We aim to develop a parallelized simulation focusing on the calculation and visualization of blood flow within human vessels. The project will prioritize developing efficient parallel algorithms for calculating blood particle positions and velocities, utilizing NVIDIA GPUs for optimization. The initial stages will concentrate on modeling blood flow accurately under static conditions, with subsequent phases introducing visualization capabilities.
The foundation of our simulation is rooted in key principles from hemodynamics and fluid dynamics, emphasizing the adaptation of these principles to a parallel computing environment to achieve real-time computation capabilities. The complexities of simulating blood flow, from calculating particle positions in parallel to handling dynamic changes in vessel conditions, present significant computational challenges that our project aims to address.
Our simulation is based on the following key principles and equations:
This principle states that the mass of blood entering a segment of a vessel must equal the mass exiting that segment, assuming the density of blood remains constant. It is given by \(Q = A \cdot v\), where \(Q\) is the blood flow rate, \(A\) is the cross-sectional area of the vessel, and \(v\) is the velocity of the blood flow. This equation is critical for determining the initial and boundary conditions of our simulation.
These equations describe the motion of viscous fluid substances and are fundamental to fluid dynamics. They account for forces that act on the fluid, such as pressure, viscous forces, and external forces. The Navier-Stokes equations are expressed as:
where \(\rho\) is the fluid density, \(\mathbf{v}\) is the velocity field, \(p\) is the pressure field, \(\mu\) is the dynamic viscosity, and \(\mathbf{f}\) represents external forces. These equations are vital for modeling the flow and pressure distribution within the vessel segment.
For laminar flow in narrow, straight tubes, Poiseuille's Law helps calculate the flow rate based on the vessel's geometry and the fluid's viscosity. It is represented as:
where \(P_1 - P_2\) is the pressure difference between the two ends of the vessel, \(r\) is the radius of the blood vessel, \(\mu\) is the dynamic viscosity of the blood, and \(L\) is the length of the vessel. This law provides a simplified model for initial simulations and helps validate more complex computational fluid dynamics (CFD) models.
The challenge of real-time simulation arises from the continuous movement and interaction of particles, requiring significant computational resources to solve the governing equations at each timestep. Parallel computing offers a solution by distributing the computations across multiple processors, reducing the overall simulation time. The use of GPUs, with their high parallelism, is particularly suited for the fine-grained calculations involved in tracking the position and velocity of thousands of blood particles. Similarly, multi-core CPUs can handle broader tasks such as solving Navier-Stokes equations for the entire vessel segment.
The first major challenge is dynamically calculating and updating the positions of thousands of individual particles (representing blood cells and plasma) as they flow through the intricate network of human blood vessels. This task must account for varying vessel diameters, bifurcations, and the physicochemical properties of blood. The complexity is compounded by the need to adjust these calculations in real-time as vessel conditions change due to factors such as vessel constriction/dilation and variations in blood pressure and flow velocity.
The second challenge involves dividing the 3D space representing a segment of the vascular system into a uniform grid, wherein each cell of the grid must manage the particles it contains. This spatial discretization is crucial for efficiently calculating inter-particle forces and interactions but introduces complexity in ensuring that particles are correctly assigned to grids and seamlessly transition between them as they move.
Efficiently scaling the simulation to utilize the full potential of parallel computing resources is a significant challenge. The need to constantly synchronize the state of particles across multiple processors or nodes introduces a high communication to computation ratio, potentially leading to bottlenecks that can diminish the benefits of parallelization.
Optimizing memory access patterns to enhance performance and reduce latency is critical, especially given the irregular memory access patterns that can arise from the dynamic nature of the simulation. Ensuring data locality, where data is kept as close to the processing unit as possible, is challenging but essential for achieving real-time simulation speeds.
We will develop our simulation from scratch, with a strong emphasis on parallel computation for simulating blood flow dynamics. Throughout the implementation process, we will refer to the paper "A Comprehensive Review on Blood Flow Modeling for Blood-Related Diseases" for accurate blood flow calculations and modeling insights. Our implementation will also utilize tools like the CADSS framework and FluidX3D for aspects of fluid dynamics analysis and visualization. The computational workloads will be executed on GHC machines and PSC resources, exploiting their parallel processing capabilities to achieve our objectives.
Our project employs GHC machines and PSC resources, using C++ with CUDA for computational efficiency. This combination optimally supports our blood flow simulation's computational demands and real-time processing needs.
GHC and PSC Resources will provide the necessary high-performance computing power, enabling extensive parallel processing capabilities essential for our simulation's large-scale, real-time computations.
C++ with CUDA ensures efficient, low-level computational performance, exploiting GPU acceleration to manage the simultaneous interactions and dynamics of millions of particles, crucial for modeling blood flow accurately in real-time.
The use of a parallel computing system is driven by the inherently parallel nature of fluid dynamics simulations, requiring the concurrent processing of multiple data points. This setup significantly reduces computation times, enabling real-time simulation and analysis, and making it an ideal choice for the complex workload of simulating human blood flow.