The Excerpt below, from the Technical Report, also provides a description of the model
Prepared by:
Dr. Scott D. Phillips, Principal Investigator
Dr. Darin A. Knaus, Project Engineer
Creare, Hanover, NH 03755
High Level Description
Overall schematic of the integrated system level model. The model includes functional components of the circulatory system, the CSF fluid system, and the aqueous humor fluid system. The colored blocks in the figures represent the various sub-models and associated user model input.
Circulatory sub-model
We simulate the heart as a pressure-driven flow source designed to roughly mimic the waveform of a heartbeat by using the peak of a sine wave with the amplitude and duration of a heartbeat. Connected in series with a built-in check valve model, this produces a pressure and flow pulse that prevents backflow from the aorta. Experimentally-measured heart rates and systolic pressures feed into this signal providing a heartbeat trace that roughly matches the actual heartbeat. Blood flow branches after the aorta into the body circulation and the head circulation loops. Figure 2 shows a schematic representation of our high-level circulatory model, and Figure 3 shows the Simscape implementation. Our model is a lumped parameter analysis, so the circulatory system vessels are broken into separate elements describing the flow through the vessels. Each element is described in Section 3.1.3 of this report.
Our simplified body circulatory loop consists of the upper and lower body arteries, peripheral system, upper and lower body veins, and the inferior vena cava. The peripheral system includes smaller arteries and veins in the body’s extremities and the related capillary interfaces. The body circulation is split into the upper and lower body parallel segments.
The simplified head loop consists of the carotid arteries, head arteries, brain capillaries, head veins, jugular veins, and the vertebral plexus. The head arteries branch off from the aortic arch and the head veins return blood in the inferior vena cava via the jugular vein and vertebral plexus. Figure 4 shows an illustration and Simscape model schematic of the parallel jugular and vertebral plexus vessels used to construct the head drainage portion of the circulatory model. Physiologically, in the supine or prone position, the internal jugular veins form the primary blood drainage pathway. However, in the upright orientation, the jugular veins collapse under the low cranial blood pressures and blood shunts through the vertebral plexus. This behavior has been captured in the circulatory system model. We created a flexible tube model that not only tracks the internal pressure of the vessel, but also includes a term for the transmural pressure, the difference between the pressure on the inside and outside of the vessel. The area of the vessel is dependent on this transmural pressure. The vein collapse is implemented with a prescribed relationship between the vessel cross-sectional area and the pressure difference across the wall. To compute the pressure difference, the internal pressure is assumed to be the average of the inlet and outlet pressures of the vein. As the orientation change induces a lower vein internal pressure, the collapsible vein closes. The flow is shunted to the rigid venous plexus, and the vein inlet pressure reduction is somewhat slowed by the flow passage reduction. By providing each of these pathways, the model captures shunting of flow from the jugulars to the vertebral plexus in conditions that cause a drop in venous pressure relative to the external pressure, such as in an upright orientation.
The body peripheral system and the brain capillaries are modeled differently than the other vessels because these flow channels are so small, numerous, and multi-directional that the impact of gravity on flow is assumed to be negligible. The peripheral system is modeled as a resistance and an inertance in series. The brain capillaries are represented as a resistance between the head arteries and head veins with no inhertance.
CSF Sub-Model
The goal of the CSF sub-model is to output a representative ICP, which is used as a boundary condition for the structural eye model. We investigated CSF flow dynamics and developed a simplified model that captures the key features likely to be affected by microgravity. The Simscape implementation of the CSF sub-model is illustrated below.
The cardiovascular system generates blood pulsations in and out of the cranium during each cardiac cycle. The pressure in the blood vessels is communicated to the CSF-containing volumes via flexible membranes. As the pressure in the cranium oscillates, the overall fluid volume within the rigid cranium must remain constant. This is a constraint that is enforced in the integrated Circulatory-CSF model. Thus, the balance between the flexibility of the cranial blood vessels, the brain tissue, and the CSF volume determines the distributions of fluids and pressures within the head for a given condition. The CSF spinal volume also provides an overflow mechanism with a flexible sac at the base of the spine. We can think of the CSF, arterial, and venous volumes as three separate balloons inside the cranium; when the volume of one balloon increases, the others vary according to the pressure-volume-flow balance with the other tissues and fluids in the head.
On Earth, the average human has a total blood volume of about 5 L, of which about 0.5 L is located in the head. When the body first enters zero gravity, a sudden shift of fluid distribution in the head occurs in the absence of hydrostatic forces. In the initial transition to microgravity, additional fluid may accumulate in skin tissue outside of the skull, creating the “puffy face” seen in many astronauts. Over longer duration stays in microgravity, the total blood volume of the body actually reduces by 16%, which may be in part due to the shifts in blood pressure distribution throughout the body (Watenpaugh 2001).
