A multivariate distribution can be represented in terms of its underlying margins by binding these margins together using a copula function (Sklar, 1959). Here, we propose a new class of survival FGM-type modification truncated copulas which quantify dependency and incorporate directional dependence. In addition, we apply our proposed methods to the analysis of directional dependence relationships between genes. Finally, we employ the Akaike Information Criterion (AIC) to check the goodness of fit for our proposed copula models.