In the name of GOD

1. In the name of GOD

2. Chapter 11 Methods for measuring speed, attenuation, Absorption and Scattering

3. For a better understanding of the ultrasonic images we have to measure different ultrasonic properties of biological tissues. Most important parameters are: • Velocity • Attenuation • Scattering • Absorption

4. Velocity • In vitro Methods • Can be measured with continuous or pulse wave • Interferometeric method • Use a continuous wave • Accuracy can be of the order of 0.1% • A standing wave is set up between reflector and transducer • Wavelength can be measured by adjusting the position of the reflector

5. Pulse echo method • Arrangement as above can be used for pulse excitation • TOF method is used (t=2x/c) • The accuracy depends on the sharpness of the pulse and the attenuation in the sample • Improvement in accuracy can be made using substitution method, in this case we have:

6. To eliminate tissue thickness below set up can be used. • Tm and Tw are TOF with and without sample in the propagation path • T1 and t2 are TOF for pulse to travel from the transducer to the front and rare faces of the sample • cw and cm are sound velocity in the sample and water

7. Velocity difference method • An extremely accurate (0.01%) method for fluid • A reference liquid and the sample separated by a thin membrane. • If a carriage move the T and R Transducers by Δx, it can be shown that Δt is given by: • In this equation all parameters are known except cm • CW can also be used. In this case phase change must be measured instead of TOF

8. In vivo methods • Very few of the in-vitro methods can be applied to in-vivo conditions • One method for in-vivo measurements is registration method (Chen et al, 1987) • If a target D can be found by B-scan at a position, we have AB=c0Δt . Δt is the TOF. • At another position A’ we have A’B’=c0Δt’ • In triangle AA’D we have: • C1 is the true velocity and AB=(c0/c1)AD • We can write: • L can be measured physically and l estimated from the image • The method has several problems: • 1-Assume no refraction at the boundaries • 2-Target can be found

9. Another approach used by Kondo et al (2000) is with a linear array • If the distance between two elements Δy and sinθ0 is known • T1AR1=t11 and t12=T2BR2 and t21=T2CR2 can be measured, the local sound speed c0 can be defined by ABC as: • It is assumed that θ0 =θ1

10. Attenuation • In vitro methods • A) Transmission methods • Can be done with narrow or broadband pulse • Both can be done with fixed or variable path • Advantage of fix path is the reduction of the error due to diffraction • Setting for fixed path is the same as for velocity measurement • If attenuation coefficient in reference liquid and sample is α0 and α and the pressure p0 and p after the carriage movement we have: • This is not a suitable method for biological tissue

11. A better method is substitution method • To reduce phase cancellation a small hydrophone used for receiving signal • If the scope has capability of FFT then: • Rt is the transfer function of the system • T=Transmission coefficient • α0 and α are attenuation coefficient in reference and sample • Dividing the two we have • If T≈1 then • Advantage: not necessary to no Rt • In attenuation measurement thickness measurement is not critical as in velocity measurement

12. Transient thermoelectric method • As mentioned earlier attenuation consists of absorption+Scattering • In the medical range 2 to 15MHz scattering loss is minimal • More than 99% of absorbed energy change to heat • If we measure the temperature change we can calculate absorption by: • Cp, J and I are the specific at constant pressure of tissue, mechanical heat conversion (4.18)J/cal) and acoustic intensity • denotes the slope of temperature rise as a function of time at time t0

13. The first phase of the curve can not be used because of the heat exchange • This method to be valid • The thermocouple wire and bead should be very thin (<75um) • The half power beam width grater than 3mm to minimize heat loss • Temperature rise <1 degree • The method is useful for high frequency and tightly focused beam

14. Another approach is Parkers (1983) for pulse decay technique: • A Gaussian intensity profile beam is assumed. • Beam is scanned across an embedded thermocouple of 51um diameter • The intensity profile is • X0 is a measure of beam width • After Δt and assuming no significant heat conduction, temperature distribution along x is: • From main equation we have: • The temperature decay as a function of time found by Parker is • At x=0 or on beam axis: • Kd is the thermal diffusitivity of the medium surrounding the sensor and is equal to 1.5x10-3 cm2/s • Tm can be estimated from the temperature decay history on the beam axis • Other parameters of Im, Δt Cp and J are known

15. In vivo methods • Methods can be classified into two categories of: • Amplitude loss methods • Frequency shift methods

16. Amplitude loss methods • If amplitude loss in terms of thickness is measured the attenuation coefficient can be calculated • In this method diffraction compensation must be done

17. Frequency shift method • The basics is shown in figure • Two spectral region at different depth is selected and the spectral of each region is obtained. • The two spectral at analog frequencies are divided • Slope of the logarithmic graph is the attenuation coefficient • The method should be repeated several time to obtain meaningful results

18. Scattering • Scattering can be measured only for two extreme cases of Scatterer size>>wavelength and Scatterer size<<wavelength • If scatterer concentration is n is very small then: 2α=n(σs+σa) • If the scattering is the dominate (σs>>σa) then attenuation is equal to scattering • For the cases when scatterer size<<λ wavelength than from figure we have:

19. If the transmitted ultrasound is a burst at frequency f, the scattered intensity from a region of tissue can be selected by time gating and we have: • η=nσb andσb is backscattering cross section for very small n ηV can be used for volume scattering For dense scatterer such as biological tissue, the power received by the transducer of aperture size A is (assuming R>>z0) By measuring S, P0, α, and α0 the backscattering coefficient can be calculated. The need for measuring P0 can be eliminated by using a reflected pulse from a reflector

20. For a nonfocused transducer, we can assume, the transducer in the far field is a point source. • Applying mirror theory, the transducer as a receiver would appear as if it were located at a distance 2R from the source. • The received power from the reflector with aperture A is: • Г is reflectivity of the reflector and is about one • Dividing the above two equations we have: • This equation can be converted to dB as: • It can be seen that the backscattering coefficient can be calculated by measuring the difference in the scattering power and reflected power in dB if other parameters are known • This method not be used for focused beam as it result a large error

21. The method can be used for wideband pulse using FFT for received pulse • Other methods can also be used such as comparative method

22. In vivo methods • Gray level of a tissue in ultrasonic B-mode can be used to calculate scattering coefficient • Raw data also can be obtained and used to measure backscattering coefficient