Patient-specific cranio-spinal compliance distribution using lumped-parameter model: its relation with ICP over a wide age range

Abstract

Background: The distribution of cranio-spinal compliance (CSC) in the brain and spinal cord is a fundamental question, as it would determine the overall role of the compartments in modulating ICP in healthy and diseased states. Invasive methods for measurement of CSC using infusion-based techniques provide overall CSC estimate, but not the individual sub-compartmental contribution. Additionally, the outcome of the infusion-based method depends on the infusion site and dynamics. This article presents a method to determine compliance distribution between the cranium and spinal canal non-invasively using data obtained from patients. We hypothesize that this CSC distribution is indicative of the ICP.

Methods: We propose a lumped-parameter model representing the hydro and hemodynamics of the cranio-spinal system. The input and output to the model are phase-contrast MRI derived volumetric transcranial blood flow measured in vivo, and CSF flow at the spinal cervical level, respectively. The novelty of the method lies in the model mathematics that predicts CSC distribution (that obeys the physical laws) from the system dc gain of the discrete-domain transfer function. 104 healthy individuals (48 males, 56 females, age 25.4 ± 14.9 years, range 3-60 years) without any history of neurological diseases, were used in the study. Non-invasive MR assisted estimate of ICP was calculated and compared with the cranial compliance to prove our hypothesis.

Results: A significant negative correlation was found between model-predicted cranial contribution to CSC and MR-ICP. The spinal canal provided majority of the compliance in all the age groups up to 40 years. However, no single sub-compartment provided majority of the compliance in 41-60 years age group. The cranial contribution to CSC and MR-ICP were significantly correlated with age, with gender not affecting the compliance distribution. Spinal contribution to CSC significantly positively correlated with CSF stroke volume.

Conclusions: This paper describes MRI-based non-invasive way to determine the cranio-spinal compliance distribution in the brain and spinal canal sub-compartments. The proposed mathematics makes the model always stable and within the physiological range. The model-derived cranial compliance was strongly negatively correlated to non-invasive MR-ICP data from 104 patients, indicating that compliance distribution plays a major role in modulating ICP.

Keywords: Cerebrospinal fluid dynamics; Cranio-spinal compliance distribution; Intracranial pressure.

Fig. 1

Cranio-spinal model and its electrical analogous circuit. The cranio-spinal model is divided into two compartments, cranium and spinal canal. The MR derived net transcranial blood flow Q_A−V and CSF flow Q_CSF are used as input and output to the model, respectively. The lumped mechanical dampers or flow resistances in the cranial and spinal compartment are denoted by R_C and R_S respectively. The compliances of the cranium and spinal canal are denoted by C_C and C_S respectively. The inertial component of the CSF flow from the cranium into the spinal canal is denoted by L_S

Fig. 2

Example of determination of cranial contribution to cranio-spinal compliance from sample input and output waveforms. a Flow compensated magnitude image showing bright signal from blood vessels. b High-velocity encoding images used for measurements of arterial inflow and venous outflow. c Low-velocity encoding images used for measurements of CSF flow. d Phase contrast MRI derived cardiac cycle of Q_A−V (red) and Q_CSF (green) in an 21-year-old healthy female subject is plotted. Q_A−V is used as input to the model, which predicts the inverted Q_CSF (black) waveform. e Histogram corresponding to model-derived spinal contribution to cranio-spinal compliance, C_S/(C_C + C_S), is plotted for all the model parameters that give E > 0.7. The final spinal contribution to CSC is chosen from the mode of the histogram (60%)

Fig. 3

Effect of age on cranial contribution to cranio-spinal compliance distribution and MR-ICP. a The plot shows significant positive correlation (p < 0.001, R = 0.33) between cranial contribution to CSC and age. b The plot shows significant negative correlation (p < 0.001, R = − 0.55) between non-invasively determined MR-ICP and age

Fig. 4

Effect of age and gender on cranial contribution to cranio-spinal compliance distribution. a Boxplot of cranial contribution to CSC and stratified age shows the cranial compliance contribution decreases slightly in the younger population before increasing in the 20+ population. b Boxplot of cranial contribution to CSC does not vary significantly with gender (p = 0.88)

Fig. 5

Relationship between cranial contribution to cranio-spinal compliance distribution and MR-ICP. Significant negative correlation is shown between cranial contribution to CSC on MR-ICP (p < 0.001, R = − 0.69)

Fig. 6

Effect of CSF stroke volume on spinal contribution to cranio-spinal compliance distribution. The plot shows a significant positive regression of spinal contribution to CSC on CSF stroke volume (p = 0.001, R = 0.32)

Fig. 7

Effect of age on CSF stroke volume and mean cranial blood flow. a Significant negative correlation is shown between CSF stroke volume (mL per cardiac cycle) at C2 level and age (Spline fit p < 0.001, R = − 0.74). b Significant negative correlation is shown between transcranial blood flow and age (Spline fit p < 0.001, R = 0.82)