Effects of fluid structure interaction in a three dimensional model of the spinal subarachnoid space

Numerical analysis of the effect of Syringomyelia on cerebrospinal fluid dynamics

Spinal cord enlargement (SCE) includes conditions such as Syringomyelia, tumors, and tumor-like cases of demyelination, edema, or inflammation. These conditions involve fluid-filled cysts, known as syrinx, or masses of tissue, referred to as tumors, which cause increased pressure within the spinal cord (SC) and obstruct cerebrospinal fluid (CSF) circulation. To assess the impact of SCE location and diameter, we constructed fifteen computational SC models, each featuring a SCE placed in one of five probable locations with 20 %, 40 %, and 60 % stenosis. Our objective was to investigate how the location, diameter, and length of the SCE influence CSF velocity pattern and to identify the most critical location in the SC associated with this condition. The results indicated a velocity increase of 0.5 cm/(s) near models with 60 % stenosis. Importantly, SCE located from T1 to T5 exhibit a more pronounced reduction, exceeding 6.5, in the Womersley number. Our finding suggests that this region is the most vulnerable for SCE formation due to its significant impact on fluid circulation. The identification of specific locations within the SC associated with heightened risk can contribute to an improved understanding, treatment and management of SCE.

Cerebro-spinal flow pattern in the cervical subarachnoid space of healthy volunteers: Influence of the spinal cord morphology

INTRODUCTION

Toward further cerebro-spinal flow quantification in clinical practice, this study aims at assessing the variations in the cerebro spinal fluid flow pattern associated with change in the morphology of the subarachnoid space of the cervical canal of healthy humans by developing a computational fluid dynamics model.

METHODS

3D T2-space MRI sequence images of the cervical spine were used to segment 11 cervical subarachnoid space. Model validation (time-step, mesh size, size and number of boundary layers, influences of parted inflow and inflow continuous velocity) was performed a 40-year-old patient-specific model. Simulations were performed using computational fluid dynamics approach simulating transient flow (Sparlart-Almaras turbulence model) with a mesh size of 0.6, 6 boundary layers of 0.05 mm, a time step of 20 ms simulated on 15 cycles. Distributions of components velocity and WSS were respectively analyzed within the subarachnoid space (intervertebral et intravertebral levels) and on dura and pia maters.

RESULTS

Mean values cerebro spinal fluid velocity in specific local slices of the canal range between 0.07 and 0.17 m.s-1 and 0.1 and 0.3 m.s-1 for maximum values. Maximum wall shear stress values vary between 0.1 and 0.5 Pa with higher value at the middle of the cervical spine on pia mater and at the lower part of the cervical spine on dura mater. Intra and inter-individual variations of the wall shear stress were highlighted significant correlation gwith compression ratio (r = 0.76), occupation ratio and cross section area of the spinal cord.

CONCLUSION

The inter-individual variability in term of subarachnoid canal morphology and spinal cord position influence the cerebro-spinal flow pattern, highlighting the significance of canal morphology investigation before surgery.

A New Method to Evaluate Pressure Distribution Using a 3D-Printed C2-C3 Cervical Spine Model with an Embedded Sensor Array

Cervical degenerative disc diseases such as myelopathy and radiculopathy often require conventional treatments like artificial cervical disc replacement or anterior cervical discectomy and fusion (ACDF). When designing a medical device, like the stand-alone cage, there are many design inputs to consider. However, the precise biomechanics of the force between the vertebrae and implanted devices under certain conditions require further investigation. In this study, a new method was developed to evaluate the pressure between the vertebrae and implanted devices by embedding a sensor array into a 3D-printed C2-C3 cervical spine. The 3D-printed cervical spine model was subjected to a range of axial loads while under flexion, extension, bending and compression conditions. Cables were used for the application of a preload and a robotic arm was used to recreate the natural spine motions (flexion, extension, and bending). To verify and predict the total pressure between the vertebrae and the implanted devices, a 3D finite element (FE) numerical mathematical model was developed. A preload was represented by applying 22 N of force on each of the anterior tubercles for the C2 vertebra. The results of this study suggest that the sensor is useful in identifying static pressure. The pressure with the robot arm was verified from the FE results under all conditions. This study indicates that the sensor array has promising potential to reduce the trial and error with implants for various surgical procedures, including multi-level artificial cervical disk replacement and ACDF, which may help clinicians to reduce pain, suffering, and costly follow-up procedures.

