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The Photoacoustic Doppler effect (PAD) is a physical phenomenon involving a Doppler Frequency Shift in the generated acoustic waves when absorbing particles flowing with a net velocity within a medium are excited by visible light. This phenomenon is based on the principles of photoacoustics, discovered by Alexander Graham Bell in 1880, where acoustic waves are generated by modulated or pulsed optical radiation. The Doppler effect is an observed frequency shift in the acoustic signal generated by a moving object. The extent of the frequency shift is proportional to the velocity of the object.

Background

Photoacoustic Imaging or Photoacoustic Tomography is an imaging modality that combines the best features of ultrasound imaging and optical imaging and is especially useful in biomedical imaging applications. Ultrasound imaging is characterized by excellent lateral resolution but it is limited in its application by a lack of contrast in biological tissue. Conversely, optical imaging is able to achieve high contrast in biological tissue via the strong optical absorbance of red blood cells, but its lateral resolution and imaging depth is compromised by the strong scattering of tissue. By combining the two, it is possible to achieve the imaging depth and lateral resolution of ultrasound along with the excellent contrast of optical imaging.

A Potential Application

One important problem in fluid dynamics is the remote measurement of flow rates and flow velocities. This can be extended to biomedicine in the measurement of blood flow through veins, arteries and capillaries. Measuring flow velocity in capillaries is a particularly difficult problem due to the low flow rate, small size, and the limitations of current instruments. Blood flow rates in capillaries are important in diagnosis of a variety of diseases including diabetes and cancer. One aspect of blood that makes it especially attractive for optical imaging is the strong optical absorption of red blood cells. Blood has the ability to deliver oxygen, which is necessary to sustain life and can be the difference between tissue death in a diabetic patient or the extent of tumor growth in a cancer patient.

Limitations of Current Techniques

There are several techniques based on both ultrasound and optical imaging that are used to measure blood flow in a clinical setting. All currently available techniques have limitations that prevent the measurement of blood flow velocity in capillaries.

Doppler Ultrasound

Doppler ultrasound techniques use Doppler frequency shifts in ultrasound and are currently used in biomedicine to measure blood flow in arteries and veins. They are limited to higher flow rates (>1cm/s) due to the high background ultrasound signal from biological tissue.

Laser Doppler Flowmetry

Laser Doppler Flowmetry uses light instead of ultrasound to detect flow rates. The much shorter optical wavelength means this technology is able to detect low flow rates outside the range of Doppler Ultrasound. But this technique is limited by high background noise and low signal due to multiple scattering. This limits both the lateral resolution to no more than 1 cubic millimeter and the imaging depth to 1mm. This technique is able to measure average velocity within the above resolution limits but is unable to detect flow direction.

Optical Doppler Flowmetry

Optical Doppler Flowmetry is an optical technique that eliminates multiple scattering by removing all non-ballistic or scattered photons using coherence gating or other methods. This technique is able to detect flows as low as 100um/s with a spatial resolution of $5x5x15\mu m^{3}$. The only drawback to this technique is that the detection depth is limited to <1mm.

In contrast, the Photoacoustic Doppler method is able to overcome the many of the limitations outlined above and achieve an improved signal to noise ratio. Light absorbing tracer particles such as red blood cells can absorb light 100 times more than the background at specific wavelengths creating good contrast. Here, scattering plays a much smaller role since it does not matter if photons are scattered or not before they are absorbed and cause heat release and thermal expansion, which leads to the acoustic signal. The wavelength of the resultant pressure wave is long enough not to be affected by scattering in biological tissue and easily reaches the detector from depths well below the limits of traditional optical techniques.

Theory of the Photoacoustic Doppler Effect

For the case of a clear medium, with small particle absorbers contained within a flowing fluid traveling with net velocity ${\vec {V}}$, the velocity can be determined non-invasively using the photoacoustic doppler effect. In this technique, the particles within the medium are irradiated with an amplitude modulated continuous wave laser with frequency $f_{0}$, and the resultant acoustic wave is detected by an ultrasonic transducer. The intensity of the source laser is given by:

$I={I}_{0}\left[1+cos\left(2\pi f_{0}t\right)\right]/2$

Figure 1: Photoacoustic Doppler Effect

If the particles were stationary, the resultant acoustic wave would have the same frequency ($f_{(}0)$) as the source. If the particles are moving at ${\vec {V}}$, there is a shift in the frequency of the generated acoustic wave that depends on ${\vec {V}}$, the angles between the flow direction and the photon density wave $\alpha$ and the acoustic wave $\theta$.

