We simulated the pulsatile CSF flow dynamics and matched the flow measurement in 3 areas of interest as shown in Figure 1, for subject 1. The CSF stroke volumes per cardiac cycle between measurement data and simulations agree within 0.9% at C4, 1.6% at T6, and 1.5% at L4 spinal level. The simulations reproduce the flow field and the CSF pressure pulsations along the entire neuronal axis as a function of time. Taken together we have in detail quantified the CSF flow conditions in the subject-specific anatomical spaces using MRI data. We have further created a subject-specific computer model that is capable of predicting the flow field, which drives drug biodistribution.
In Vitro CSF Flow and Drug Dispersion Model
We constructed a bench-top surrogate based on the anatomical MRI data of subject 1. The dimensions of the in vitro model and the human subject data are shown in Table 2. A tracer is tracked with optical methods described in Methods and Figure 2 visualizes drug dispersion for a 5-mL injection bolus at a rate of 1 mL/min as a function of time. The species transport study compared drug spread of the bench-top surrogate in Figure 2 with computations showing peak difference of the mixing-front position less than 5.2% and average difference of 1.8%.
Human IT Infusion Simulation
We inserted to the reconstructed human CNS model in Human Data, a commercial intrathecal catheter and meshed both domains, as shown in Figure 3. The simulations show that drug pump infusions with flow rates of 0.0167 mL/min did not significantly alter the pulsatile CSF flow field. These findings provide evidence in this model that with lower flow rates the dispersion is governed mainly by cardiac-driven CSF pulsations. Large-volume injections of 10 mL/min, or ~10% of spinal CSF volume, could result in forceful jets that override natural baseline pulsatile CSF flow. These jets can rapidly propel the infusate cranially along the spine. After the bolus injection phase, which typically lasts only a few minutes, CSF flow returns to the cardiac-driven pulsations with stroke volumes of 0.5 to 2 mL depending on the individual subject’s CSF dynamics.
The infusion profiles in Figure 4 allow a comparison of drug spread for low- and high-volume injection in 2 subjects. The natural CSF flow field at the T11-L4 spinal level was visualized by white streamlines in Figure 4A, and flow induced by the injection impulse was colored with blue-green streamlines. Low-rate injections, 1 mL/min for a total volume of 1 mL, are overpowered during caudal flow in systole. The forceful jet of the high-rate injections, 10 mL/min for a total infusion volume of 10 mL, overrides the direction of baseline CSF flow and pushes cranially even during systole.
Figure 4B shows simulated volume of distribution for 4 different injection volumes after 60 seconds for visual inspection (top) and also quantified with a tabular representation (bottom). For a 1-mL infusion, the entire volume of distribution of drug is confined to an area close to the lumbar injection site that covers 1.8 mL of space. The 2.5-mL injection leads to a volume of distribution of 6.2 mL, which reaches the lower thoracolumbar region after 1 minute. In 5- and 10-mL injections, medication can be seen in the thoracic region. A rapid 10-mL infusate travels cranially 18 cm from the site of injection to the T9 nerve root achieving a volume of distribution of 40 mL, which is a larger spread than produced by lower injection volumes. These results in the model provide evidence that the injection volume could be directly related to the achievable biodistribution of the drug in the spinal canal.
We simulated continuous drug infusion mimicking an external drug pump, set at a flow rate of 0.005 mL/min. Figure 4C visualizes differences in drug spread simulated for 2 different subjects. In subject 1, drug spread reached 4.2 cm rostral and 2.9 cm caudal of injection site. In subject 2, the distribution region spanned 5.3 cm rostral and 2.7 cm caudal from the site of injection. Subject 1 has spinal CSF dimensions, 65 cm length, 51 mL lumbosacral volume, and 98 mL spinal CSF volume. Subject 2 spinal length is 70 cm, 44 mL lumbosacral volume, and total spinal CSF 106 mL. Supplemental table in the Appendix (See Appendix, Supplemental Digital Content, http://links.lww.com/AA/B701) compares subject 1 with a previous clinical study by Carpenter et al, which measures patient height and spinal CSF volumes.26
Reaction Kinetics: Computational Fluid Dynamic Subject-Specific Model of CNS.