Fluid-structure interactions of peripheral arteries using a coupled in silico and in vitro approach

Vascular compliance is considered both a cause and a consequence of cardiovascular disease and a significant factor in the mid- and long-term patency of vascular grafts. However, the biomechanical effects of localised changes in compliance cannot be satisfactorily studied with the available medical imaging technologies or surgical simulation materials. To address this unmet need, we developed a coupled silico-vitro platform which allows for the validation of numerical fluid-structure interaction results as a numerical model and physical prototype. This numerical one-way and two-way fluid-structure interaction study is based on a three-dimensional computer model of an idealised femoral artery which is validated against patient measurements derived from the literature. The numerical results are then compared with experimental values collected from compliant arterial phantoms via direct pressurisation and ring tensile testing. Phantoms within a compliance range of 1.4-68.0%/100 mmHg were fabricated via additive manufacturing and silicone casting, then mechanically characterised via ring tensile testing and optical analysis under direct pressurisation with moderately statistically significant differences in measured compliance ranging between 10 and 20% for the two methods. One-way fluid-structure interaction coupling underestimated arterial wall compliance by up to 14.7% compared with two-way coupled models. Overall, Solaris™ (Smooth-On) matched the compliance range of the numerical and in vivo patient models most closely out of the tested silicone materials. Our approach is promising for vascular applications where mechanical compliance is especially important, such as the study of diseases which commonly affect arterial wall stiffness, such as atherosclerosis, and the model-based design, surgical training, and optimisation of vascular prostheses.

Human in silico trials for parametric computational fluid dynamics investigation of cerebrospinal fluid drug delivery: impact of injection location, injection protocol, and physiology

Background

Intrathecal drug delivery has a significant role in pain management and central nervous system (CNS) disease therapeutics. A fluid-physics based tool to assist clinicians in choosing specific drug doses to the spine or brain may help improve treatment schedules.

Methods

This study applied computational fluid dynamics (CFD) and in vitro model verification to assess intrathecal drug delivery in an anatomically idealized model of the human CSF system with key anatomic features of the CNS. Key parameters analyzed included the role of (a) injection location including lumbar puncture (LP), cisterna magna (CM) and intracerebroventricular (ICV), (b) LP injection rate, injection volume, and flush volume, (c) physiologic factors including cardiac-induced and deep respiration-induced CSF stroke volume increase. Simulations were conducted for 3-h post-injection and used to quantify spatial–temporal tracer concentration, regional area under the curve (AUC), time to maximum concentration (T_max), and maximum concentration (C_max), for each case.

Results

CM and ICV increased AUC to brain regions by ~ 2 logs compared to all other simulations. A 3X increase in bolus volume and addition of a 5 mL flush both increased intracranial AUC to the brain up to 2X compared to a baseline 5 mL LP injection. In contrast, a 5X increase in bolus rate (25 mL/min) did not improve tracer exposure to the brain. An increase in cardiac and respiratory CSF movement improved tracer spread to the brain, basal cistern, and cerebellum up to ~ 2 logs compared to the baseline LP injection.

Conclusion

The computational modeling approach provides ability to conduct in silico trials representative of CSF injection protocols. Taken together, the findings indicate a strong potential for delivery protocols to be optimized to reach a target region(s) of the spine and/or brain with a needed therapeutic dose. Parametric modification of bolus rate/volume and flush volume was found to have impact on tracer distribution; albeit to a smaller degree than injection location, with CM and ICV injections resulting in greater therapeutic dose to brain regions compared to LP. CSF stroke volume and frequency both played an important role and may potentially have a greater impact than the modest changes in LP injection protocols analyzed such as bolus rate, volume, and flush.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12987-022-00304-4.

