In this paper, we aim to model the formation of data dissemination in online social networks (OSNs), and measure the transport difficulty of generated data traffic. We focus on a usual type of interest-driven social sessions in OSNs, called \emph{Social-InterestCast}, under which a user will autonomously determine whether to view the content from his followees depending on his interest. It is challenging to figure out the formation mechanism of such a Social-InterestCast, since it involves multiple interrelated factors such as users' social relationships, users' interests, and content semantics. We propose a four-layered system model, consisting of physical layer, social layer, content layer, and session layer. By this model we successfully obtain the geographical distribution of Social-InterestCast sessions, serving as the precondition for quantifying data transport difficulty. We define the fundamental limit of \emph{transport load} as a new metric, called \emph{transport complexity}, i.e., the \emph{minimum required} transport load for an OSN over a given carrier network. Specifically, we derive the transport complexity for Social-InterestCast sessions in a large-scale OSN over the carrier network with optimal communication architecture. The results can act as the common lower bounds on transport load for Social-InterestCast over any carrier networks. To the best of our knowledge, this is the first work to measure the transport difficulty for data dissemination in OSNs by modeling session patterns with the interest-driven characteristics.