## 2 Materials and Methods
### Measurement Method of Sound Velocity in Human Crus  
An experiment was conducted to measure the sound velocity in human fat and muscle in the crus using the method of simultaneous US imaging and MRI. The probe was placed on the top of the crus. The focal length for the transmission beam was set at 30 mm. The MRI scan parameters for human crus imaging are shown in Table 3. An RF receiving coil for the knee was used in the MRI setup. The thickness, L, of muscle and fat was measured by MRI. The time-of-flight, T, was measured by using an ultrasonic echo signal. Thus, the sound velocity, c, was estimated to be c = 2L/T. The crura of three subjects were measured. Experimental Imaging of an Abdominal Phantom using the Proposed Method of Compensating for the Sound Velocity Distribution to Correct Beamforming  
An experiment was conducted to evaluate the accuracy with which the sound velocity distribution was measured during simultaneous US imaging and MRI of an abdominal phantom. Image degradation was compensated for by correcting beamforming using the measured sound velocity \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Maximum Number of** & **Number of TX/RX** & **A/D** & **Sampling** & **Memory** \\
**Probe Interface** & **Channels** & **Resolution** & **Frequency** & **Capacitance** \\  & **Channels** & **(Bits)** & **(Hz)** & **Channel (MB)** \\ \hline
256 & 128 & 12 & 31.25 & 256 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specifications of US imaging equipment. Figure 3: A simultaneous multimodality imaging system consisting of ultrasound (US) imaging equipment (RSYS0006 MRF, Microsonic Co., Tokyo, Japan) and an MRI scanner (Echelon Vega, 1.5T, Hitachi Co., Tokyo, Japan). The probe that was placed in the MRI scanner was connected to the US imaging equipment via a connector that passed through the walls shielding the MRI room and the control room. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sequence** & **TR** & **TE** & **Thickness** & **Slices** & **Frequency Encoding** & **Phase Encoding** \\ \hline SE & 937 ms & 19.7 ms & 2.0 mm & 30 & 256 & 180 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: MRI scan parameters for human crus. distribution. The Model 075A abdominal phantom (Triple Modality 3D Abdominal Phantom, CIRS, USA) was used in the experiment. The probe was placed on the top of the phantom. Agar gel containing 5% glycerol was placed between the phantom and the probe to avoid air cavities, as shown in Figure 4. The driving waveform to the transducers was a square wave containing 1.5 sinusoidal waves. The pulse repetition time was 190 \(\upmu\)s. The focal length for the transmission beam was set at 30 mm using the conventional array focusing technique. Since the phantom consists of four regions with different sound velocities as shown in Figure 4, the sound velocity in each region was estimated using simultaneous US imaging and MRI. For each region, the length was represented by L and the time-of-flight was represented by T, so the sound velocity c was estimated to be c = 2L/T. The delay time for each element to form a beam must be calculated based on the estimated value of sound velocity on the path from an element to an arbitrary position during simultaneous imaging. The signal processing was as follows: (1) RF data acquisition of 128 elements in a 128-channel digital format at 12 bits and 31.25 MHz; (2) the RF data of each channel were delayed by a certain amount of time calculated by Equations (1) or (2); (3) after quadrature detection at 5.0 MHz, the magnitude was calculated; and (4) the B-scan image was calculated using the logarithmic magnitude in a dynamic range of 60 dB. For the conventional dynamic focusing in reception, the delay time of the \(i\)th element of the transducers \(\tau_{i}\) is expressed as  
\[\tau_{i}=-\frac{(i\Delta x-a/2)^{2}}{2 cl_{F}} \tag{1}\]  
where \(\Delta x\) is the element pitch, \(a\) is the aperture length, \(c\) is the sound velocity, and \(l_{\text{F}}\) is the focal length.