The application is an implanted sensor and I am asked to characterize the transmission channel. I did measurements with bio-equivalent liquid and got a plot of the path loss over distance. The professor asked me to apply the log-distance path loss model to my result and I got a nice figure by fitting the measured results in a semi-log graph. However, I highly doubt if it makes sense as I do not think the wave in the bio-equivalent liquid is the same as that in the air (even with obstacles).
First consider what the Free Space Path Loss (FSPL) equation is modeling. As power propagates from the transmitting antenna in free space, it continues to spread out, lowering the power density (watts per square meter) at the receive antenna locus. On the receive side, the effective aperture (square meters) of the receive antenna is fixed for a given frequency. So as the distance is increased, the received power is decreased according to the inverse square law. The balance of the formula adjusts for the gain of the receive and transmit antennas.
Now consider what is not included in the FSPL equation:
The human body acts as a dielectric. This dielectric will likely introduce additional path loss. The permittivity ε, permeability μ, and conductivity σ of the human dielectric would have to be included in the model.
The FSPL equation requires that the receive and transmit antennas be oriented such that the direction of their stated gains are pointed toward each other. This may not consistently be the case in your application so you may need to include some factor to adjust for potential misalignment of the antennas. In the simple case of polarity misalignment, this could introduce a significant loss factor.
The FSPL equation does not include any effects from absorption, scattering, reflection or refraction of signals. Depending on the frequencies involved, any bones, cartilage, denser tissues, urolithiasis, nephrolithiasis, etc. may cause such effects that would then need to be included in the model.
There are probably a few additional considerations that are not coming to mind at the moment but the above exemplify the need for a more rigorous model beyond simple FSPL.
In response to questions by the OP in the comments:
Using an SA is an excellent choice provided that the target receiver has been well characterized and documented so as to be able to translate SA observations to the expected receiver performance. The receive antenna, feedline, and feedline length should be identical to the target configuration to avoid errors in projected performance. If the complex input impedance of the SA does not match that of the target receiver, construct and characterize an appropriate impedance transformation network if you are not comfortable with mathematically netting out the effects of the mismatch.
Regarding the challenges of modelling or testing a heterogeneous medium, I must say I am not a biomed engineer. But I would consider volunteer, cadaver or animal testing in order to validate my models. The biomed engineering field is well established and may have suitable, qualified models for your application that could raise the confidence level of the prediction.
When you have completed and have validated your heterogeneous model(s), describe the results in the form of a link budget. You can add a further burden to the budget to ensure an appropriate safety factor. Depending on the application, there may be safety or regulatory requirements that must also be addressed.