Tissue Harmonic Ultrasound Imaging | Ultrasound Physics Course | Radiology Physics Course #24

Hello and welcome back. Today we're going to be looking at tissue harmonic imaging.

Now, up until now in this course, we predominantly looked at pulse echo ultrasonography, where we send an ultrasound pulse into tissues. That pulse will reach a tissue boundary, and if the tissues on either side of that boundary differ in acoustic impedance values, some of that pulse will return back to the transducer as an echo, and some of it will be transmitted through deeper into the tissues. And it's those returning echoes, the timing and the intensity of those returning echoes, that we can then use to create our B-mode image.

Now, tissue harmonic imaging has the same basic principle. We send an ultrasound pulse into the tissue at a set frequency, and we wait for those returning echoes to come back, using the timing and intensity of those returning echoes in order to create a B-mode image. Now, where tissue harmonic imaging differs is the returning echoes are selected out by our transducer. We only listen for set frequency returning echoes, and those frequencies are what is known as harmonic frequencies.

Now, what exactly is a harmonic frequency? Now, throughout this course, we've looked at our piezoelectric material as being similar to a cymbal. When you hit a cymbal on a drum set, that cymbal will resonate at a set frequency, and the frequency that that cymbal resonates at will be dependent on the diameter of that cymbal, as well as the material that the cymbal is made out of. Much like our piezoelectric crystal, the frequency that we transmit into the tissues is dependent on the thickness of that piezoelectric material. We've also looked at a piezoelectric material being similar to a guitar string. Now, a guitar string is set between two fixed points, and if we pluck that guitar string, it will resonate at a certain frequency depending on how far those set points are apart and how taut that string is, much like the width of our piezoelectric material.

Now, in all of these cases, the resonance will happen at a specific frequency based on the characteristics of the instrument or the piezoelectric material that is creating that resonance frequency. Now, this frequency that we transmit into the tissues is what's known as the fundamental frequency, based on the thickness of our piezoelectric material. So, if we had a look at a guitar string and we pluck a guitar string, we get this half wavelength standing wave resonating at our fundamental frequency. Now, a harmonic frequency is an integer multiple of this resonance frequency.

Now, what is an integer multiple mean? It means it's a whole number multiple of this frequency. So, if this was resonating at two megahertz, the first multiple integer that we can get is four megahertz. We times this base resonance frequency by two. We can then times it by three, we get six megahertz. Times by four, get eight megahertz. And what we can see is that this fundamental frequency can be separated into smaller harmonic frequencies.

Now, when a wave interacts with tissues, the echo returning will be the same as the fundamental frequency, and there are a couple of reasons. Now, that we're going to look at will also get returning echoes coming in these harmonic frequencies, integer multiples of that original fundamental frequency. So, here we can see we've got a frequency that's double that of our fundamental frequency. This is our first harmonic, or two times our fundamental frequency. And these regions where the wave is still, these are what's known as the nodes, and the waves moving up and down like this are called standing waves. They will resonate, maintaining the shape here. This node will be a point that doesn't move on the wave. We can then get second and third order harmonics, which represents three and four times the fundamental frequencies. We can't get two and a half times the fundamental frequencies. It has to be a whole number, an integer of that original fundamental frequency. So, these waves, these higher frequencies, are what is known as the harmonic frequencies, and they're based on this fundamental frequency.

Now, when we're looking at a wave like this, we're looking at a one-dimensional wave. It's only got magnitude, it's got frequency, it doesn't have direction, and it is not moving through time and space. These are standing waves here. Now, we can get fundamental and harmonic frequencies in the two-dimensional realm as well. Now, this is a little bit more difficult to conceptualize, and there are some videos on YouTube that you can go and search where people have made a speaker and placed sand on top of that speaker, and when a specific note is played, a certain frequency is played, the sand will make specific patterns on top of that speaker. So, I've drawn a diagram here. If you think of this as the top of the speaker here, and we're playing a specific note, the speaker is resonating at a specific frequency, you can see that the sand, represented by these light lines here, will fall down to the nodes on those standing waves, the parts of the speaker that aren't moving. The sound, because of gravity, will fall into those regions and will make a specific pattern here. This is representing the two-dimensional harmonic frequencies. If we were to change the note, change that fundamental frequency, we would see the pattern on top of that speaker change. And I'd encourage you to go and look at those YouTube videos. I'll link one below in the description.

