The liver is the largest internal organ in the human body and performs a wide range of essential functions. Early detection of liver disease is crucial, as its progression can lead to life-threatening conditions. Currently, liver disease is commonly diagnosed using images obtained through Azan staining or hematoxylin and eosin (HE) staining. However, these staining methods do not visualize capillaries, and therefore, structural changes in capillaries are typically not considered during clinical diagnosis. According to experts’ knowledge, liver capillaries undergo specific structural transformations as the disease progresses. Until recently, there was no established method to evaluate these changes. In our previous research, we developed techniques that enable such analysis. In this paper, we use fluorescently stained images and apply our previously proposed algorithm to extract the capillary network structure in the liver. We design a method that estimates disease progression based on the cumulative distribution of path lengths in linear segments. Our findings show that disease progression results in distinct differences in the path length distribution in the linear segments of the capillary network structure, suggesting that changes in capillary structure could serve as a basis for a novel diagnostic method.