A Java High Performance Tool For Topological Data Analysis

Topological Analysis of Epidermal Cells

We applied jHoles for the study of the epidermis cells before and after a tumor. The in silico model has been obtained following the indications provided in [1]. Briefly, models for tumor growth and skin turnover are combined with pharmacokinetic (PK) and pharmacodynamic (PD) models to assess the impact of two alternative dosing regimens on efficacy and safety. We studied the evolution of the topology (or the local connectivity). Epidermal cells sequentially pass three compartments, named proliferative (pc), differentiated (dc), and stratum corneum (sc) compartments. We obtained a network representation of the compartments connecting the cells using both their admissible evolution (i.e., proliferative are connected only with differentiated and differentiated with stratum) and their concentration. 

The statistics of the networks are:

The homological analysis of the network for the healthy epidermis shows a higher number of holes that means a more spread cells distribution (the Betti numbers sequence: β0 = 1, β1 = 28698 and β2 = 351), due to the presence of the three compartments. After the tumor the topology of network changed and the new sequence of Betti number is β0 = 1 and β1 = 24698 with a reduced number of holes that means healthy cells disappeared and the network is less connected [2].

Pathological tissue - Persistent diagrams for β1

Before Cancer After Cancer
Number of Nodes: 98
Number of Links: 393
Average Node Degree: 4.01
Average Clustering Coefficient: 0.190
Number of Nodes: 48
Number of Links: 269
Average Node Degree: 5.60
Average Clustering Coefficient: 0.165

Healthy tissue - Persistent diagrams for β1


[1] RONALD GIESCHKE AND DANIEL SERAFIN. Development of Innovative Drugs via Modeling with MATLAB. Springer, 2013.

[2] JACOPO BINCHI, EMANUELA MERELLI, MATTEO RUCCO, GIOVANNI PETRI, AND FRANCESCO VACCARINO. jHoles: A tool for understanding biological complex networks via clique weight rank persistent homology. Electronic Notes in Theoretical Computer Science, 306:5–18, 2014.