Now, when we are creating ultrasound waves, it's quite difficult to imagine these fundamental and harmonic frequencies because not only are we creating a 2D pulse, we are also propagating that through time and space. We've got a three-dimensional wave being formed here, and it's very difficult to visualize the harmonic frequencies returning in a three-dimensional way. And it's helpful to return back to this one-dimensional wave as a good conceptual understanding of how fundamental and harmonic frequencies work.

Now, we've been looking at an ultrasound wave as a longitudinal wave passing through a medium. It requires a medium, it requires units in that medium to propagate, and we've seen that the speed of that wave is dependent on the bulk modulus and the density of the tissue through which the ultrasound wave is traveling. The speed is dependent on the tissue through which it's traveling, and we've represented this longitudinal wave as a sine wave, regions of compression and regions of rarefaction.

Now, when we look at these regions of compression versus the regions of rarefaction, we'll see that in the compressed region, the molecules or units in that medium are closer together. Now, when those units get closer together, the bulk modulus of that piece of tissue changes. The compressibility gets less, or the stiffness of the tissue gets more. It's much more difficult to further compress these units within the medium. When we look at the region of rarefaction, our bulk modulus actually decreases. And it's this slight change in bulk modulus that means the regions of compression actually move slightly faster than the regions of rarefaction as an ultrasound wave propagates through tissues. So, initially, we draw our ultrasound wave as the sinusoidal wave, and because of the changing bulk modulus in the regions of compression, the compression region on our sinusoidal wave will be moving faster, relatively speaking, to the rarefaction region here. And it's this slight difference in speed as that ultrasound wave is propagating through tissue that means we get this non-linear distortion of the ultrasound wave. This is what's called non-linear behavior in an ultrasound wave. The regions of compression are moving slightly faster than the regions of rarefaction, and we get this distortion, this non-linear behavior of the ultrasound wave.

Now, this is the basic principle for why we get harmonic frequencies returning back to the ultrasound machine. If the wave remained in its sinusoidal waveform, we would only get the fundamental frequency returning from tissue boundaries. As the wave exhibits this non-linear behavior, we start to get harmonic frequencies returning to the ultrasound machine, and this only happens in regions of high intensity within our ultrasound beam.

Now, this is the first reason for why we would get harmonic frequencies returning back to the ultrasound transducer. The second reason is if an ultrasound wave comes into contact with what is known as a microbubble. When this bubble of air is smaller than the wavelength itself, it will expand and contract based on these regions of compression and rarefaction, and that expansion and contraction will cause this bubble to resonate at a harmonic frequency to the incident ultrasound wave, emitting harmonic frequency waves back to our ultrasound transducer.

Now, we're going to be focusing on tissue harmonics here. It's actually the tissue's response to this ultrasound wave that is causing those harmonic frequencies to return to the ultrasound pulse. You can think of that tissue as resonating at a harmonic frequency and creating a separate ultrasound pulse that is heading back towards our transducer. Now, because this non-linear behavior of the ultrasound wave happens as the wave is traveling through tissue, we get more and more production of harmonic frequencies as that wave travels deeper into tissues. So, the quantity of harmonics that are returning to our ultrasound probe increases with depth within the tissue. We start off with very few harmonic frequencies returning to the transducer probe, and as we get deeper and deeper into the tissues, we get more and more harmonics, first, second, third, fourth order harmonics being formed deeper into the tissue.

Now, we can superimpose this over our ultrasound beam here. We can see that our ultrasound beam is traveling through tissues with our near field and our far field, with our focal zone here, as we've seen before when we looked at the ultrasound beam. Now, because of this non-linear behavior of that ultrasound beam propagating through tissue, we start to get harmonic formation deeper into the tissues. Now, I mentioned, and this is really important, harmonic frequencies only happen at intense parts of the ultrasound beam, and that's why we can see we only get harmonic formation here in the center of our beam, the most intense region of our beam. We are not getting harmonic frequencies on the lateral portions of the ultrasound beam here.