Next, we studied the impact of biochemical reaction kinetics on the drug dispersion after IT drug distribution. For all drug distribution simulations with reaction kinetics, an infusion volume of 1 mL was administered at a rate of 1 mL/min for 1-minute duration. The first scenario considered morphine, which has a relatively slow tissue uptake. The drug concentration profiles are plotted against time in Figure 5A and spatially in Figure 5B. The bar graphs in Figure 5C quantify the drug remaining in the CSF space and the amount taken up by spinal tissue. Immediately following injection, the concentration is greatest surrounding the injection site in the lumbar region. After 30 minutes the concentration of morphine was reduced by half at the injection site and its front spread reaches the upper thoracic region at T2. Because of low tissue uptake, 94% remains in the CSF. Sixty minutes after injection morphine distributes across the whole spine up to the cisterna magna. The bulk of the drug resides in the thoracolumbar region and 81% still remains in the CSF.
The second scenario considered the drug alfentanil, which has high tissue uptake. Following injection, the drug resides in the lumbar region; however, 5% of the drug is rapidly uptaken by the tissue. At 30 minutes postinjection, alfentanil spreads from the midthoracic region (T6) to the lumbar region (L5) and only 46% remains in the CSF. After 60 minutes, it is predicted that the majority of alfentanil has been taken up by the tissue with only 14% remaining in the CSF. High tissue uptake reduces the volume of distribution of alfentanil in the spinal SAS so that the front cannot advance past the midthoracic spinal level T6.
Reaction kinetics scenario 3 describes a very low tissue uptake drug, like sufentanil. After 60 minutes, simulations show that sufentanil would reach the CM, and almost all the drug, 99.3%, remains in the CSF space.
In scenario 4, morphine uptake with circulation clearance is considered without accounting for vascular redistribution, morphine-blood clearance. Following injection, the biodistribution of morphine-blood clearance is comparable to the previously discussed scenario 1, as demonstrated by the bar graph in Figure 5C. After 60 minutes, the morphine-blood clearance scenario is predicted to reach spinal level C2, 79% is in the CSF, 15% is in the tissue, and 6% would have been cleared from the CNS via a vascular route.
Following a 5-mL IT bolus injection in the model for subject 1, CSF flow pulsatility, ω = (40, 72, 120 BPM) was varied to study the impact on drug spread. At excited heart rate (120 BPM), drugs disperse faster than a resting individual (72 BPM). A simulated case of brachycardia (40 BPM) results in the smallest volume of distribution. Drug mixing front was tracked for up to 4 hours and mixing-front velocity was calculated for the postinjection phase at 0.47, 0.63, and 1.02 cm/min for the 40, 72, and 120 BPM cases.
Modelling Targeted Spinal Levels
Pathologies occurring at different levels of the spine require distinct targeting strategies to localize delivery of therapeutics. In Figure 6 are shown the results for a slow continuous infusion mimicking an external drug pump using a rate of 0.0167 mL/min. This rate is higher than what is typically selected for implantable drug pumps. For example, the Medtronic pump has a maximal flow rate of 0.01 mL/min. The Flowonix drug pump can deliver pulses up to 2 to 3 µL with locked intervals of 10 s between boluses. Peak concentration at L1 occurs after 1 hour with dye spread contained between T9 and L4. Acute targeting of the lumbar region was achieved with a single bolus injection at 1 mL/min. Drug concentration was localized to spinal T8-L3 with peak concentration at the injection site. A condition in the cervical spine can benefit from large-volume infusions as discussed in Human IT Infusion Simulation. A multibolus infusion protocol was simulated with 5 mL drug at a rate of 1 mL/min immediately followed by 5 mL artificial CSF (aCSF) at a rate of 10 mL/min. The region of high concentration spread between C3 and T4 after 1 hour. Further cranial advancement may be achieved with greater injection volumes with aCSF flushing. This technique is used to target the brain by a 5-mL drug injection at 1 mL/min followed by a 10-mL aCSF injection at 10 mL/min. The bulk of infused drug traveled to the upper cervical spine and brain parenchyma.
Intrathecal drug administration has gained a significant role in pain management through its increased efficacy and reduced adverse systemic effects. Despite this trend, there are few platforms to study optimal infusion guidelines. A tool to assist clinicians in choosing the parameters of bolus infusion or drug pump settings to administer specific drug doses to the spine or the brain could improve treatment schedules. Testing various formulations provides empiric evidence in patient care. Through a subject-specific patient model, we hope to provide more precise and accurate drug targeting to reduce side effects. There are clear limitations that include the model utilizes only 2 healthy test subjects and the need for clinical validation, but the results provide some general basis to relate infusion parameter choices to administer drug distributions in target locations.
