Abstract
The pathophysiology of syringomyelia remains poorly understood. Two prevailing challenges stand out: the need for a comprehensive understanding of its diverse types and the yet-to-be-explained mechanism of cerebrospinal fluid (CSF) retention in the syrinx despite its higher pressure than that in the adjacent subarachnoid space. Expanding on our previous proposal that direction-selective resistance to subarachnoid CSF flow drives syringomyelia genesis, this study uses a computer model to explore this mechanism further. We developed a computer simulation model to study spinal CSF dynamics, employing a lumped parameter approach with multiple compartments. This model replicated the to-and-fro movement of CSF in the spinal subarachnoid space and within an intraspinal channel. Subsequently, a direction-selective resistance―opposing only the caudal subarachnoid CSF flow―was introduced at a specific location within the subarachnoid space. Following the introduction of the direction-selective resistance, a consistent pressure increase was observed in the intraspinal channel downstream of the resistance. Importantly, this increase in pressure accumulated with every cycle of to-and-fro CSF flow. The accumulation results from the pressure drop across the resistance, and its effect on the spinal cord matrix creates a pumping action in the intraspinal channel. Our findings elucidate the mechanisms underlying our hypothesis that a direction-selective resistance to subarachnoid CSF flow causes syringomyelia. This comprehensively explains the various types of syringomyelia and resolves the puzzle of CSF retention in the syrinx despite a pressure gradient.
Keywords: syringomyelia, pathophysiology, simulation, hypothesis
Introduction
Syringomyelia remains a puzzle in the medical community. Despite numerous studies and theories,1-13) its pathophysiology remains inadequately understood. Two central theoretical challenges persist. First, one must comprehensively understand the various types of syringomyelia. Second, the mechanism by which the cerebrospinal fluid (CSF) enters and stays within the syrinx―despite its higher pressure than that in the adjacent subarachnoid space―remains enigmatic, a phenomenon we term the “pressure-gradient paradox.” Addressing these gaps in knowledge is essential for improving the diagnosis, treatment, and management of syringomyelia.
Our previous work critiqued the prevailing theories' inability to satisfactorily address these challenges, emphasizing the need for a fresh theoretical perspective.14) Stemming from this critique, we hypothesized that direction-selective resistance to subarachnoid CSF flow generates syrinx formation.14) This notion explains the diverse manifestations of syringomyelia and elucidates the conundrum of CSF retention within the higher-pressure syrinx. However, it is limited from a detailed explanation of the mechanism by which the direction-selective subarachnoid resistance creates a pumping-like function in the intraspinal channel. In the current article, we explain the detailed mechanism using a computer simulation model of the spinal CSF dynamics.
Materials and Methods
In this study, we refined our model of spinal CSF dynamics used in our previous simulation studies.11,12) This model is based on the lumped parameter model―a widely used approach in biological fluid dynamics. In the lumped parameter model, the fluid dynamics within an elastic conduit are represented as an electric circuit. Specifically, resistance to fluid flow is depicted by an electric resistor, while the conduit's elasticity is mirrored by an electric capacitor.
Figure 1 illustrates the schematic of our spinal CSF dynamics model. The model comprises two CSF channels running alongside the spinal cord. The first is the spinal subarachnoid space, represented by the resistors labeled R. The second is an intraspinal channel, represented by resistors labeled r. While this intraspinal channel might represent the central canal, it could also signify any other CSF channel within the spinal cord. Our reasons for including the intraspinal channel in this model are elaborated in our previous article.14) Dural elasticity is depicted by capacitors labeled D, while the elasticity of the intraspinal channel is signified by capacitors labeled C. The elasticity of the major cistern and the lumbar theca are denoted by Ccist and Cthec, respectively.
Fig. 1.
The schematic of the electric circuit simulating spinal cerebrospinal fluid dynamics. There are two channels: the spinal subarachnoid space, represented by R resistors, and an intraspinal channel, represented by r resistors. The D capacitors depict the elasticity of the dura, while the C capacitors illustrate the elasticity of the spinal cord matrix.
Figure 2 depicts the stripped-down electric circuit derived from Fig. 1. This model's behavior can be described by a set of differential equations. We used computer software (Mathematica version 12, Wolfram Research, Champaign, IL, USA) to numerically solve this system of differential equations. The boundary conditions of the system were set as follows.
Fig. 2.
Simplified electric circuit diagram derived from Fig. 1.
