Elsevier

Journal of Biomechanics

Volume 48, Issue 10, 16 July 2015, Pages 2144-2154
Journal of Biomechanics

CNS wide simulation of flow resistance and drug transport due to spinal microanatomy

https://doi.org/10.1016/j.jbiomech.2015.02.018Get rights and content

Abstract

Spinal microstructures are known to substantially affect cerebrospinal fluid patterns, yet their actual impact on flow resistance has not been quantified. Because the length scale of microanatomical aspects is below medical image resolution, their effect on flow is difficult to observe experimentally. Using a computational fluid mechanics approach, we were able to quantify the contribution of micro-anatomical aspects on cerebrospinal fluid (CSF) flow patterns and flow resistance within the entire central nervous system (CNS). Cranial and spinal CSF filled compartments were reconstructed from human imaging data; microscopic trabeculae below the image detection threshold were added artificially. Nerve roots and trabeculae were found to induce regions of microcirculation, whose location, size and vorticity along the spine were characterized. Our CFD simulations based on volumetric flow rates acquired with Cine Phase Contrast MRI in a normal human subject suggest a 2–2.5 fold increase in pressure drop mainly due to arachnoid trabeculae. The timing and phase lag of the CSF pressure and velocity waves along the spinal canal were also computed, and a complete spatio-temporal map encoding CSF volumetric flow rates and pressure was created.

Micro-anatomy induced fluid patterns were found responsible for the rapid caudo-cranial spread of an intrathecally administered drug. The speed of rostral drug dispersion is drastically accelerated through pulsatile flow around microanatomy induced vortices. Exploring massive parallelization on a supercomputer, the feasibility of computational drug transport studies was demonstrated. CNS-wide simulations of intrathecal drugs administration can become a practical tool for in silico design, interspecies scaling and optimization of experimental drug trials.

Introduction

Despite precise MR observations of cerebrospinal fluid (CSF) velocities (Laitinen 1968), brain motion (Zhu et al., 2006) and ventricular wall dilatations (Enzmann and Pelc, 1992), critical questions remain about CSF dynamics in the CNS: What is the exact nature of the force coupling between the pulsatile blood circulation and CSF displacements? (Marmarou et al., 1975, Marmarou et al., 1978) How is the pulsatile expansion and contraction of the cerebrovascular bed transmitted to the CSF and the brain? The source of the volumetric dilations that actually induce CSF motion remain uncertain, even though major cerebral arteries, the oscillatory displacement by the parenchyma or choroid plexus expansion are likely involved. Moreover, the caudal decrease in CSF flow amplitude along the spinal canal (Alperin et al., 2005, Tain et al., 2011) supports the notion of compliant leptomeningeal boundaries lining the fluid-filled spinal subarachnoid space (SAS). Hence, the observed CNS compliance could result from cyclic displacement of blood inside large spinal veins, or the expansion of CSF-filled spaces against elastically deformable epidural tissues. Nevertheless, the biomechanics of deformations of the entire spinal compartment remain unclear.

Subject-specific CSF flow measurements may be significant for improving noninvasive diagnostics of pathological conditions. For example, the amplitude ratio between the aqueduct and prepontine CSF flows were found elevated in hydrocephalus patients compared to normal subjects (Zhu et al., 2006). Because in vivo MR measurements have limited image resolution and practical scan durations restrict the number of observed regions of interest, many researchers have attempted to address fundamental questions regarding CNS with computational fluid dynamics (CFD) techniques dynamics especially under pathological conditions.

Early CFD models used small sections of the CNS with idealized geometries (Gupta and Poulikakos, 2008, Kurtcuoglu et al., 2005, Kurtcuoglu et al., 2007, Linge et al., 2010, Loth et al., 2000). Other approaches used medical image reconstruction to represent subjects-specific anatomical spaces to enhance the model fidelity (Gupta et al., 2010, Linninger et al., 2007, Roldan et al., 2009, Rutkowska et al., 2012, Somayaji et al., 2008, Sweetman and Linninger, 2011, Sweetman et al., 2011). Haller and Low (1971) showed that spinal microanatomy induces complex mixing eddies. Stockman studied the impact of nerve roots and trabeculae on convective flow with Lattice Boltzman simulations in idealized cylindrical spine models (Stockman, 2005, Stockman, 2007). Gupta presented an analytical solution to oscillating fluid in a representative elliptical annulus representing a spinal segment directly inferior to the cisterna magna (Gupta et al., 2009). Based on a simulated porous model of the cerebromeduallary cistern and spinal SAS, they conclude that subresolution microstructure density and radius can triple the pressure drop in CSF flow (Gupta et al., 2009, Gupta et al., 2010).

Several groups investigated CSF flow patterns in Chiari patients relative to normal subjects (Martin et al., 2013, Roldan et al., 2009, Rutkowska et al., 2012). Yiallourou et al. (2012) compared flow measurements in normal subjects and patients suffering from Chiari malformation with a CFD model of a cervical segment of the spine. During the review process of this paper, an updated report to the earlier CFD simulation paper of the same group including artificial nerve roots appeared (Heidari Pahlavian et al., 2014). Yet none of these studies performed CFD simulations on the entire CNS and included microanatomical trabeculae in the spinal SAS.

