Vanderbilt University

Department of

Biomedical Engineering

Developing a Model of the Inferior Cardiovascular Venous System

April 27, 2009

James ClearChase HoughtonMeghan Murphy

Table of Contents……………………………………………………………………………………………………………… 1

Abstract…………………………………………………………………………………………………………………………… 2

Introduction…………………………………………………………………………………………………………………….. 3

Available Models ………………………………………………………………………………………………….. 3

Model Objectives…………………………………………………………………………………………………... 5

Methodology…………………………………………………………………………………………………………………….. 5

Water Retention……………………………………………………………………………………………………. 6

Closed Circuit & Flow Dynamic………………………………………………………………………………. 7

Catheter Insertion Points……………………………………………………………………………………….. 7

Size & Portability…………………………………………………………………………………………………… 8

Heart Design Improvements…………………………………………………………………………………... 9

Results…………………………………………………………………………………………………………………………….... 9

Conclusions……………………………………………………………………………………………………………………….. 11

Recommendations…………………………………………………………………………………………………………….. 12

References…………………………………………………………………………………………………………………………. 12

1

Abstract

Currently, interactive cardiovascular models exist as specific models for accommodating specific devices. These models are expensive and generally do not allow for visualization of the device inside of the model. We set out to develop a model of the inferior venous cardiovascular system for visualizing catheterizations and testing new catheter technologies. In our design, we considered specifications presented by Vanderbilt University Cardiology Fellow Dr. Michael Barnett, the relevant technology available, the design flaws of a previous prototype, and machining constraints. The primary objectives were to make the model anatomically accurate, eliminate water leakage, create a simulated venous flow and increase its portability. Our final model achieved our design objectives, the expectations of Dr. Michael Barnett and functioned in the catheterizations identified as specific devices to be tested. The model that was constructed has commercial and instructional applications. Expansion of the model is possible in order to simulate arterial or other systems, as well as identifying the source and following the progression of air embolisms during catheterization.

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Figure 1. Mentice VIST endovascular simulator1

Introduction

In today’s quickly changing field of medical research, attracting venture capitalists and making proof of concept presentations is essential in developing potential devices. This need presented a challenge for Dr. Michael Barnett, a Fellow of Cardiology at Vanderbilt University Medical Center. Dr. Barnett is actively researching and developing several cardiac catheters. His research requires a model of the inferior venous system for demonstrating catheter function at conferences. Two particular catheters are currently in development and require a model for demonstration: one is a steerable catheter and the second is an optical scope catheter. The steerable catheter is intended to improve the maneuverability of catheters through complex motions while en route to the intended destination. The optical scope catheter is intended to add a visual display for the doctor of the internal anatomy of the veins while en route and at the destination site.

In proof of concept studies, Dr. Barnett’s research requires a model to study how feasible catheter development is, offer metrics of catheter performance, identify any technical issues with the catheter function, and establish a budget for catheter production. A model of the inferior venous system that meets these demands does not currently exist. The relevant technology that is currently available includes catheterization simulators, cast models of the heart or the veins exclusively, and various models designed for device specific testing. Each of these models has restrictions which do not allow clear visualization of catheterizations.

Available Models

The Mentice VIST is a pricey endovascular simulator which is commonly used in clinical training. The simulator is able to present the physician with various scenarios that occur during catheterizations. Unfortunately the simulator does not allow for any visualization of catheter movement within the patient, as would be the case during actual surgery. While the simulator has a series of available modules, no modules are available for testing Dr. Barnett’s developing prototypes.1 For these reason, the simulator does not meet the demands of Dr. Barnett. Further, the cost of the Mentice, approximately $40,000, puts it well outside a reasonable price range for a clear system offering visualization of catheter movement.

