Summary The cells of the sinoatrial node (SAN) are self‐excitable entities that show a coupled electrical pattern that consists of the synchronized activation of action potentials that determine the heart rate. To accurately describe the behavior of cell membrane proteins, theoretical biophysicists have devoted themselves to the study of the electrical activity of individual cells, which involves solving a large number of coupled differential equations. This computational limitation makes the modeling of a large number of cells unattainable, since the intracellular distribution of Ca2+ must be considered and this fact increases in grand extent the number of differential equations involved. In this work, we explore different parallel architectures (using OpenMP, MPI, and CUDA libraries) to show advances in the computational modeling and simulation of the SAN using a multicellular array in which the cells are endowed of heterogeneous conductances and are electrically coupled, considering a variable connectivity among them.

The sinoatrial node (SAN) has the function of initiating a depolarizing wave that runs throughout the heart. This wave produces the muscular contraction necessary to blood pumping in animals. In recent years different works have been proposed to simulate the electric potential behaviour of a single sinoatrial cell (SANC) and groups of cells, hence a set of differential equations needs to be solved for each microsecond of simulation. An important drawback comes up when the synchronization of millions of SANCs is required involving a huge processing time. Since the simulation of the behavior of a set of cells is an open research topic, it is important to propose efficient tools to reduce response times; unfortunately, because the complexity of the existent models of SANC, very scarce work has been done to this end. This paper proposes three parallel algorithms to simulate the synchronization of a set of SANCs based on the model of Severi (2012). The proposed approaches are built using OpenMP, MPI, and CUDA, in order to compare the benefits given by different computing platforms. We found that all parallel versions perform better when defining a cell per processing unit; however the CUDA version gives the best results in scalability and performance.

Pore networks can be simulated in silico by using the dual site-bond Model. In this approach, a set of cavities (sites) are interconnected to each other by means of a set of throats (bonds), while considering that each site should be always larger than any of its delimiting bonds. The NoMISS greedy algorithm has been implemented recently in order to address this task; nevertheless, even if this procedure is relatively fast, there arises problems related to large memory consumption and long computing time, as pore networks become somewhat large. Here, three parallel methods are proposed to allow a proficient construction of large pore networks. The first method is a parallel Monte Carlo procedure, which applies a number of exchanges among pore sizes in order to obtain a valid pore network. The other two methods are parallel versions of the pioneering NoMISS greedy algorithm. The first version uses a static data partitioning to speed up the running time, whilst the second applies a dynamic data distribution policy to improve the pore network quality. The obtained results show the behavior of each proposed version with respect to their performance and quality, by employing the resources of a 125-core Linux cluster.

Porous media simulation is an important contribution in the study of many physical phenomena. The No MISS greedy algorithm outstands from the existing sequential algorithms for constructing a pore sub network, in a relatively fast way. However, despite the No MISS time reduction, there are still problems related to the required processing time when very large networks need to be studied. In this work, a non scalable parallel version of the No MISS algorithm is presented, and a new approach is proposed to alleviate this issue, in both versions cluster cores work simultaneously on different porous sub network spaces. The first approach, named as Unbounded-No MISS, allows the cores to go forward with the initialization of the porous sub network space, applying a balancing policy when a core needs more data. At the end, the cores require a sequential synchronization to finish the porous network construction. The second approach, named as Bounded-No MISS, controls the porous sub network initialization by considering a site-size boundary, avoiding the final strong synchronization and improving considerably the scalability. The obtained results using a 125-core cluster are presented.

Load balancing algorithms are an essential component of parallel computing reducing the response time of applications. Frequently, balancing algorithms have a centralized behavior requiring a lot of messages to operate, thus causing scalability problems. A solution to improve scalability is to define a decentralized algorithm, avoiding the generation of bottlenecks. DLML (Data List Management Library) is a tool that, in a transparent way, allows the parallel processing of data that are organized through a List. One drawback of this tool is the global bidding algorithm used to distribute the data (work) generated during the execution. In this paper two load balancing algorithms for DLML handling partial information are proposed. The first algorithm considers a logical Torus topology and the second one follows a Binary Tree topology for communications. Results show how the scalability of DLML was improved, using two clusters of 40 and 1024 processing units, and executing dynamic and static applications.