(1) The voltage at the two cranial nodes was set to a sine wave oscillating at approximately 10 cmH2O, with an amplitude of 2 cmH2O at one cycle per second.
(2) The original dural pressure was set at 10 cmH2O in all segments.
We set the numerical solution's step to 1/5000 seconds and estimated the solution from 0 to 20 seconds. The actual Mathematica codes can be found in our GitHub repository at https://github.com/chang-hs/syrinx_simulation.git.
In our previous studies,11,12) we examined the system's response to a sudden increase in CSF pressure on the cranial side. In the present study, we have refined the model to analyze the system's reactions to cyclic CSF flow oscillations. The specifics of this update are described in the Appendix.
We evaluated three different system configurations. In the first setting, termed “Normal State,” we simulated the standard state of the original system. In the second, termed “Direction-selective Resistance,” we introduced a direction-selective subarachnoid resistance at point 25, enhancing solely the resistance to caudal flow by a factor of 20. In the third setting, termed “Simple Resistance,” we increased the subarachnoid resistance bidirectionally at point 25 (R25) by a factor of 20.
Results
System's responses in animation
Supplementary Videos 1-3 animate the system's responses to the three configurations. Supplementary Videos 4 and 5 display partial parameters extracted from them. Each animation's x-axis represents the 100 nodes of the circuit. Specifically, zero corresponds to the rostral-most point of the spinal cord, and 100 to the caudal-most point. The y-axis displays values of four parameters:
1. The dural tension (voltage in D capacitors as shown in Figs. 1 and 2).
2. The intraspinal-channel tension (voltages in C capacitors as depicted in Figs. 1 and 2).
3. The subarachnoid CSF flow (flows in R resistors as presented in Figs. 1 and 2).
4. The channel flow (flows in r resistors in Figs. 1 and 2).
Each of these parameters is plotted as a line graph, with the first twenty cycles being animated. Positive flow parameter values indicate the caudal direction, whereas negative values suggest the rostral direction. Pressure values are given in cmH2O, and flow rates in mL/sec.
To consolidate the four parameters into a single animation, the values of three parameters were adjusted using specific coefficients:
1. The intraspinal-channel tension was multiplied by 50.
2. The subarachnoid flow by 0.005.
3. The channel flow by 1.5 × 105.
Response to direction-selective resistance
In the “Normal State,” the system exhibited smooth to-and-fro CSF movements within the subarachnoid space in response to cyclic cranial pressure changes (see Supplementary Video 1). There was a minimal pressure elevation within the intraspinal channel.
The system's response dramatically changed when we introduced a direction-selective resistor at point 25 in the “Direction-Selective Resistance” setting. In this setting, sustained high pressure accumulated in the intraspinal channel distal to the introduced resistor (Fig. 3). This sustained pressure gradually accumulated as the flow cycle progressed (refer to Fig. 3 and the orange line in Supplementary Video 2). The build-up of this pressure is evident in Supplementary Video 4, which exclusively displays the intrachannel tension extracted from Supplementary Video 2. Additionally, a sustained low pressure was observed in the segment rostral to the inserted resistor (see Fig. 3 and the orange line in Supplementary Video 2).
Fig. 3.
The gradual accumulation of intrachannel pressure due to the cyclic to-and-fro movement of cerebrospinal fluid. The numbers indicate the cycle sequence.
This sustained pressure increase was absent in the “Simple Resistance” setting, wherein the introduced resistor was bidirectional (Supplementary Video 3). Alternating pressure increases appeared in the intraspinal channel on each side of the inserted resistor, synchronized with the to-and-fro CSF flow in the subarachnoid space. However, it never developed into a sustained pressure increase (Supplementary Video 3).
We closely examined the system's responses and understood how this sustained pressure increase arises. The flow within the intraspinal channel exhibits to-and-fro movements, synchronizing with the to-and-fro motion of the subarachnoid CSF, both in the “Direction-Selective Resistor” and the “Simple Resistor” settings (see the red lines in Supplementary Video 2 and 3). However, in the “Direction-Selective Resistor” setting, the caudal flow is more pronounced than the rostral flow, whereas they are equal in the “Simple Resistor” setting. Figure 4 and Supplementary Video 5 clearly illustrate this discrepancy by juxtaposing the intrachannel flow from both settings. As a result, the net difference between the caudal and rostral flows pushes the CSF caudally with each cycle of to-and-fro movement.
