Acta Neurochirurgica

, Volume 160, Issue 3, pp 655–661 | Cite as

Mathematical model of perineural tumor spread: a pilot study

  • Joshua J. Jacobs
  • Stepan CapekEmail author
  • Robert J. Spinner
  • Kristin R. Swanson
Original Article - Neurosurgical Techniques



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.


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.


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.


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.


Mathematical model Perineural spread Lumbosacral plexopathy Treatment response Pelvic cancer 



National Institute of Health provided financial support in the form NIH grant R01 CA 164371. The sponsor had no role in the design or conduct of the study.

Compliance with ethical standards

Conflict of interest

All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers’ bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

Ethical approval

All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee (name of institute/committee) and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. For this type of study formal consent is not required.

Supplementary material

701_2017_3423_MOESM1_ESM.avi (14.8 mb)
Video 1 Subject 1: simulated progression of perineural spread of prostate cancer. This video shows 3D visualization of perineurally spreading prostate cancer in subject 1. Growth is projected on an atlas images derived from a healthy subject; the simulation starts at a presumed point of entry of the cancer cells to the lumbosacral plexus (day 0) and continues “into the future” to emulate progression of an untreated tumor. (AVI 15172 kb)
701_2017_3423_MOESM2_ESM.avi (6.3 mb)
Video 2 Subject 2: simulated progression of perineural spread of cervical cancer. This video shows 3D visualization of perineurally spreading cervical cancer in subject 2. Growth is projected on an atlas images derived from a healthy subject; the simulation starts at a presumed point of entry of the cancer cells to the lumbosacral plexus (day 0) and continues “into the future” to emulate progression of an untreated tumor. (AVI 6463 kb)


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2017

Authors and Affiliations

  • Joshua J. Jacobs
    • 1
  • Stepan Capek
    • 2
    Email author
  • Robert J. Spinner
    • 1
  • Kristin R. Swanson
    • 3
  1. 1.Department of NeurosurgeryMayo ClinicRochesterUSA
  2. 2.Department of NeurosurgeryUniversity of VirginiaCharlottesvilleUSA
  3. 3.Department of NeurosurgeryMayo ClinicScottsdaleUSA

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