A Framework for Interpreting White Blood Cell Counts from Lumbar Punctures in Pediatric Acute Lymphoblastic Leukemia

In pediatric acute lymphoblastic leukemia (ALL), central nervous system (CNS) involvement is staged using white blood cell (WBC) counts from lumbar punctures (LPs), microscopy of LP-derived cells, and CNS imaging. CNS staging informs the need for additional intrathecal chemotherapy, which can result in side-effects including significant neurotoxicity. However, nearly 20% of LPs are traumatic, or contaminated by peripheral blood. In these cases, the Steinherz-Bleyer (S-B) algorithm is used instead of WBC counts to determine CNS involvement. The intuition for this algorithm has not been presented. In this work, we conceptualize LP lab values as a mixture of blood and cerebrospinal fluid (CSF) and present this mixture as a convex combination problem. Then, we demonstrate that the S-B algorithm asks whether the CSF to blood WBC ratio is at or above that of the mixing ratio (i.e., contaminated to uncontaminated ratio). Additionally, we derive an expression for estimating the true but unobserved CSF WBC in traumatic LP cases such that the existing atraumtic CSF WBC guidelines may be used. Finally, we present a Bayesian approach to incorporate non-zero CSF red blood cell (RBC) counts and suggest that this biologically-motivated assumption underlying S-B is likely not clinically relevant for the majority of patients.