Fig. 4.
This figure highlights the pumping effect of the cerebrospinal fluid (CSF) within the intraspinal channel, driven by bidirectional flows through the direction-selective resistance. The intrachannel flow from the Simple Resistance model (indicated by the dotted line) is contrasted against the flow from the Direction-Selective Resistance model (represented by the solid line), wherein the caudal flow is selectively obstructed. Part A shows the caudal intrachannel flow during the caudal-flow phase, and Part B presents the rostral intrachannel flow during the rostral flow phase.
This mechanism can also be reflected in the opposite direction. A direction-selective resistance to the rostral flow leads to a comparable sustained pressure rise in the intraspinal channel situated rostral to the resistance (data not shown).
Discussion
This article evaluated the movement of CSF in the spine theoretically using a mathematical model. Moreover, this system introduced a direction-selective resistance to CSF flow in the subarachnoid space, which resists only the caudal flow. When to-and-fro CSF flows were applied to this system, a sustained pressure elevation was observed in the segment distal to the inserted resistance. If this theoretical observation is confirmed in practice, it can unify the explanations for the pathophysiology of syringomyelia and help resolve the pressure-gradient paradox.
In this model, we observed the strict consequences of the differential equations. However, these can be simply interpreted, as shown in Fig. 5. The pressure in the subarachnoid space pushes against the spinal cord material and affects the pressure within the intraspinal channel. As depicted in Fig. 2, the total pressure inside the intraspinal channel is the sum of the subarachnoid and channel tension (equivalent to the voltages of Ck and Dk in electrical terms).
Fig. 5.
Illustrations detailing how direction-selective resistance leads to CSF accumulation in the distal intraspinal channel. A distinct valve-like structure in the subarachnoid space introduces a selective resistance to CSF flow in the caudal direction.
A. During the caudal-flow phase, the resistance from the valve-like structure results in a pressure drop across the resistance point, decreasing the distal subarachnoid pressure. This subsequently decreases the pressure on the distal spinal cord matrix, creating a pronounced pressure gradient within the intraspinal channel and enhancing the caudal flow of CSF within this channel.
B. Conversely, during the rostral flow phase, the CSF encounters no resistance, negating the previously mentioned pressure gradient. Consequently, the rostral flow of CSF within the intraspinal channel is lesser than the caudal-flow phase.
This cyclical motion of CSF, influenced by the direction-selective resistance, produces a “pumping” effect within the intraspinal channel, leading to CSF accumulation.
Consider a one-way valve, represented by the red line in Fig. 5, that selectively resists the caudal flow in the subarachnoid space. A caudal CSF flow results in a pressure drop across this valve in the subarachnoid space, with the caudal pressure being lower than the proximal pressure (as illustrated in Fig. 5A). Consequently, the absolute pressure in the intraspinal channel located distally to the valve decreases due to the reduced external subarachnoid pressure, leading to a heightened pressure gradient in the intraspinal channel at the valve's location, increasing the distal CSF flow at that point (Fig. 5A).
In contrast, rostral flow, which faces no resistance, does not lead to a pressure drop (as seen in Fig. 5B). While some of the CSF pushed caudally during the caudal-flow phase will return in the rostral direction, its amount will decrease. Therefore, one cycle of to-and-fro CSF movement results in a net transfer of some CSF moving caudally within the intraspinal channel. Over time, CSF accumulates distally to the resistance, as visualized in Fig. 3 and Supplementary Video 2. We hypothesized that this phenomenon is connected to the mechanism responsible for syrinx formation.
Our theory clarifies the paradox of how CSF is driven into the high-pressure syrinx and held within the pressure gradient. In the direction-selective resistance model, the caudal segment of the intraspinal channel maintains a higher pressure than the adjacent subarachnoid space. However, the energy from the to-and-fro CSF movement creates an alternating pressure gradient in the rostrocaudal direction.
Since this rostrocaudal pressure gradient exceeds the sustained high pressure inside the intraspinal channel, CSF flows into the caudal segment from the rostral side during the caudal-flow phase (Fig. 5A). During the rostral flow phase, the rostrocaudal pressure gradient shifts direction. Consequently, the pressure on the rostral side becomes lower than that on the caudal side. While CSF does flow out rostrally from the caudal intraspinal channel, the absence of the pressure drop effect from the subarachnoid resistance in this phase reduces the rostrocaudal pressure gradient inside the intraspinal channel. As a result, the rostral CSF flow is less significant than the caudal flow during the caudal-flow phase (Fig. 5B), leading to the retention of CSF in the high-pressure intraspinal channel. We posit that this mechanism accounts for the CSF's paradoxical behavior in syringomyelia.
