Subject is one 24-year-old healthy male. A measurement area is skin in his forearm.

The velocity induced by the pulsation was measured from the RF echo data of the fixed position by implementing a 1-D cross correlation method. RF signal of time t at depth z was defined as r _t (z). Analytical signal g _t (z) was obtained by applying the Hilbert transform to the RF signal r _t (z). Pulse waves with angular frequency ω ₀ = 2πf ₀ were transmitted at a time interval of ΔT. Analytical signal of time t and t + ΔT at depth z can be modeled as

where u(z) was the envelope of the analytical signal, f _s was the sampling frequency, c ₀ was the sound speed, θ ₀ was the initial phase, and z _τ was the true displacement induced by the pulsation. The complex cross-correlation function γ(z _lag ) at lag z _lag was defined as

where N was 1-D cross correlation window of 256 pixels, corresponding to 195 μm depth window with 91 % overlap using hamming window. An index at maximum value of the real part of the Eq. (21.3) corresponded to the index of . In this paper, f _s was 1 GHz, and the temporal resolution was enough high to observe the deformation with HFUS of 100 MHz. Additionally, the received RF signal was up-sampled to 4 GHz before implementing the 1-D cross-correlation. Because of these reasons, the estimated displacement was almost equal to the true displacement z _lag . The velocity, denoted by v _{t + ΔT/2}(z), of the skin in his forearm between the interval was given as follows:

The acceleration was calculated from the measured velocity. The acceleration was calculated by differentiating the measured velocity as

By comparing an acceleration at reference depth with an acceleration at interest depth, a velocity of shear wave propagating from an artery toward a skin surface can be calculated from a relationship between the depth and the arrival time of shear wave at the depth. The relationship φ(z) can be expressed as

where N _α was an estimation window of 50 pixels, corresponding to a 50 ms time. A hamming window was used for the estimation. A variable z ₀ was a reference depth, and a variable z was an interest depth. A time lag between the reference depth and the interest depth was expressed as follows:

The center frequency f _c was obtained from the power spectrum calculated by applying the Fourier transform to the acceleration signals. Figure 21.3 shows the relationship between the depth z and the time lag. A regression line can be obtained by applying the least square method to the relationship. A slope a ₁ of the regression line can be obtained by minimizing a least mean square error e as follows:

A variable Z _N is a total number of the region of interest. The velocity C _s of shear wave was given by dividing the depth distance Δz by the estimated slope value