Now, we can plot the various different harmonic frequencies that are returning to our transducer on a graph based on how deep we are within the tissues. Initially, we have our fundamental frequency, the pulse echo frequency that we've been looking at throughout this ultrasound course. And as we've seen before, that pulse echo gets attenuated as it travels into tissue here, and that attenuation is dependent on the frequency of that ultrasound wave. The higher the frequency, the more it gets attenuated. Now, as you can see here, we get first order harmonic frequencies, or two times our fundamental frequencies, forming just before the focal zone of our ultrasound beam here. And we can see that as we travel further into the tissue, we start getting a peak of this first order harmonic. As we travel deeper into the tissue, we get more and more non-linear behavior of this ultrasound wave, and we start to see second order, or three times the fundamental frequency, returning back to our ultrasound probe.

Now, although we are returning more harmonic frequencies the deeper we head into the tissues, those harmonic frequencies, the second and third order harmonics, are very high frequency ultrasound waves, and they won't be able to make it all the way back to our ultrasound transducer because high frequency ultrasound waves get attenuated quickly. So, although we're creating a lot of higher order harmonic frequencies, those aren't very useful to us because they don't make it back to the ultrasound transducer. They're attenuated before they can travel back, and we generally focus on this first order harmonic, two times the fundamental frequency of our ultrasound transducer.

Now, why do we focus on harmonic frequencies? Well, harmonic frequencies one, only occur at the intense part of the beam. We've got a very narrow beam being formed here, we get great lateral resolution here. And two, harmonic frequencies, tissue harmonic frequencies, only occur at tissue boundaries. They're created by the tissues. It's true signal heading back to our ultrasound transducer. The scatter that happens or the noise that happens in a normal B-mode ultrasound image aren't at harmonic frequencies. And if we can select specifically for those harmonic frequencies that are returning back to our ultrasound transducer, we get true signal heading back. We can eliminate some of that scatter, eliminate some of that background noise, get better spatial resolution, and ultimately better contrast within our ultrasound image. What we see on that B-mode image more accurately represents the true tissue boundaries within the tissues.

Now, if we take a specific point along this ultrasound beam, we can see the types of frequencies that are returning back towards our ultrasound transducer. Say this transducer was a two megahertz transducer, we would get a first order frequency of four megahertz, then a second order of six, and a third order of eight megahertz. And we can see that if we take a specific point along this beam, the majority of them are still the fundamental frequency, but we're getting first order and second order harmonic frequencies returning to the ultrasound machine. And we want to now isolate these specific first order harmonic frequencies returning. They best represent the tissue boundaries.

Now, there are three main ways that we can isolate this first order harmonic frequency. Now, this only works if we know what our initial frequency is. We want a high quality factor ultrasound beam heading into the tissues, a very narrow bandwidth that is specific around a certain frequency. That way, we know what the harmonic frequencies are returning. There'll be integer values of this fundamental frequency. Now, how do we create a high quality wave? We've seen this before. We can increase our spatial pulse length, we can allow that piezoelectric material to resonate at its resonance frequency, and that will give us a narrow bandwidth, a very specific frequency heading into tissues. The shorter and shorter our spatial pulse length, the wider the bandwidth, and the less pure the harmonic frequencies are that are returning towards our ultrasound machine.

Now, the problem with having a high quality factor wave, an undampened wave that has a long spatial pulse length, is we get a reduction in axial resolution. We've seen that axial resolution is dependent on the spatial pulse length. So, it's a little bit of a trade-off: how pure can we make the frequencies heading into the tissue without losing too much axial resolution? And we'll see how we can get back some of that axial resolution.

Now, what we want to do is isolate this specific first order harmonic frequency that's heading back towards our ultrasound transducer and only use those returning echoes to create our B-mode image. That image is going to have much better contrast and spatial resolution. Now, there are three main ways that I want to talk about today for isolating this specific harmonic frequency.

