## 2 Materials and Methods
### Experimental System  
The experimental system used for this method was the same as that for DOT. Figure 1 illustrates the schematic of our fast DOT system, which was reported and described in detail previously [35] (pages 7 and 8). Briefly, the light beams from forty-eight high-power NIR LEDs (Epitex, Inc., Kyoto, Japan) at a wavelength of 780 nm were delivered sequentially to forty-eight source positions on the interface via optical fiber bundles. The diffused light received by the detection fiber bundles was detected by high-sensitivity avalanche photodiodes (APDs) (Hamamatsu, El Cajon, CA, USA, C5460-01) and then collected through a data acquisition system (NI, PXI-6358). A field programmable gate array (FPGA) core board (NI, PCI-7811R) was used to control the LED timing sequence and synchronize the data acquisition of the whole system. The output power of LEDs was adjustable through a DC power supply to achieve optimal signal-to-noise ratio (SNR). The photograph inserted in Figure 1 shows the cylindrical optical fiber interface. Forty-eight optical source/detector pairs were distributed equally along the interface with an inner diameter of 4 cm. A single-element, spherically concaved HIFU transducer (H-101, Sonic Concept, Bothell, WA, USA) with a center frequency of 1.1 MHz and focal length of 5 cm was used to treat tissue samples in this study. The transducer had a 64 mm aperture and 62.4 mm radius of curvature. An electrical radiofrequency (RF) signal (sine wave: 1.1 MHz; \(\pm\)10 V peak-to-peak voltage) generated by an arbitrary function generator (AFG3022B, Tektronix, Beaverton, OR, USA) was amplified by an RF power amplifier (PAB LA0005-10, Delta RF technology, Reno, NV, USA; 10 W output) and then was unitized to drive the HIFU transducer. To record the temperatures invasively, a T-type thermocouple (Omega engineering Inc., Norwalk, CO, USA, TJC36-CPSS-020G-6) with a diameter of 500 \(\upmu\)m was inserted into the sample close to the HIFU focus point, and the measured temperature values were synchronously sent to and acquired by the computer through a USB cable. A LabVIEW program was developed to control both the DOT imaging and thermocouple measuring systems. To alleviate the impact of water temperature on the tissue samples, a membrane attached to the bottom of DOT interface was used not only to hold the sample tissues but also to insulate the tissues from water. The water level was carefully adjusted to just reach to the membrane in order to realize good coupling of acoustic signal between water and sample tissues. As the focal length of the HIFU transducer is known and it was easy to determine the focal zone in the water, the relative positions of the HIFU transducer, DOT interface and thermocouple could be set and fixed prior to the HIFU experiments in the water tank without a tissue sample. The HIFU focal point was set to the center of the DOT interface. Then, the water level was adjusted to be the same height as the membrane attached to the DOT interface, which also served as a position marker for the DOT interface in the subsequent experiments. The thermocouple was fixed on a manual translation stage which could move vertically. A marker indicating the insert depth in the tissue was made on the probe to make sure that the thermocouple reached to the focal point of HIFU. Due to the miniaturized size of the thermocouple, its interference on DOT data collection was minimal. A calibration method further alleviated the noise from the thermocouple to the DOT recording [38]. We were careful about the repeatability of thermocouple positioning in tissue and minimized the impact on the temperature measurement using a motion control system with high precision (<0.5 mm), giving the relatively larger focal zone of the HIFU (-4 mm). The measured temperature data shown in the next section indicate that our temperature measurement is repeatable. Moreover, averaging of \(\mu_{s}^{\prime}\) in an area with a diameter of 3 mm was performed to stand for the \(\mu_{s}^{\prime}\) value at the HIFU focus point.