The influence of IT volume and CSF pulse frequency were systematically quantified in a bench-top CNS surrogate model derived from human MRI data. Increased volumetric flow rate of injection was shown to extend the range of drug coverage. The velocity of dye spread was found to have 2 phases, the first dominated by injection impulse and the second governed by convective dispersion due to CSF pulsation. Computational predictions of the bench-top model were found in good agreement with the CNS surrogate suggesting that the subject-specific computational approach presented here potentially predicts drug distribution owing to different mode of injection and CSF pulsations. There is growing interest in the study of CSF dynamics to investigate the impact of respiration on the flow field. The CSF flow predicted in this model was driven only by cerebrovascular pulsatile expansion and matched with CINE-MRI–measured velocities.12 Future models of CSF flow fields may study the impact of respiration, however, that was beyond the scope of this article.
An important result of the computation is the influence of pulsation and injection rate during a bolus. In a model with weaker pulsation rate in the subject, we found the drug spread to be slower, which could localize drug to the site of infusion. This simulated reduced heart rate setting does not attempt to emulate an anesthesia response, but merely elucidates the effect of reduced CSF pulse frequency on drug dispersion. These results confirm previous studies on the significance of pulsatility on drug spread.6
Low-rate injections exhibited a similar effect of reduced rostral spread. However, a high-volume injection of drug such as morphine may rapidly progress even reaching the brain, because of large-injection–induced flow jets. This scenario is concerning in that a large volume of drug going to the brain and brainstem could lead to respiratory complications. Through the model, we hope to examine high-risk infusion scenarios, and provide information to clinicians on infusion parameters, which could reduce complications associated with IT of anesthetic agents. In high-volume injection, the initial volume of distribution could be extended by a factor of 10 over low-volume infusion.
In drug injection pumps for chronic use, the largest effect on biodistribution would stem from natural CSF pulsatility and drug half-life. Simulation results on subject 1 and subject 2 for drug pump infusion rate of 0.005 mL/min demonstrated drug distribution remained close to the injection site. If the drug is very readily uptaken in the tissue, it will not travel far when administered slowly with a drug pump. Therefore, use of lipophilic drugs is preferential for lower regions over a long-term treatment. Local delivery can be maximized by low-uptake drugs with a slow-release mechanism. Caution must be exercised with low infusion settings since locally high concentrations administered over midchronic durations can cause spinal granuloma.21
We have further demonstrated fluid coinfusion for the purpose of advancing a drug faster to reach more rostral targets. The rationale for including a bolus with flush was to target a local region of the spine higher than the infusion point and limit dosing along the spine up to that point. Multiple bolus infusions with drug-free components are of investigative interest to gene therapy studies or rostral spinal cord targets. Multibolus and high-volume injections may also in the future become relevant for enzyme replacement or gene therapies targeting the brain parenchyma.27–29 The computational model provides a platform that can test new hypotheses and other nonconventional treatment methodologies for feasibility before testing in animal and human models. However, there is a limit on how much fluid can be inserted into the CSF. In our experience with small animals (data not shown here), injection volumes of 10% to 15% total CSF volume are an upper limit. Currently, our model does not account for the capacity of CSF compartments to uptake additional fluid volume.
Modeled scenarios for targeting drugs to spinal locations do not correspond with specific clinical case studies. Rather, results in Modelling Targeted Spinal Levels may serve as a demonstration for the utility of computational modeling for optimizing drug delivery strategies. Future studies would need to rigorously adhere to a specific IT drug delivery case study to compare results and suggest alternative delivery strategies. The overview of simulated drug dispersion following different infusion protocols is shown in Figure 6 and is a conceptual first step to optimize methods for deliberate control over the targeted region after IT. Different delivery strategies such as a single-injection bolus or multiple bolus infusions with a CSF flush can achieve markedly different distribution profiles. Follow-up modeling studies could account for specific patient cases.
Our study also quantifies how reaction kinetics influences the specific location of drug action. Because of differing tissue uptakes of 3 agents (morphine, sufentanil, alfentanil), a higher fraction of sufentanil and morphine remains in the CSF, thus reaching further along the neuroaxis, thereby inducing stronger action in the upper cervical region. In clinical management of cervical pain, these agents could be utilized with more potency, while our preliminary simulation demonstrates that alfentanil could be better suited for low back pain based on our high rate of tissue uptake assumption. However, for a cancer-associated pain, morphine more readily distributes along the spinal axis.
CSF dynamics research is an active field and new insights about the role of respiration, body motion, and spinal compliance are becoming available. Because more precise models of CSF pulsatility affect drug distribution, we expect our computational models to be continuously updated to keep the model current and improve matching between predictions and experimental observations.