Now, the first way we can do it is by changing the receiver bandwidth. When we have a two megahertz ultrasound transducer, we will generally have a receiver bandwidth that flanks the two megahertz here, and we will receive any echoes returning from the tissues that lie between this one and four megahertz, for example. I've got a fairly wide receiver bandwidth so we can get all those scattered echoes, we can get those tissue boundary echoes, and we'll get some of the noise coming back from our tissues. And this is how we traditionally create our pulse echo ultrasonography image. Now, what we can do is actually change that receiver bandwidth. We can say to the ultrasound machine, "Only listen for echoes that are returning at four megahertz in frequency." Now, what that does, we're still getting all those other echoes back, but electronically, when we're sending signals via the amplifier towards the machine for processing, for displaying that B-mode image, we only want to process and display four megahertz. We only want to display the harmonic frequency, the first order harmonic frequency here, two times the fundamental frequency. That allows us to only display harmonic frequencies coming back, true tissue boundary frequencies. Those harmonic frequencies have been created within the tissue. Now, when you set harmonic mode on the ultrasound machine itself, it will automatically do this. It will narrow down the receiver bandwidth. This requires the ultrasound machine to pull out only those returning echoes that have our first order harmonic in them. It requires that Fourier transform that we've mentioned before.

Now, there are other ways that the machine doesn't have to manipulate the data returning, and it will only get harmonic frequencies coming back predominantly to the ultrasound machine. The first way we can do this is what is known as pulse inversion harmonics. We can send two separate pulses down an individual a-line towards a tissue boundary here. Now, the pulses are out of phase. They're 180 degrees out of phase. The second pulse is an inversion of the first pulse. That's why it's called pulse inversion harmonics. Those pulses head towards a tissue boundary at the fundamental frequency, and they will create echoes at the fundamental frequency that will cancel one another out. There will be destructive interference of those echoes. We won't get fundamental frequencies returning to the ultrasound machine here.

Now, we've also seen that when these pulses travel through a certain depth of tissue in an intense part of the wave, because of that non-linear behavior of this ultrasound pulse, they are also going to generate harmonic frequencies at tissue boundaries. The tissue is responding to this fundamental frequency and resonating at a harmonic frequency, an integer multiple of this fundamental frequency. Now, these echoes coming back at the fundamental frequency will be inversions of one another and destructively interfere with one another, making no fundamental frequencies head back towards a transducer.

Now, a property of the harmonic waves that head back from tissue boundaries means that they are going to actually head back in sync, despite the initial waves being inversions of one another. If you think back to the first slide of this talk, when we looked at one, two, and three-dimensional harmonic ultrasound waves, so it is quite difficult to conceptualize two and three-dimensional waves. And this is a property of these waves heading back. They're going to be in phase because the tissue boundaries are essentially creating these harmonic frequencies. That's why it's called tissue harmonics. The tissue is creating that harmonic frequency heading back to our ultrasound probe. Now, these are actually going to constructively interfere with one another and give us a higher intensity harmonic frequency heading back towards the ultrasound transducer, and we can use this to create our harmonic imaging.

There's one last method that allows the ultrasound transducer to only accept the harmonic frequencies heading back from tissue boundaries, and that's what's known as power modulation harmonics. Again, we send two ultrasound pulses down one a-line within our B-mode image. We send down an intense ultrasound pulse and a slightly weaker or less intense ultrasound pulse. They still have the same fundamental frequency. Now, when these pulses reach a tissue boundary, they are going to echo back a fundamental frequency. Here, we see they don't cancel one another out. Now, as we've discussed multiple times now, only regions of high intensity will create a harmonic frequency heading back. So, when these ultrasound pulses reach a slightly deeper tissue boundary here, because of the non-linear behavior of this ultrasound pulse and the high intensity of the ultrasound pulse, there will be a harmonic created at this tissue boundary. This second ultrasound pulse doesn't have enough intensity to create that tissue harmonic. Again, we'll get those returning back to the ultrasound transducer.

