Mathematical model of perineural tumor spread: a pilot study

Joshua J. Jacobs, Stepan Capek, Robert J. Spinner, Kristin Swanson

Research output: Contribution to journalArticle

1 Scopus citations


Background: Perineural spread (PNS) of pelvic cancer along the lumbosacral plexus is an emerging explanation for neoplastic lumbosacral plexopathy (nLSP) and an underestimated source of patient morbidity and mortality. Despite the increased incidence of PNS, these patients are often times a clinical conundrum—to diagnose and to treat. Building on previous results in modeling glioblastoma multiforme (GBM), we present a mathematical model for predicting the course and extent of the PNS of recurrent tumors. Methods: We created three-dimensional models of perineurally spreading tumor along the lumbosacral plexus from consecutive magnetic resonance imaging scans of two patients (one each with prostate cancer and cervical cancer). We adapted and applied a previously reported mathematical model of GBM to progression of tumor growth along the nerves on an anatomical model obtained from a healthy subject. Results: We were able to successfully model and visualize perineurally spreading pelvic cancer in two patients; average growth rates were 60.7 mm/year for subject 1 and 129 mm/year for subject 2. The model correlated well with extent of PNS on MRI scans at given time points. Conclusions: This is the first attempt to model perineural tumor spread and we believe that it provides a glimpse into the future of disease progression monitoring. Every tumor and every patient are different, and the possibility to report treatment response using a unified scale—as “days gained”—will be a necessity in the era of individualized medicine. We hope our work will serve as a springboard for future connections between mathematics and medicine.

Original languageEnglish (US)
Pages (from-to)1-7
Number of pages7
JournalActa Neurochirurgica
StateAccepted/In press - Dec 21 2017


  • Lumbosacral plexopathy
  • Mathematical model
  • Pelvic cancer
  • Perineural spread
  • Treatment response

ASJC Scopus subject areas

  • Surgery
  • Clinical Neurology

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