Model Pertumbuhan Diffuse Large B-Cell Lymphoma di Germinal Center Mempertimbangkan Centrocytes dalam Keadaan Steady-State

Najida Humaira, Prof. Dr. Fajar Adi Kusumo, S.Si., M.Si.

2026 | Tesis | S2 Matematika

Penelitian ini berfokus pada pemodelan matematika dan analisis pertumbuhan diffuse large B-cell lymphoma (DLBCL) di germinal center. Penelitian ini bertujuan untuk menjelaskan dinamika interaksi antara centroblast, plasmablast, sel DLBCL, dan sel efektor, mempertimbangkan centrocytes dalam keadaan steady-state. Model matematika yang dikembangkan berupa sistem persamaan diferensial nonlinear empat dimensi. Interaksi penghambatan sel DLBCL terhadap sel normal dimodelkan menggunakan kinetika Michaelis Menten untuk menggambarkan adanya efek kejenuhan dalam interaksi biologis. Analisis dilakukan dengan menentukan titik ekuilibrium, syarat eksistensi, dan kestabilan lokal. Selanjutnya simulasi numerik dilakukan menggunakan Maple dan Python untuk menganalisis perilaku solusi pada beberapa daerah bifurkasi. Penelitian ini diharapkan dapat memberikan wawasan mengenai peran kapasitas pertumbuhan sel DLBCL dan inaktivasi sel efektor dalam menentukan dinamika perkembangan DLBCL.

This study focuses on the mathematical modeling and analysis of the growth of diffuse large B-cell lymphoma (DLBCL) in the germinal center. This study aims to explain the interaction dynamics among centroblasts, plasmablasts, DLBCL cells, and effector cells by considering centrocytes in a steady-state condition. The mathematical model developed in this study is a four-dimensional nonlinear system of differential equations. The inhibitory effect of DLBCL cells on normal cells is modeled after Michaelis Menten kinetics to represent the saturation effect in biological interactions. The analysis is carried out by determining the equilibrium points, their existence conditions, and local stability. The numerical simulations are performed using Maple and Python to analyze the behavior of solutions in several bifurcation regions. This study is expected to provide insight into the roles of DLBCL cell growth capacity and effector cell inactivation in determining the dynamics of DLBCL progression.

Kata Kunci : diffuse large B-cell lymphoma, germinal center, mathematical model