Numerical Models of Spinal Cord Trauma: The Effect of Cerebrospinal Fluid Pressure and Epidural Fat on the Results

Spinal cord injury (SCI) is commonly caused by traumatic mechanical damage. Although numerical models can help predict the mechanics of SCI without putting the subjects in danger, previous studies did not focus on alternations in cerebrospinal fluid (CSF) pressure and did not account for the presence of epidural fat. This study aims to numerically compare the mechanical behavior of the human spine when subjected to contusion and burst fracture with varying CSF pressure, either normal or elevated pressure that represents intracranial hypertension. An additional aim is to find out how the presence of the fat in the model affects the SCI calculations. CSF and epidural fat were modeled as smoothed-particle hydrodynamics (SPH) and the soft tissues were modeled as hyperelastic. This approach made it possible to account for CSF pressure alteration and its effect on the cord. Validation models resulted in good correlation with previous numerical and experimental studies. The results were able to capture the fluid dynamics of the CSF while demonstrating a considerable change in the stresses of the spinal cord. The comparison of the CSF pressures demonstrated that SCI in patients with elevated pressure and in regions where insufficient epidural fat exists might lead to higher spinal cord stresses. Yet, in regions with enough fat, the fat can absorb energy and counteract the effect of the elevated pressure. These results indicate important aspects that need to be accounted for in future numerical models of SCI while also demonstrating how the injury might be aggravated by preexisting conditions.

Correlation of a new hydrodynamic index with other effective indexes in Chiari I malformation patients with different associations

This study aimed to find a new CSF hydrodynamic index to assess Chiari type I malformation (CM-I) patients’ conditions and examine the relationship of this new index with morphometric and volumetric changes in these patients and their clinical symptoms. To this end, 58 CM-I patients in four groups and 20 healthy subjects underwent PC-MRI. Ten morphometric and three volumetric parameters were calculated. The CSF hydrodynamic parameters were also analyzed through computational fluid dynamic (CFD) simulation. The maximum CSF pressure was identified as a new hydrodynamic parameter to assess the CM-I patients’ conditions. This parameter was similar in patients with the same symptoms regardless of the group to which they belonged. The result showed a weak correlation between the maximum CSF pressure and the morphometric parameters in the patients. Among the volumetric parameters, PCF volume had the highest correlation with the maximum CSF pressure, which its value being higher in patients with CM-I/SM/scoliosis (R² = 65.6%, P = 0.0022) than in the other patients. PCF volume was the more relevant volumetric parameter to assess the patients’ symptoms. The values of PCF volume were greater in patients that headache symptom was more obvious than other symptoms, as compared to the other patients.

Effects of different non-Newtonian models on unsteady blood flow hemodynamics in patient-specific arterial models with in-vivo validation

The aim of this study is to demonstrate the implications of using different blood rheological models in the simulation of blood flow dynamics in atherosclerotic coronary arteries. Computational fluid dynamics simulation was performed using three-dimensional (3D) patient-specific models of diseased left anterior descending (LAD) coronary arteries with varying degrees of stenosis severity. The three-dimensional arterial models were reconstructed from 3D quantitative coronary angiography, and input flow conditions were prescribed with blood flow conditions measured in-vivo. Different blood viscosity models were used for the simulations, and they include Newtonian and also non-Newtonian models such as Bingham, Carreau, Carreau-Yasuda, Casson, modified Casson, Cross, modified Cross, simplified Cross, Herschel Bulkley, Kuang-Luo (K-L), PowellErying, modified PowellErying, Power-law, Quemada and Walburn-Schneck models. Results from this study show that the time-averaged velocity at the centre of the arteries produced in the CFD simulations that uses the Carreau, modified Casson or Quemada blood viscosity models corresponded exceptionally well with the clinical measurements regardless of stenosis severities and hence, highlights the usefulness of these models to determine the potential determinants of blood vessel wall integrity such as dynamic blood viscosity, blood velocity and wall shear stress.