Our simplified CSF system model consists of the cranial CSF volume, which includes the ventricles and the cranial subarachnoid spaces, and the spinal CSF volume. The CSF pulsatile flow is caused by the head arteries pressure oscillations, which push on the compliant cranial CSF volume. Pressure sensors model this pressure dependence and connect the CSF sub-model to the circulatory numerical loop. The pulsatile flow between the cranial and spinal CSF spaces is on the order of 100‒200 mL/min. Adult CSF production varies between 400 and 600 mL/day (Sakka et al. 2011). CSF production is primarily driven by the pressure difference between blood flow in brain capillaries and the CSF pressure in the ventricles of the brain. Since the CSF production is three orders of magnitude lower than the CSF pulsatile flow, the CSF production is currently modeled as a constant zero flow source. The CSF drainage or reabsorption into the venous system can also be described as a pressure-dependent flow. The reabsorption is implemented as a resistance, analogous to the arachnoid granulations in the brain, between the CSF system and the head veins. In the current implementation of the model, the exchange of fluid between the CSF system and the circulatory system is set to zero by turning off the CSF production source and setting a very high resistance at the CSF drainage point. The two fluid systems interact via pressure-compliance connections and volume constraints only. Future studies with this model can include the CSF flow by adjusting these two parameters, but the rate of exchange is not large enough to be significant in the scope of the current study and adds numerical complexity to the solver.
Aqueous Humor Sub-Model
The goal of the aqueous humor sub-model is to use an eye compliance derived from the structural eye model and output a representative IOP. After several iterations of transferring the ICP pressure from the fluid model to the structural eye model and the eye compliance from the structural model to the fluid model, the IOP output from both models should match.
The aqueous humor is formed at the ciliary bodies via diffusion, ultrafiltration and active transport (To et al. 2002; Gabelt and Kaufman 2011). The formation is mostly driven by blood flow, blood pressure, and ion concentration. Our model focuses on applying the blood flow and pressure components of the aqueous humor formation. The blood flows to the eye ciliary processes where the aqueous humor is formed. The aqueous humor flows from the posterior chamber to the anterior chamber and is drained via the trabecular and uveoscleral pathways to the episcleral vein. Our Simscape representation captures these flows of the aqueous humor system as illustrated in Figure 6. The blood flows in from the outlet of the head arterioles and out to the inlet of the small head veins.
The Simscape representation incorporates four resistance terms, four gravity terms, a compliant volume, and two drainage terms. Two of the resistances, termed “AH loop” and “Eye vasculature” in Figure 6, are used to tune the blood flow going to the eye and getting filterted to form aqueous humor. This framework allows incorporating an ionic component in the future to model active transport, which is an important contributor to aqueous humor formation.
The four gravity terms account for the hydrostatic gradients: 1) from the center of the head to the center of the eye, 2) from the center of the eye to the front of the eye, 3) from the front of the eye back to the center of the eye, and 4) from the center of the eye back to the center of the head. We are interested in the IOP at the center of the eye because this is the IOP output from the structural model developed on the EPSCoR project. We are also interested in the IOP at the front of the eye because it is where the pressure is measured in the experiments and it is where drainage occurs.
The eye compliance is modeled using the linear volume-pressure relationship provided by the structural model:
Veye = Ceye * IOP + Veye initial (1)
where:
Veye is the eye volume
Ceye is the eye compliance from the structural model
Veye initial is initial eye volume from the structural model
Currently, the eye volume is only a function of IOP, but we have the framework in place to account for inputs from the ICP.
Finally, the aqueous humor system includes the trabecular and uveoscleral drainage pathways. The trabecular drainage flow is pressure-driven and calculated using the outflow facility times the pressure difference between IOP and episcleral venous pressure (EVP). The outflow facility is measured experimentally by tonography, the value used in the model is 0.29 μL/mL/mmHg (Selvadurai et al. 2010). The uveoscleral drainage is usually constant at about 1.64 μL/mL (Toris et al. 1999), but when the IOP is above 25 mmHg, the drainage increases by about 2% per mmHg above 25 mmHg (Johnson and Erickson 2000).
Multi-System Interactions
The CSF, Circulatory, and Aqueous Humor flow systems interact with each other through shared pressure boundaries and through indirect fluid transfer mechanisms. For instance, the CSF system interacts with the circulatory system at the CSF secretion and absorption sites (direct fluid exchange), at the contact zones between the CSF space and cerebral vessels (pressure/volume boundaries), and at the brain regulatory nuclei with the expansion of the ventricular system.
The sub-models exchange information and act as a coherent representation of the body’s fluid mechanical processes via a single “working fluid.” The model exchanges this “working fluid” between the sub-models by passing the fluid through flow restrictions that represent the creation/destruction of one fluid and the destruction/creation of another (e.g., blood in the ocular arteries being converted into aqueous humor in the ciliary body and being drained back to the venous system in the trabecular meshwork and uveoscleral pathways). This simplification greatly stabilizes the model and allows the underlying equations to conserve mass.