam, each creating its own set of ultrasound waves. Now, we can see that this ultrasound wave is out of phase with this ultrasound wave in these two elements here. When the waves are out of phase, we get destructive interference. This peak here, this region of compression, matches up with this region of rarefaction, and we get a reduction in the intensity in this region here. If our transducer elements are in phase, we get addition of these regions of compression here. We get an increased intensity in the overlap of these two transducer elements, and this increased intensity is what happens when we propagate an ultrasound beam through tissues.
Now, when we run an ultrasound beam through a tissue, we get what is known as a near field here, where the beam actually converges on itself to a focal point. We then get divergence of that beam in the far field here, and we're going to look specifically at beam properties in a later talk. What I want to show you is that the ultrasound beam has varying intensities as we cut it in cross-section. The middle of that ultrasound beam has the most intensity, and that's because of that constructive interference of our ultrasound beam. And the outer edges of our ultrasound beam have the least intensity. And as that beam converges, as the area gets smaller and smaller, we can see that intensity is related to area. As that area gets smaller, the intensity of that ultrasound beam gets more intense.
Now, we can take a cross-section of this ultrasound beam, let's say this one here, and plot that on a graph. On our y-axis, we've got intensity change, and our x-axis, we've got the area of this ultrasound beam. Now, we can see that in the center of the ultrasound beam, we've got our maximal intensity. And this is what's known as the spatial peak intensity, the most intense part of our beam. What is the most intensity that we'll get over this cross-sectional part of our ultrasound beam? The spatial average takes all of the intensities in this beam and it's a mathematical average of that intensity. So at any given cross-section here, what is the mathematical average of that ultrasound beam? And we can use these values to get an idea of the intensity of that ultrasound beam, and we'll use them later on when we're looking at the mechanical and thermal indices of our ultrasound beam, when we look at the bioeffects of the ultrasound beam.
Now, this is what's known as spatial intensity. We are taking a cross-section of the ultrasound beam. We can also look at temporal intensity as the ultrasound wave travels through tissue over a period of time. What is the intensity? Now, again, we're going to continually come back to this diagram here as we add more and more parameters onto our ultrasound beam. We've looked at frequency and period, wavelength and speed. Now we've added the amplitude of our wave, the local pressure change within the wave. We've also looked at the power of the wave, the wattage, our joules per second. Time the power of the wave is proportional to the amplitude of the wave squared. The local pressure change within the wave squared is proportional to the power of our wave. We've also looked at the intensity of the wave, and the intensity of the wave is the power per unit area, the power in time per unit area and distance. That's why I've drawn the intensity here, it uses both time and distance. And we've looked at the relative change in intensity as our decibel scale.
Now, when I draw this ultrasound pulse here, I've drawn it as a uniform pulse with the amplitudes being exactly the same. Now, later on, when we look at the production of ultrasound waves in our ultrasound transducer, we'll see that that wave produced is actually not uniform like this. There will be varying amplitudes of our wave. Now, we can take what is known as the temporal peak, the greatest amplitude of our wave, and these are the temporal intensities that I was talking about. We can use this temporal peak when looking at bioeffects in our tissues. We can then take what is known as the pulse average, which is the average intensity of this specific pulse here. We can also look at the temporal average here, which takes into account our pulse average as well as a factor known as our duty factor, which we're going to be looking at in a future talk. And we can use these five parameters here, our spatial intensities and our temporal intensities, to calculate the bioeffects of our ultrasound beam.
So I hope that's managed to give you an idea of what intensity is in our ultrasound beam. We can take a cross-sectional look at our ultrasound beam and get our spatial intensities. We can look at the ultrasound wave itself and look at our temporal intensities. And the local pressure changes within our ultrasound beam are exponentially proportional to our power output, and as a result, they are also exponentially proportional to our intensities. When we look at the decibel scale, we are getting the relative intensity changes from one intensity to another, and that scale is logarithmic. A 10 decibel change results in a 10-fold change, and a three decibel change results in a two-fold change, either a halving or a doubling of those intensities.
In our next talk, we are going to be looking at the core principles of ultrasound image acquisition, known as pulse echo ultrasonography. Now, all of these parameters that we are looking at here are crucially important if you are studying for an ultrasound physics exam. And if you are studying for an ultrasound physics exam, I've linked below a question bank that I've curated from multiple different past papers going back multiple years from multiple different countries. If that's something you're interested, go and test yourself with that question bank below. Otherwise, I'll see you all in the next talk. Goodbye, everybody.