Novel hybrid GPU-CPU implementation of parallelized Monte Carlo parametric expectation maximization estimation method for population pharmacokinetic data analysis

Abstract

The development of a population PK/PD model, an essential component for model-based drug development, is both time- and labor-intensive. A graphical-processing unit (GPU) computing technology has been proposed and used to accelerate many scientific computations. The objective of this study was to develop a hybrid GPU-CPU implementation of parallelized Monte Carlo parametric expectation maximization (MCPEM) estimation algorithm for population PK data analysis. A hybrid GPU-CPU implementation of the MCPEM algorithm (MCPEMGPU) and identical algorithm that is designed for the single CPU (MCPEMCPU) were developed using MATLAB in a single computer equipped with dual Xeon 6-Core E5690 CPU and a NVIDIA Tesla C2070 GPU parallel computing card that contained 448 stream processors. Two different PK models with rich/sparse sampling design schemes were used to simulate population data in assessing the performance of MCPEMCPU and MCPEMGPU. Results were analyzed by comparing the parameter estimation and model computation times. Speedup factor was used to assess the relative benefit of parallelized MCPEMGPU over MCPEMCPU in shortening model computation time. The MCPEMGPU consistently achieved shorter computation time than the MCPEMCPU and can offer more than 48-fold speedup using a single GPU card. The novel hybrid GPU-CPU implementation of parallelized MCPEM algorithm developed in this study holds a great promise in serving as the core for the next-generation of modeling software for population PK/PD analysis.

Fig. 1

Flow chart of MCPEM_GPU algorithm in heterogeneous GPU–CPU computing platform. Boxes highlighted in gray computation within GPU processor cores

Fig. 2

Box plots of percent relative estimation error (RER) for model parameters in MCPEM_GPU for a first and b second model/sampling design scenario. CL clearance; V _c volume of distribution at central compartment; Q distribution clearance; V _p volume of distribution at peripheral compartment; ω ² _CL population variance of CL; ω ² _Vc population variance of V _c; ω ² _Q population variance of Q; ω ² _Vp population variance of Vp; σ ² variance of intra-individual proportional error model. N _MC = 10000; N _SUB = 100. Both MCPEM_GPU and MCPEM_CPU produced identical results

Fig. 3

a The relationships between mean model computation time of the MCPEM_CPU, MCPEM_GPU and MCPEM_NONMEM, and speedup factor of MCPEM_GPU with N _MC for first model/sampling design scenario. N _SUB = 100; Number of simulated trials = 100. b The relationships between mean model computation time of the MCPEM_CPU, MCPEM_GPU, and MCPEM_NONMEM, and speedup factor of MCPEM_GPU with N _SUB. N _MC = 1000; Number of simulated trials = 100. Closed circle MCPEM_CPU; closed square MCPEM_GPU; closed triangle MCPEM_NONMEM; open circle speedup factor (SF)

Fig. 4

a The relationships between mean model computation time of the MCPEM_CPU, MCPEM_GPU, and MCPEM_NONMEM and speedup factor of MCPEM_GPU with N _MC for second model/sampling design scenario. N _SUB = 100; Number of simulated trials = 100. b The relationships between mean model computation time of the MCPEM_CPU, MCPEM_GPU, and MCPEM_NONMEM, and speedup factor of MCPEM_GPU with N _SUB. N _MC = 1,000; Number of simulated trials = 100. Closed circle MCPEM_CPU; closed square MCPEM_GPU; closed triangle MCPEM_NONMEM; open circle speedup factor (SF)