A limitation of our current model concerns tissue uptake across the pia membrane into the parenchyma. The model does not differentiate between spinal cord tissue uptake and drug in the interstitial space. This is a limitation that should be included in future works of predictive drug distribution following IT delivery. A more complete model should also include vascular uptake of the drug across the blood-brain barrier. By tracking drug on the systemic circulation, possible subsequent vascular redistribution may also be accounted for; however, a systemic drug circulation model exceeds the scope of the current work. Additionally, the experimental and simulated IT drug administration assumed isobaric solutions. The baricity of infusions of future models for IT infusion could be a parameter of interest to more accurately represent clinical scenarios.
In the current model, all computational scenarios were conducted on subject 1 only, except for a comparative drug pump infusion scenario, which included subject 2. This preliminary study of the same infusion scenario in multiple subjects showed very similar drug distribution profiles for these 2 healthy subject models. We did not generate a large number of cases and report averaged trends, but rather focused on the impact of IT infusion parameters for individual patients. The computational predictions were evaluated using an individualized approach, which assesses the needs for each subject on a case-by-case basis. The results show that the idea of personalized optimal design of IT infusion procedures using the proposed computational methodology is in principle feasible. In the future, more subjects could refine the insights gained from this study. Such study could focus on a subset of patients controlled for sex, age, and size to investigate the resulting IT drug distribution patterns.
To validate drug pharmacokinetics and pharmacodynamics, in future studies, experiments in human perhaps with combined PET-MRI measurements as observed by Calias and Papisov should be undertaken.30,31 Ideally PET data would validate the subject-specific human model; however, because of ethical limitations of administering the procedure to volunteers, human experiments were not performed in this study.
We demonstrate for the same infusion parameters, pulsatility, and CSF space volume that the drug uptake and reactions kinetics could have a strong influence on the biodistribution. In the model, we provide evidence that higher-solubility drugs such as sufentanil or other opioids advance 3 times further owing to the insufficient solubility (uptake) in fatty tissue or spinal tissue. Although biodistribution has been known qualitatively before,15,17,25,32,33 a 3D subject-specific virtual patient infusion study has not been presented.
In the current study, we utilized an ideal model to predict the physics of drug transport and also the effect of reaction kinetics. However, we were not yet able to validate the biodistribution in patients because of ethical considerations. The methodology that we propose would be ideally suited for systematic studies with MRI combined with PET scanning. Drug pharmacokinetic parameters were taken from the literature, but we have demonstrated in a previous study how to infer reaction kinetics and transport parameters such as tissue half-life or molecular diffusion constants from medical images.34
An experimental study conducted on pigs by Bernards17 tested an infusion scenario of 1 mL/h (0.0167 mL/min) similar to our 0.0167 mL/min drug pump injection. In the pig study, temporal drug concentration shows high drug levels at the infusion site throughout the duration of the experiment. Drug concentrations increased at 5 cm caudad until 60 minutes and 5 cm cephalad until 200 minutes. Additionally, a more distant sampling probe at 10 cm cephalad detected some measure of drug. Our drug pump scenario with the same flow rate (0.0167 mL/min) achieves a distribution of 6.8 cm cephalad and 4.1 cm caudal at 1 hour following IT injection. The human CNS anatomy in our model is different from the porcine model; nevertheless, trends of drug spread were similar. A detailed comparative study between clinical trials and simulations would be a logical next step to further validate the computational model.
In the future, after validation is completed of the model when using drug-specific pharmacokinetic data for candidate drugs, the proposed computation methods may be utilized to design effective human trials. Existing pharmacokinetic models that do not account for patient anatomy and also lack a mechanistic transport and reaction model are unable to extrapolate to desired results or guidelines. The computations presented here give an expected distribution of the drug and present a first step toward integrating computational modeling as a tool demonstrating the safety of treatment scenarios for specific patients.
Name: Kevin M. Tangen, BS.
Contribution: This author helped design and conduct the experiments and simulations, and write the manuscript.
Name: Roxanne Leval.
Contribution: This author helped conduct the experiments.
Name: Ankit I. Mehta, MD.
Contribution: This author helped provide clinical guidance for the experimental design, and write the manuscript.
Name: Andreas A. Linninger, PhD.
Contribution: This author helped design the experiment, guide the simulations, write the manuscript, and supervise the study.
This manuscript was handled by: Honorio T. Benzon, MD.
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