Population balance equations have been used to model a wide range of processes including polymerization, crystallization, cloud formation, and cell dynamics. Rather than developing new algorithms specific to population balance equations, it is proposed to adapt the high‐resolution finite volume methods developed for compressible gas dynamics, which have been applied to aerodynamics, astrophysics, detonation waves, and related fields where shock waves occur. High‐resolution algorithms are presented for simulating multidimensional population balance equations with nucleation and size‐dependent growth rates. For sharp distributions, these high‐resolution algorithms can achieve improved numerical accuracy with orders‐of‐magnitude lower computational cost than other finite difference and finite volume algorithms. The algorithms are implemented in the ParticleSolver software package, which is applied to batch and continuous processes with one and multiple internal coordinates. © 2004 American Institute of Chemical Engineers AIChE J, 50: 2738–2749, 2004

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We studied 53 samples of cerebrospinal fluid (CSF) by cytologic examination and immunophenotyping by flow cytometry. The samples were taken from 43 patients; 25 had a previous diagnosis of malignant lymphoma/leukemia and the remaining 18 a variety of other diseases involving the central nervous system (CNS). Lymphoma/leukemia was detected in 21 samples: 12 by morphologic examination and immunophenotyping and nine by immunophenotyping alone. There were two cases with a suspicious morphologic examination and negative immunophenotyping in which the final diagnosis were cryptococcal and viral meningitis. In the group of 18 patients, one was diagnosed as a primary malignant lymphoma of the CNS and was positive with cytology and immunophenotyping. The other 17 were negative with both methods and follow-up showed no evidence of lymphoma/leukemia. This study shows that morphologic examination combined with flow cytometry enhances the detection rate by 75% over morphologic examination alone in CSF samples.