$f_{PAD}=-f_{0}{\frac {V}{c_{0}}}cos\alpha +f_{0}{\frac {V}{c_{a}}}cos\theta$

In this expression, $c_{0}$ represents the speed of light in the medium and $c_{a}$ is the speed of sound. The first term of the above expression is the shift in frequency due to the photon density wave seen by the particle acting as a moving receiver. The second term is the frequency shift that results from the photoacoustic wave as it is observed by the ultrasonic transducer. In this case, the particle is the moving source.

In reality, since ${\frac {c_{0}}{c_{a}}}\sim 10^{5}$ and $V\ll c_{a}$, only the second term is detectable. This reduces the above equation to:

$f_{PAD}=f_{0}{\frac {V}{c_{a}}}cos\theta ={\frac {V}{\lambda }}cos\theta$

Based on this, the frequency shift is not affected by the direction of the optical radiation, only by the angle between the flow direction and the detector.

This equation also holds for the case of a flow of small absorbing particles traveling through a scattering medium. In this case, the source is transformed into a diffuse photon density wave which despite having a lower phase velocity than the speed of light, still has a wavelength much longer than the acoustic wave.

Example

The first demonstration of the Photoacoustic Doppler effect was performed by Hui Fang and Konstantin Maslov in the laboratory of Dr. Lihong Wang at Washington University in St. Louis. An overview of the experimental setup is shown in Figure 2. Briefly, a continuous wave diode laser was used in a photoacoustic imaging setup with an ultrasonic transducer as the detector.

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  Figure 2: Photoacoustic Doppler Effect Experimental Demonstration Setup.
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  Figure 3: Flow Direction can be determined from the direction of the Doppler shift.
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  Figure 4: Average PAD Shift vs. Flow Velocity

Flow Measurement in a Clear Medium

An optically clear medium was used to determine the range of flow velocities detectable using PAD technology. The sample consisted of a small tube in a water bath with a syringe pump driven flow of small optically absorbing particles.

Figure 3 shows a shift in the signal from the flowing absorbing particles compared to the reference signal. This demonstrates the Photoacoustic Doppler effect in an experimental setting. Figure 4 shows a graph of average flow velocity vs. the experimental PAD frequency shift. This illustrates that the range of velocities potentially accessible using this technology. Another important feature of this technique is the capability not only to measure average flow velocity but also flow direction. In Figure 3, the top graph in the figure represents a flow away from the detector while the bottom graph represents a flow toward the detector. This result demonstrates that it is possible to determine the direction of the flow from the direction of the Photoacoustic Doppler shift. This could be useful for probing blood flow in small capillaries.

Flow Measurements in an Optically Scattering Medium

As a second example, Figure 5 shows data collected from small absorbing particles with similar size and optical characteristics as red blood cells flowing through a tube in an optically scattering medium instead of a clear water bath. In this case, like the clear medium, it is possible to determine the velocity from the observed PAD frequency shift. Scattering of the source leads to a smaller number of photons that reach the small absorbing particles so the signal has a lower intensity but the shift magnitude is not affected (See Figure 6).

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  Figure 5: Average PAD Shift vs. Velocity for a Scattering Medium
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  Figure 6: Comparison of Signal from Clear Medium and Optically Scattering Medium

The presence of the scattering medium does decrease the maximum detectable flow velocity in the experimental setup but this could be adjusted by changing the laser power or tuning the wavelength in both situations. The reported maximum detectable flow rate is 1mm/s in the scattering medium and 10mm/s in the clear medium. The ability to detect flow direction is also preserved in the scattering case.

See Also

• Photoacoustic spectroscopy
• Photoacoustic imaging in biomedicine
• Photoacoustic tomography
• Doppler effect