Obtaining true diffusivity constant

A system comprising:

• an acoustic monitoring device that detects acoustic waves that have traveled through a tissue sample;
• and
• a computing device communicatively coupled to the acoustic monitoring device, the computing device is configured to evaluate a speed of the acoustic waves based on a time of flight and including instructions, when executed, for causing the processing system to perform operations comprising:
• setting a range of candidate diffusivity constants for the tissue sample;
• simulating a spatial dependence of a reagent within the tissue sample for a plurality of time points and for a first of the range of candidate diffusivity points;
• determining a modeled time-of-flight based on the spatial dependence;
• repeating the spatial dependence simulation for each of the plurality of diffusivity constants;
• and
• determining an error between the modeled-time-of-flight for the plurality of diffusivity constants versus an experimental time-of-flight for the tissue sample;
• wherein a minimum of an error function based on the error yields a true diffusivity constant for the tissue sample.

A method of determining a diffusivity constant of a fluid diffusing into a porous material, said method comprising:

• (a) immersing a sample of the porous material into a volume of the fluid;
• (b) collecting a set of acoustic data for the sample of the porous material immersed in the volume of the fluid with an acoustic monitoring system and transmitting said acoustic data set to a signal analyzer, said acoustic data set comprising:
• (b1) absolute sound velocity of ultrasonic waves in the porous material prior to diffusion with fluid;
• (b2) TOF of ultrasonic waves through the porous material at least at one time point during diffusion of fluid into the porous material (TOFexperimental);
• (b3) absolute sound velocity of ultrasonic waves in the fluid;
• and
• (b4) a thickness of the porous material;
• (c) calculating a diffusivity constant for diffusion of the fluid into the porous material on a signal analyzer by:
• (c1) modeling a TOF trend for each of a plurality of candidate diffusivity constants by:
• (c1a) selecting a first candidate diffusivity constant;
• (c1b) selecting a plurality of diffusion times corresponding to the time points of (b2);
• (c1c) calculating a concentration of the fluid at each of a plurality of depths through thickness (b4) of the porous sample as a function of time and space;
• (c1d) calculating a total amount of diffused reagent at each time point (cdetected)
• (c1e) calculating an expected TOF differential resulting from the concentration determined in (c1d) as a linear combination of (b1) and (b3);
• and
• (c1f) repeating (c1a)-(c1e) for a plurality of candidate diffusivity constants;
• (c2) calculating an error function between the TOF of (b2) and each of the TOF differentials calculated from (c1) as a function of diffusivity constant, wherein the true diffusivity constant is a minimum of the error function.