The effects of upper airway tissue motion on airflow dynamics

The human upper airway is not only geometrically complex, but it can also deform dynamically as a result of active muscle contraction and motility during respiration. How the active transformation of the airway geometry affects airflow dynamics during respiration is not well understood despite the importance of this knowledge towards improving current understanding of particle transport and deposition. In this study, particle imaging velocimetry (PIV) measurements of the fluid dynamics are presented in a physiologically realistic human upper airway replica for (i) the undeformed case and (ii) the case where realistic soft tissue motion during breathing is emulated. Results from this study show that extrathoracic wall motion alters the flow field significantly such that the fluid dynamics is distinctly different from the undeformed airway. Distinctive flow field patterns in the physiologically realistic airway include (i) fluid recirculation at the back of the tongue and cranial to the tip of the epiglottis during mid-inspiration, (ii) horizontal and posteriorly directed flow at the back of tongue at the peak of inspiration and (iii) a more homogeneous flow across the airway downstream from the epiglottis. These findings suggest that the active deformation of the human upper airway may potentially influence particle transport and deposition at the back of the tongue and therefore, highlights the importance of considering extrathoracic wall motion in future airway flow studies. D.

Anthropomorphic Model of Intrathecal Cerebrospinal Fluid Dynamics Within the Spinal Subarachnoid Space: Spinal Cord Nerve Roots Increase Steady-Streaming

Cerebrospinal fluid (CSF) dynamics are thought to play a vital role in central nervous system (CNS) physiology. The objective of this study was to investigate the impact of spinal cord (SC) nerve roots (NR) on CSF dynamics. A subject-specific computational fluid dynamics (CFD) model of the complete spinal subarachnoid space (SSS) with and without anatomically realistic NR and nonuniform moving dura wall deformation was constructed. This CFD model allowed detailed investigation of the impact of NR on CSF velocities that is not possible in vivo using magnetic resonance imaging (MRI) or other noninvasive imaging methods. Results showed that NR altered CSF dynamics in terms of velocity field, steady-streaming, and vortical structures. Vortices occurred in the cervical spine around NR during CSF flow reversal. The magnitude of steady-streaming CSF flow increased with NR, in particular within the cervical spine. This increase was located axially upstream and downstream of NR due to the interface of adjacent vortices that formed around NR.

A Computational Model for the Dynamics of Cerebrospinal Fluid in the Spinal Subarachnoid Space

Global models for the dynamics of coupled fluid compartments of the central nervous system (CNS) require simplified representations of the individual components which are both accurate and computationally efficient. This paper presents a one-dimensional model for computing the flow of cerebrospinal fluid (CSF) within the spinal subarachnoid space (SSAS) under the simplifying assumption that it consists of two coaxial tubes representing the spinal cord and the dura. A rigorous analysis of the first-order nonlinear system demonstrates that the system is elliptic-hyperbolic, and hence ill-posed, for some values of parameters, being hyperbolic otherwise. In addition, the system cannot be written in conservation-law form, and thus, an appropriate numerical approach is required, namely the path conservative approach. The designed computational algorithm is shown to be second-order accurate in both space and time, capable of handling strongly nonlinear discontinuities, and a method of coupling it with an unsteady inflow condition is presented. Such an approach is sufficiently rapid to be integrated into a global, closed-loop model for computing the dynamics of coupled fluid compartments of the CNS.

Non-invasive assessment of pulsatile intracranial pressure with phase-contrast magnetic resonance imaging