Now, the ultrasound transducer is not seeing these waves as separate waves. It's getting a combination of that wave coming back towards the ultrasound transducer, and because of the differing amplitudes but same frequencies of the red and the blue waves here, our fundamental frequency waves heading back, the ultrasound transducer can use a Fourier transformation to cancel out the contribution of these two waves, cancel out the contribution of the fundamental frequencies heading back to the ultrasound transducer. That mathematical cancellation will allow the ultrasound transducer to calculate the harmonic frequency that is returning to the ultrasound transducer.

Now, why do we use harmonic frequencies? We've said that harmonic frequencies only happen at intense regions of the beam, and they only happen at true tissue boundaries. It's the tissue that is creating the returning harmonic frequency based on this non-linear behavior of the wave propagating through tissues. That gives us better signal-to-noise ratio. The noise or the scatter that's coming back from our fundamental wave is not contributing to those harmonic frequencies. We are canceling those out when creating our B-mode image. It also gives us better contrast. We're getting better contrast between the tissue boundaries, as well as reducing the scatter and noise that degrade contrast within the image. Because this intense part of the beam is narrower than our actual beam, we get better lateral resolution, and we're eliminating the scatter and the reflections that are happening in this subcutaneous tissue here. We've seen that the fundamental frequency heading out into tissue attenuates over time, and we get really intense echoes coming back close to the ultrasound transducer because the wave's intensity that we're heading out into the tissue is extremely high here. We can cancel out those intense waves heading back at the fundamental frequency and the reverberation that happens in the subcutaneous tissues and get better resolution in this near field. We only get those small harmonic frequencies heading back, but because the wave is so intense here, those small harmonic frequencies can still give us a good image. We can also use lower fundamental frequencies to allow us to image deeper into the patient. If we have an obese patient or we want to image deep into the abdomen, we can use a lower fundamental frequency that gets attenuated slower, but get returning harmonic frequencies, higher frequency returning waves that only have to travel half the distance. Those higher frequency waves only have to travel from the tissue boundary to the ultrasound transducer. So, we get the benefit of receiving high frequency waves, but the depth of the lower frequency fundamental wave that we propagate into the tissue. We can also reduce what is known as the side lobes and grating lobes that we've looked at in our ultrasound beam talk. We saw that when we create an ultrasound beam like this, we get a phenomenon known as side lobes heading out laterally to our beam and grating lobes also heading out lateral to the main ultrasound beam. The intensity of those lobes aren't strong enough to create tissue harmonics, so we don't get those returning echoes contributing to our ultrasound image.

Harmonic imaging is not always perfect. We've seen that if we use pulse inversion or power modulation modes, we need to send down multiple ultrasound pulses per a-line, so we can lose some temporal resolution. Our frame rate will have to slow down ever so slightly. We've also seen that we potentially need to use higher spatial pulse lengths, reducing some axial resolution. And we've seen that if we're imaging really deep here, the high frequency harmonics aren't going to make it back to our ultrasound transducer. Only those lower fundamental frequencies will make it back. We might need to use traditional pulse echo ultrasonography when imaging deeper tissues.

Harmonic imaging is a difficult concept for people to understand. Often, and I don't want you to get caught up in the core underlying physics here. The core concept here is that harmonic imaging uses tissue harmonics, the integer multiples of our fundamental frequency, and those tissue harmonics that are heading back towards the ultrasound machine represent true tissue boundaries. They are created by the tissue boundaries, giving us a much better signal-to-noise ratio and contrast within our image. And we can use varying different mechanisms to isolate those tissue harmonics that are returning to the ultrasound transducer. We can narrow our receiver bandwidth, we can use pulse inversion harmonics, and we can use power modulation harmonics, allowing us to create an image based solely on those returning harmonic frequencies.

On our next talk, we're going to be looking at ultrasound artifacts. And this is an exam favorite. If you are studying for an ultrasound physics exam, you need to understand the common types of artifacts that you see in ultrasound imaging. It comes up in every single ultrasound physics exam. And again, if you're studying for a physics exam, I've linked below a question bank that I've curated from multiple past papers from around the world, taking the most common questions and answered them in video format. So, that's you go check it out in the link below. Otherwise, I'll see you all in the next talk. Goodbye, everybody.