The concept of direction-selective resistance to CSF flow is grounded in evidence. In Chiari-I malformation, the herniated tonsils function akin to a ball valve, moving caudally during the caudal flow and rostrally during the rostral flow. Williams et al. identified a direction-selective resistance at the craniovertebral junction of Chiari-I patients, making the groundwork for their theory.15) Quigley et al.16) demonstrated in their phase-contast study that the directionality of CSF flow at the foramen magnified in patients with Chiari-I malformation.
Moreover, certain arachnoid pathologies can function as one-way valves. In 2014, we documented cases of thoracic arachnoid web associated with syringomyelia. In these cases, phase-contrast MRI highlighted the one-way valve-like behavior of the arachnoid web.17) During surgical procedures, we identified an obliquely oriented arachnoid web mirroring the function of a one-way valve.
Consequently, our hypothesis might also address one of the primary theoretical concerns previously introduced: the direction-selective resistance in the spinal subarachnoid space could be a shared mechanism driving Chiari-I-related and arachnopathy-related syringomyelia.
Our findings might clarify certain puzzling phenomena in our clinical practice. Cervical spondylosis can obliterate the subarachnoid space at the site of compression, thereby impeding CSF flow within the compressed segment. Yet, syringomyelia linked to cervical spondylosis is notably relatively rare despite the high prevalence of cervical spondylosis. This discrepancy might be attributed to the nature of the CSF blockage in cervical spondylosis: it is bidirectional rather than direction-specific. Our results indicate that a mere bidirectional block of subarachnoid CSF flow did not lead to a prolonged rise in intraspinal-channel pressure (as seen in Supplementary Video 4). For a consistent elevation in pressure to materialize, direction-selective resistance was essential. This could elucidate why syringomyelia is infrequently concomitant with cervical spondylosis.
Another observation worth highlighting is the negative pressure in the intraspinal channel located rostrally to the selective block (refer to Fig. 3 and the brown line in Supplementary Video 2). This resembles the “scalpel sign”18)―a distinctive contour in the spinal arachnoid web characterized by an expansion of the subarachnoid space preceding the syrinx. If the arachnoid web acts as a direction-selective resistance, then the negative pressure event documented in our model aligns closely with the upstream expansion of the subarachnoid space.
We utilized the lumped parameter model to simulate the spinal CSF dynamics. Lumped parameter models have been extensively employed in studies of biological fluid dynamics, especially in areas like blood and cerebrospinal fluid.19-21) This model was aptly suited for our primary goal: to elucidate the fundamental mechanisms responsible for syrinx formation. We did not aim to create a quantitatively precise model of spinal CSF flow. Instead, we aimed to develop a model encapsulating the central phenomenon.
Some aspects of our theory may be viewed as contentious. For instance, our model assumes the existence of a CSF channel within the spinal cord. This assumption might be contested since many syringes lack this communication when viewed on an MRI. However, a narrow CSF channel could still exist, though not discernible on MRI. Indeed, a standard MRI cannot display the central canal, whose diameter is around 100 micrometers. As such, postulating the existence of a CSF channel within the cord is possible.
Another potential debatable concern is the patency of the central canal in humans. Since the human central canal becomes obstructed with age, some might find it inappropriate to ascribe to it a significant role in pathophysiology. Yet, the occlusion of the central canal is a gradual process, and it typically remains unobstructed until around the fourth decade of life.22,23) Additionally, the CSF channel does not necessarily have to be the central canal; it could be any other channel embedded within the spinal cord matrix. We have investigated this topic in our prior publication.14)
It is recognized that syringomyelia is often preceded by interstitial edema, referred to as the “presyrinx” state.27) Some authors believe that this extracellular fluid accumulation results from a disturbed absorption mechanism.28) However, if we incorporate a certain degree of permeability to CSF into the intraspinal channel in our model, the CSF pumping effect created by direction-selective resistance could provoke interstitial edema in the segment distal to the resistance. Further studies are necessary to clarify this point.
