Estimating intracranial parameters using an inverse mathematical model with viscoelastic elements that closely predicts complex ICP morphologies

The quantitative relationship between arterial blood pressure (ABP) and intracranial pressure (ICP) waveforms has not been adequately explained. We hypothesized that the ICP waveform results from interferences between propagating and reflected pressure waves occurring in the cranium following the initiating arterial waveform. To demonstrate cranial effects on interferences between waves and generation of an ICP waveform morphology, we modified our previously reported mathematical model to include viscoelastic elements that affect propagation velocity. Using patient data, we implemented an inverse model methodology to generate simulated ICP waveforms in response to given ABP waveforms. We used an open database of traumatic brain injury patients and studied 65 pairs of ICP and ABP waveforms from 13 patients (five pairs from each). Incorporating viscoelastic elements into the model resulted in model-generated ICP waveforms that very closely resembled the measured waveforms with a 16-fold increase in similarity index relative to the model with only pure elasticity elements. The mean similarity index for the pure elasticity model was 0.06 ± 0.12 SD, compared to 0.96 ± 0.28 SD for the model with viscoelastic components. The normalized root mean squared error (NRMSE) improved substantially for the model with viscoelastic elements compared to the model with pure elastic elements (NRMSE of 2.09% ± 0.62 vs. 15.2% ± 4.8, respectively). The ability of the model to generate complex ICP waveforms indicates that the model may indeed reflect intracranial dynamics. Our results suggest that the model may allow the estimation of intracranial biomechanical parameters with potential clinical significance. It represents a first step in the estimation of inaccessible intracranial parameters.