assessing relative contribution of samples/ organs towards a diseases in multi-tissue RNAseq

I did an RNAseq on multiple tissues (liver, muscle, heart, kidney, etc) on two groups of mice (disease v.s. control). I wonder are there is a type of analysis I can do so that I can conclude the transcriptomic profile is highly shifted in 1 specific organ? I am not sure whether just a comparison of the crude number of DEGs is a valid way to do it.

e.g. I would like to draw a conclusion: Upon the establishment of the disease, the transcriptomic profile in muscle is the most perturbed, thus we are going to focus on understanding the role of muscle on the disease.