While our hypothesis still requires concrete evidence, it holds the potential to address two significant issues that other hypotheses have yet to tackle: the pressure-gradient paradox and a unifying explanation for various forms of syringomyelia. Understanding the pathophysiology is crucial to treating any disease effectively. This principle is especially pertinent for the currently challenging-to-treat arachnopathy-related syringomyelia. Given the present scenario where definitive knowledge of syringomyelia pathophysiology remains elusive, it is imperative to remain receptive to innovative theories. Our hypothesis merits in-depth exploration, driving advancements in syringomyelia treatment.
Conclusions
Based on our simulation of spinal CSF dynamics, introducing direction-selective resistance to CSF flow resulted in a sustained pressure increase in the distal intraspinal channel. We propose that this may cause syringomyelia. This theory could unify the explanations for various types of syringomyelia, assuming that the cerebellar tonsil and the arachnoid web function as direction-selective resistances. Additionally, this hypothesis elucidates the paradoxical behavior of CSF entering and remaining in the high-pressure syrinx. We contend that this hypothesis requires examination in subsequent research.
Conflicts of Interest Disclosure
There is no conflicts of interest.
Supplementary Material
Depicts the system behavior under the Normal setting. Responses to 20 cycles of to-and-fro CSF flow are shown. The blue line represents dural tension, the orange line illustrates intraspinal-channel tension, the green line indicates subarachnoid flow, and the red line portrays intraspinal-channel flow.
Illustrates the system behavior in the Direction-selective Resistance setting. The subarachnoid resistance, specifically for the caudal flow, is augmented by a factor of 20 at point 25. Responses to 20 cycles of to-and-fro CSF flow are displayed. The blue line indicates dural tension, the orange line presents intraspinal-channel tension, the green line shows subarachnoid flow, and the red line represents intraspinal-channel flow.
Showcases the system behavior in the Simple Resistance setting. The subarachnoid resistance at point 25 increases by a factor of 20. Responses to 20 cycles of to-and-fro CSF flow are demonstrated. The blue line symbolizes dural tension, the orange line depicts intraspinal-channel tension, the green line denotes subarachnoid flow, and the red line presents intraspinal-channel flow.
Exhibits the intraspinal-channel tension extracted from Supplementary Video 2. Observations reveal a gradual tension build-up in the segment distal to the direction-selective resistance at point 25.
The intraspinal-channel flow from two settings (Simple Resistance and Direction-Selective Resistance) is simultaneously presented (orange line for Simple Resistance and blue line for Direction-Selective Resistance). Positive values signify caudal flow, and negative values represent rostral flow. In the Simple Resistance setting, caudal and rostral flows are symmetrical. In contrast, the Direction-Selective Resistance setting has less rostral flow than the caudal flow, resulting in a net CSF movement to the caudal side during each to-and-fro CSF flow cycle.
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Associated Data
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Supplementary Materials
Depicts the system behavior under the Normal setting. Responses to 20 cycles of to-and-fro CSF flow are shown. The blue line represents dural tension, the orange line illustrates intraspinal-channel tension, the green line indicates subarachnoid flow, and the red line portrays intraspinal-channel flow.
Illustrates the system behavior in the Direction-selective Resistance setting. The subarachnoid resistance, specifically for the caudal flow, is augmented by a factor of 20 at point 25. Responses to 20 cycles of to-and-fro CSF flow are displayed. The blue line indicates dural tension, the orange line presents intraspinal-channel tension, the green line shows subarachnoid flow, and the red line represents intraspinal-channel flow.
Showcases the system behavior in the Simple Resistance setting. The subarachnoid resistance at point 25 increases by a factor of 20. Responses to 20 cycles of to-and-fro CSF flow are demonstrated. The blue line symbolizes dural tension, the orange line depicts intraspinal-channel tension, the green line denotes subarachnoid flow, and the red line presents intraspinal-channel flow.
Exhibits the intraspinal-channel tension extracted from Supplementary Video 2. Observations reveal a gradual tension build-up in the segment distal to the direction-selective resistance at point 25.
The intraspinal-channel flow from two settings (Simple Resistance and Direction-Selective Resistance) is simultaneously presented (orange line for Simple Resistance and blue line for Direction-Selective Resistance). Positive values signify caudal flow, and negative values represent rostral flow. In the Simple Resistance setting, caudal and rostral flows are symmetrical. In contrast, the Direction-Selective Resistance setting has less rostral flow than the caudal flow, resulting in a net CSF movement to the caudal side during each to-and-fro CSF flow cycle.