The goal of this paper is to address several critical questions regarding the spatiotemporal coupling of the cranio-spinal CSF compartments by performing CFD simulation on an entire CNS model of a normal subject. This study tests the hypothesis that microanatomical structures generate significant vortex phenomena in spinal CSF flow which increase flow resistance, raise pressure drop, and induce complex mixing patterns responsible for the rapid biodispersion of moieties administered to the spinal SAS. To account for the influence of detailed spinal anatomical structures, nerve roots were reconstructed from medical images; arachnoid trabeculae below the imaging threshold were artificially incorporated to the subject-specific computational mesh. This paper constitutes a first step towards a complete in silico model of CNS dynamics with full coupling between CSF, blood and brain. To augment the limited scope of previous studies, it is critical to account for the entire CNS including the cranial and spinal SAS with their microscopic aspects. Modeling the complete CNS eliminates the burden of introducing uncertain assumptions about internal boundary conditions. Therefore, a parametric study to quantify the influence of microanatomical aspects on CSF dynamics and flow resistance and drug transport was conducted.

Section snippets

CSF spaces, in vivo velocity measurements and CFD simulations

Methods used are summarized here in brief, while details are presented in the Supplementary Material. A subject-specific computational model of the cranial and spinal CSF-filled spaces including nerve roots was reconstructed from medical images, up to detail limited by resolution of the dataset using MIMICS image processing software (Appendix 1.2). CSF flow measurements were acquired from the 29 year old volunteer with CINE MRI at three planes in the spinal SAS (Appendix 1.1).

The cranial pial

Analysis of CSF flow fields in the full SAS model

The simulated CSF flow velocities are visualized as contour plots on axial planes of interest for a full cardiac cycle, in Fig. 2. Systole lasts about 25–35% of the cardiac cycle with a sharp forceful peak in the craniocaudal direction, this phase is color coded in red. Diastole covers the remainder of the cardiac cycle with a slower, more even flow in the caudocranial direction, color coded in blue. Regions of low velocities, ||v||<0.1 cm s−1, are coded in green to highlight temporary stagnation

Discussion

This computational study aimed at predicting the CSF dynamics in a subject-specific model of the entire CNS including microanatomical aspects. The massive CFD computations assessed the effect of microanatomy on CSF flow and flow resistance. Simulations found the caudal flow phase to last 20–30% of the cardiac cycle, which agreed with MRI measurements. The cisterna magna had a stroke volume of 0.76 mL with caudal decrease in amplitudes.

Pressure pulsatility along the spinal canal was

Conclusions and limitations

The dynamic 3D model presented above is a first attempt to predict CSF circulation in the entire CNS of an individual subject. The timing of the pressure and fluid velocity fields was carefully quantified and encoded in a comprehensive Fourier Map. The microcirculatory flow pattern introduced by nerve roots and arachnoid trabeculae were characterized with the use of massively parallel supercomputer simulations.

The actual functional role of trabeculae has not been established, but our results

Conflict of interest

None of the authors has a conflict of interest regarding this work.

Acknowledgments

The authors would like to gratefully acknowledge partial support from the National Science Foundation Grant CBET-0756154. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation Grant number OCI-1053575. Specifically, it used the Blacklight system at the Pittsburgh Supercomputing Center (PSC). We would like to thank C. Wivel from Materialize Inc. for providing a research license for Mimics image reconstruction software.

References (40)

  • M.W. Cloyd et al.

    Scanning electron microscopy of the subarachnoid space in the dog. I. Spinal cord levels

    J. Comp. Neurol.

    (1974)
  • D.R. Enzmann et al.

    Brain motion: measurement with phase-contrast MR imaging

    Radiology

    (1992)
  • S. Gupta et al.

    Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid

    Phys. Fluids

    (2008)
  • S. Gupta et al.

    Three-dimensional computational modeling of subject-specific cerebrospinal fluid flow in the subarachnoid space

    J. Biomech. Eng.

    (2009)
  • S. Gupta et al.

    Cerebrospinal fluid dynamics in the human cranial subarachnoid space: an overlooked mediator of cerebral disease. I. Computational model

    J. R. Soc. Interface

    (2010)
  • F.R. Haller et al.

    The fine structure of the peripheral nerve root sheath in the subarachnoid space in the rat and other laboratory animals

    Am. J. Anat.

    (1971)
  • S. Heidari Pahlavian et al.

    The Impact of spinal cord nerve roots and denticulate ligaments on cerebrospinal fluid dynamics in the cervical spine

    PLoS ONE

    (2014)
  • H.D.M. Hettiarachchi et al.

    The effect of pulsatile flow on intrathecal drug delivery in the spinal canal

    Ann. Biomed. Eng.

    (2011)
  • Y.B. Hsu et al.

    The frequency and magnitude of cerebrospinal fluid pulsations influence intrathecal drug distribution: key factors for interpatient variability

    Anesth. Analg.

    (2012)
  • V. Kurtcuoglu et al.

    Computational modeling of the mechanical behavior of the cerebrospinal fluid system

    J. Biomech. Eng.

    (2005)
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