Invasive monitoring of pulsatile intracranial pressure can accurately predict shunt response in patients with idiopathic normal pressure hydrocephalus, but may potentially cause complications such as bleeding and infection. We tested how a proposed surrogate parameter for pulsatile intracranial pressure, the phase-contrast magnetic resonance imaging derived pulse pressure gradient, compared with its invasive counterpart. In 22 patients with suspected idiopathic normal pressure hydrocephalus, preceding invasive intracranial pressure monitoring, and any surgical shunt procedure, we calculated the pulse pressure gradient from phase-contrast magnetic resonance imaging derived cerebrospinal fluid flow velocities obtained at the upper cervical spinal canal using a simplified Navier-Stokes equation. Repeated measurements of the pulse pressure gradient were also undertaken in four healthy controls. Of 17 shunted patients, 16 responded, indicating high proportion of “true” normal pressure hydrocephalus in the patient cohort. However, there was no correlation between the magnetic resonance imaging derived pulse pressure gradient and pulsatile intracranial pressure (R = -.18, P = .43). Pulse pressure gradients were also similar in patients and healthy controls (P = .26), and did not differ between individuals with pulsatile intracranial pressure above or below established thresholds for shunt treatment (P = .97). Assessment of pulse pressure gradient at level C2 was therefore not found feasible to replace invasive monitoring of pulsatile intracranial pressure in selection of patients with idiopathic normal pressure hydrocephalus for surgical shunting. Unlike invasive, overnight monitoring, the pulse pressure gradient from magnetic resonance imaging comprises short-term pressure fluctuations only. Moreover, complexity of cervical cerebrospinal fluid flow and -pulsatility at the upper cervical spinal canal may render the pulse pressure gradient a poor surrogate marker for intracranial pressure pulsations.

A numerical investigation of intrathecal isobaric drug dispersion within the cervical subarachnoid space

Intrathecal drug and gene vector delivery is a procedure to release a solute within the cerebrospinal fluid. This procedure is currently used in clinical practice and shows promise for treatment of several central nervous system pathologies. However, intrathecal delivery protocols and systems are not yet optimized. The aim of this study was to investigate the effects of injection parameters on solute distribution within the cervical subarachnoid space using a numerical platform. We developed a numerical model based on a patient-specific three dimensional geometry of the cervical subarachnoid space with idealized dorsal and ventral nerve roots and denticulate ligament anatomy. We considered the drug as massless particles within the flow field and with similar properties as the CSF, and we analyzed the effects of anatomy, catheter position, angle and injection flow rate on solute distribution within the cerebrospinal fluid by performing a series of numerical simulations. Results were compared quantitatively in terms of drug peak concentration, spread, accumulation rate and appearance instant over 15 seconds following the injection. Results indicated that solute distribution within the cervical spine was altered by all parameters investigated within the time range analyzed following the injection. The presence of spinal cord nerve roots and denticulate ligaments increased drug spread by 60% compared to simulations without these anatomical features. Catheter position and angle were both found to alter spread rate up to 86%, and catheter flow rate altered drug peak concentration up to 78%. The presented numerical platform fills a first gap towards the realization of a tool to parametrically assess and optimize intrathecal drug and gene vector delivery protocols and systems. Further investigation is needed to analyze drug spread over a longer clinically relevant time frame.

Characterization of the discrepancies between four-dimensional phase-contrast magnetic resonance imaging and in-silico simulations of cerebrospinal fluid dynamics

The purpose of the present study was to compare subject-specific magnetic resonance imaging (MRI)-based computational fluid dynamics (CFD) simulations with time-resolved three-directional (3D) velocity-encoded phase-contrast MRI (4D PCMRI) measurements of the cerebrospinal fluid (CSF) velocity field in the cervical spinal subarachnoid space (SSS). Three-dimensional models of the cervical SSS were constructed based on MRI image segmentation and anatomical measurements for a healthy subject and patient with Chiari I malformation. CFD was used to simulate the CSF motion and compared to the 4D PCMRI measurements. Four-dimensional PCMRI measurements had much greater CSF velocities compared to CFD simulations (1.4 to 5.6× greater). Four-dimensional PCMRI and CFD both showed anterior and anterolateral dominance of CSF velocities, although this flow feature was more pronounced in 4D PCMRI measurements compared to CFD. CSF flow jets were present near the nerve rootlets and denticulate ligaments (NRDL) in the CFD simulation. Flow jets were visible in the 4D PCMRI measurements, although they were not clearly attributable to nerve rootlets. Inclusion of spinal cord NRDL in the cervical SSS does not fully explain the differences between velocities obtained from 4D PCMRI measurements and CFD simulations.