DataSheet1_Computational fluid dynamics model to predict the dynamical behavior of the cerebrospinal fluid through implementation of physiological boundary conditions.docx

Cerebrospinal fluid (CSF) dynamics play an important role in maintaining a stable central nervous system environment and are influenced by different physiological processes. Multiple studies have investigated these processes but the impact of each of them on CSF flow is not well understood. A deeper insight into the CSF dynamics and the processes impacting them is crucial to better understand neurological disorders such as hydrocephalus, Chiari malformation, and intracranial hypertension. This study presents a 3D computational fluid dynamics (CFD) model which incorporates physiological processes as boundary conditions. CSF production and pulsatile arterial and venous volume changes are implemented as inlet boundary conditions. At the outlets, 2-element windkessel models are imposed to simulate CSF compliance and absorption. The total compliance is first tuned using a 0D model to obtain physiological pressure pulsations. Then, simulation results are compared with in vivo flow measurements in the spinal subarachnoid space (SAS) and cerebral aqueduct, and intracranial pressure values reported in the literature. Finally, the impact of the distribution of and total compliance on CSF pressures and velocities is evaluated. Without respiration effects, compliance of 0.17 ml/mmHg yielded pressure pulsations with an amplitude of 5 mmHg and an average value within the physiological range of 7–15 mmHg. Also, model flow rates were found to be in good agreement with reported values. However, when adding respiration effects, similar pressure amplitudes required an increase of compliance value to 0.51 ml/mmHg, which is within the range of 0.4–1.2 ml/mmHg measured in vivo. Moreover, altering the distribution of compliance over the four different outlets impacted the local flow, including the flow through the foramen magnum. The contribution of compliance to each outlet was directly proportional to the outflow at that outlet. Meanwhile, the value of total compliance impacted intracranial pressure. In conclusion, a computational model of the CSF has been developed that can simulate CSF pressures and velocities by incorporating boundary conditions based on physiological processes. By tuning these boundary conditions, we were able to obtain CSF pressures and flows within the physiological range.</p

Image1_Computational fluid dynamics model to predict the dynamical behavior of the cerebrospinal fluid through implementation of physiological boundary conditions.JPEG

Cerebrospinal fluid (CSF) dynamics play an important role in maintaining a stable central nervous system environment and are influenced by different physiological processes. Multiple studies have investigated these processes but the impact of each of them on CSF flow is not well understood. A deeper insight into the CSF dynamics and the processes impacting them is crucial to better understand neurological disorders such as hydrocephalus, Chiari malformation, and intracranial hypertension. This study presents a 3D computational fluid dynamics (CFD) model which incorporates physiological processes as boundary conditions. CSF production and pulsatile arterial and venous volume changes are implemented as inlet boundary conditions. At the outlets, 2-element windkessel models are imposed to simulate CSF compliance and absorption. The total compliance is first tuned using a 0D model to obtain physiological pressure pulsations. Then, simulation results are compared with in vivo flow measurements in the spinal subarachnoid space (SAS) and cerebral aqueduct, and intracranial pressure values reported in the literature. Finally, the impact of the distribution of and total compliance on CSF pressures and velocities is evaluated. Without respiration effects, compliance of 0.17 ml/mmHg yielded pressure pulsations with an amplitude of 5 mmHg and an average value within the physiological range of 7–15 mmHg. Also, model flow rates were found to be in good agreement with reported values. However, when adding respiration effects, similar pressure amplitudes required an increase of compliance value to 0.51 ml/mmHg, which is within the range of 0.4–1.2 ml/mmHg measured in vivo. Moreover, altering the distribution of compliance over the four different outlets impacted the local flow, including the flow through the foramen magnum. The contribution of compliance to each outlet was directly proportional to the outflow at that outlet. Meanwhile, the value of total compliance impacted intracranial pressure. In conclusion, a computational model of the CSF has been developed that can simulate CSF pressures and velocities by incorporating boundary conditions based on physiological processes. By tuning these boundary conditions, we were able to obtain CSF pressures and flows within the physiological range.</p

Intraluminal pressure indexes with changes in Young’s modulus.

<p>Values of predicted true (TL) and false lumen (FL) systolic pressure (SP), diastolic pressure (DP) and pulse pressure (PP), computed for different values of Young’s modulus for scenarios <i>S_4,4</i> and <i>S_10,10</i>. The value of <i>E = E^ref</i> corresponds to the reference Young’s modulus of the lumen wall, resulting from the calibration of the computational model to the experimental one.</p

Relative root square mean error (rRMSE) between predicted and measured pressures at the proximal and distal tears, for each scenario.

<p><i>TL</i>, True lumen; <i>FL</i>, False lumen</p><p>Relative root square mean error (rRMSE) between predicted and measured pressures at the proximal and distal tears, for each scenario.</p

Pressure gradients across the tears with changes in Young’s modulus.

<p>Variations in predicted false lumen systolic (FPI_systolic%) and diastolic pressure (FPI_diastolic%) indexes with changes in Young’s modulus, at the proximal and distal tears for scenarios <i>S_4,4</i> and <i>S_10,10</i>. The value of <i>E = E^ref</i> corresponds to the reference Young’s modulus of the lumen wall, resulting from the calibration of the computational model to the experimental one.</p

Proposed experimental representation of a clinical aortic dissection and its equivalent lumped-parameter model.

<p>(a) Clinical appearance of a descending aortic dissection in the longitudinal plane. Transversal plane showing the distinction between TL and FL (Bottom right) (b-c) Proposed anatomic representation of a descending aortic dissection. Longitudinal diagram of the experimental model (b) and cross-sectional plane of the dissected segment (c). (d) Schema of the lumped-parameter model. The dissected region was modelled as two parallel compartments communicated by resistances (rigid tears). Dashed lines enclose the different compartments of the model: Proximal tear (PT), false lumen (FL), true lumen (TL), distal tear (DT) and peripheral (PH) bed.</p

Changes in flow direction across the tears with changes in Young’s modulus.

<p>Index of direction (ID) computed for different values of Young’s modulus for scenarios <i>S_4,4</i> and <i>S_10,10</i>. The ID quantifies the change of direction between the flows across the proximal and distal tears, so that high ID values mean proximal and distal flows simultaneously moving from the true lumen to the false lumen or vice versa. The value of <i>E = E^ref</i> corresponds to the reference Young’s modulus of the lumen wall, resulting from the calibration of the computational model to the experimental one.</p

Changes in intraluminal pressures with changes in Young’s modulus.

<p>Variations in predicted intraluminal true (TL) and false lumen (FL) pressures, close to the proximal tear, with changes in Young’s modulus, for scenarios <i>S_4,4</i> and <i>S_10,10</i>. The value of <i>E = E^ref</i> corresponds to the reference Young’s modulus of the lumen wall, resulting from the calibration of the computational model to the experimental one. Intraluminal pressures did not show substantial differences when the Young’s modulus was increased more than 1e2 <i>E</i>.</p

Estimated parameters’ values of the lumped-parameter model.

<p><i>PT</i>: proximal tear; <i>DT</i>: distal tear; <i>TL</i>: true lumen; <i>FL</i>: false lumen; <i>PH</i>: peripheral</p><p>Estimated parameters’ values of the lumped-parameter model.</p

Experimental versus predicted intraluminal pressures and velocities across the tears.

<p>Comparison at the proximal and distal sites of the model, for scenarios <i>S_4,4</i> and <i>S_10,10</i>. Doppler positive velocities are directed from the TL to the FL and negative velocities the other way around.</p