A method of fixing tissue sample, said method comprising: (a) immersing an unfixed tissue sample in a volume of a fixative solution at a temperature from 0 to 10 °C; (b) monitoring a rate of diffusion of the fixative solution into the tissue sample by: transmitting an ultrasonic acoustic signal through the tissue sample and detecting the ultrasonic acoustic signal after the ultrasonic signal has passed through the tissue sample; calculating the time of flight of the ultrasonic acoustic signal; repeating and at a plurality of subsequent time points; calculating a rate of diffusion at least at each of the subsequent time points by analyzing a slope of a curve of the TOFs calculated from the ultrasonic acoustic signals measured at each of the time points; determining when the rate of diffusion falls below a predetermined threshold, the determination comprising: repeating - and fitting the TOFs of two or more of the time points to a single exponential curve until the fit exceeds a predetermined confidence cutoff; and after the fit exceeds the predetermined confidence level, calculating an amount of time needed to reach the predetermined threshold rate of diffusion, wherein the predetermined threshold rate of diffusion has been met when the amount of time needed to reach predetermined threshold rate of diffusion has expired; and (c) after the rate of diffusion falls below the predetermined threshold, allowing the tissue sample to warm to a temperature in the range of 20 °C to 55 °C for a period of time sufficient to permit fixation of the tissue sample. (a) immersing an unfixed tissue sample in a volume of a fixative solution at a temperature from 0 to 10 °C; (b) monitoring a rate of diffusion of the fixative solution into the tissue sample by: transmitting an ultrasonic acoustic signal through the tissue sample and detecting the ultrasonic acoustic signal after the ultrasonic signal has passed through the tissue sample; calculating the time of flight of the ultrasonic acoustic signal; repeating and at a plurality of subsequent time points; calculating a rate of diffusion at least at each of the subsequent time points by analyzing a slope of a curve of the TOFs calculated from the ultrasonic acoustic signals measured at each of the time points; determining when the rate of diffusion falls below a predetermined threshold, the determination comprising: repeating - and fitting the TOFs of two or more of the time points to a single exponential curve until the fit exceeds a predetermined confidence cutoff; and after the fit exceeds the predetermined confidence level, calculating an amount of time needed to reach the predetermined threshold rate of diffusion, wherein the predetermined threshold rate of diffusion has been met when the amount of time needed to reach predetermined threshold rate of diffusion has expired; and transmitting an ultrasonic acoustic signal through the tissue sample and detecting the ultrasonic acoustic signal after the ultrasonic signal has passed through the tissue sample; calculating the time of flight of the ultrasonic acoustic signal; repeating and at a plurality of subsequent time points; calculating a rate of diffusion at least at each of the subsequent time points by analyzing a slope of a curve of the TOFs calculated from the ultrasonic acoustic signals measured at each of the time points; determining when the rate of diffusion falls below a predetermined threshold, the determination comprising: repeating - and fitting the TOFs of two or more of the time points to a single exponential curve until the fit exceeds a predetermined confidence cutoff; and after the fit exceeds the predetermined confidence level, calculating an amount of time needed to reach the predetermined threshold rate of diffusion, wherein the predetermined threshold rate of diffusion has been met when the amount of time needed to reach predetermined threshold rate of diffusion has expired; and repeating - and fitting the TOFs of two or more of the time points to a single exponential curve until the fit exceeds a predetermined confidence cutoff; and after the fit exceeds the predetermined confidence level, calculating an amount of time needed to reach the predetermined threshold rate of diffusion, wherein the predetermined threshold rate of diffusion has been met when the amount of time needed to reach predetermined threshold rate of diffusion has expired; and (c) after the rate of diffusion falls below the predetermined threshold, allowing the tissue sample to warm to a temperature in the range of 20 °C to 55 °C for a period of time sufficient to permit fixation of the tissue sample.