Dynamic Med Demo is second producer with interactive medical products. Dynamic Med offers models meeting more of the demands Dr. Barnett is seeking, including clear acrylic casts, but the models do not offer both venous vasculature and access to the heart. Dynamic Med offers a peripheral showcase and a heart valve replacement demonstrator. The peripheral showcase shown in Figure 2 would allow visualization of catheter movement through the vasculature but being an open circuit, no flow would be possible and access to the heart would not be feasible.2 The heart valve replacement demonstrator (Figure 3) offers a crystal clear heart for visualizing a heart valve replacement but lacked

1 http://www.mentice.com/archive/pdf_products/Mentice_A4_broschyr_LR2.pdf2 http://www.dynamicdemo.net/an_05.html

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Figure 2. Dynamic Med Demo Peripheral Showcase

Figure 3.Dynamic Med Heart Valve Replacement Demo

anatomical accuracy. The system does involve full flow by manually squeezing a bilge pump but a secondary technician would be necessary to introduce flow during catheterization. The model also included external equipment (a flat screen display of the valve replacements) that was costly and of no use in Dr. Barnett’s proof of concept demonstrations. Costing $8,000, the model was outside Dr. Barnett’s price range, especially considering the model lacks anatomical accuracy.3

In a second form of device testing, there exist

companies that will perform testing particular devices at a high cost. Mecmesin is one such company. Mecmesin’s purpose is to test the usability and “fitness-for-purpose” of medical devices and whether the device conforms to regulatory standards. Device testing offered by Mecmesin includes tensile and compressive strength testing for materials, sharpness and penetration forces, torque testing, etc.4

Other device specific models have been patented with the same purposes. The models are developed with very specific purposed and do not accommodate for visualization or modularity. For example, a model was patented for testing prosthetic tricuspid valve replacements. The leaflet valve is exposed to in vivo loading including forward pressure applied to the valve as well as backflow pressure. This device was intended to simulate the fatigue experienced by prosthetic valves in term long use. The device was also intended to test for defects affecting functionality.5 Another model that has been created is used for modeling flow dynamics through a prosthetic bicuspid valve. The model uses an agar gel with characteristics of biological tissue and an ultrasound to study flow through the left ventricular and aortic chambers.6 A third model was identified that tests ventricle assist devices (LVAD). The model demonstrates pumping performance and flow dynamics through LVADs with resistance comparable to the native heart.7

3 http://www.dynamicdemo.net/dem_01.html4 http://www.mecmesin.com/test-solutions/solutions-by-industry/medical-devices5 Appartus for Testing Prosthetic Heart Valve Hinge Mechanism. More RB et al., inventors. United States Patent US5531094. http://www.freepatentsonline.com/5531094.pdf accessed 12 Nov 20096 Durand LG, Garcia D, Sakr F, et al. A New Flow Model for Doppler Ultrasound Study of Prosthetic Heart Valves. Journal of Heart Valve Disease. [Internet] 2006 Nov 4 [cited 12 November 2009]; 17. Available from: http://www.icr-heart.com/journal/7 Pantalos GM, Koenig SC, Gillar KJ, Giridharan GA, Ewert DL. Characterization of an adult mock circulation for testing cardiac support devices. ASAIO. Feb 2004; 50(1):37-46

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Model Objectives

The goal of our design process was to develop a portable and anatomically accurate model of the inferior venous system for demonstrating various catheter insertions. Further, we felt making such a model commercially available would potentially expand research in catheter development. A senior design group attempted to address this need in 2009and generated a model that was somewhat functional for Dr. Barnett (Figure 4). However, there were fundamental issues with the model which we intended to address in our model’s design.

Figure 4. Prototype established in 2009 under Dr. Barnett

To fulfill the goals of our design process and in light of the prototype established in 2009, we established several design objectives for our model. The first objective was to establish a clear model free of visual obstruction. The second objective was to ensure the model was entirely water tight yet capable of being emptied and refilled. After achieving a clear model without leaking, the next objective was to generate an anatomically representative venous flow gradient. The fourth objective was to create an anatomically representative heart that would allow for catheter access. The fifth objective was to meet the size constraints of carry-on luggage with model dimensions of 22” x 14” x 9”8. Finally, we established a manufacturing cost objective of approximately $2,000 considering the costs of currently available models.

Methodology

The ultimate design of our cardiovascular model entailed prioritizing the features we were seeking and making adjustments to the model previously created by the senior design team in 2009. Considering the aforementioned design objectives and the previous model, we sought to eliminate all leaking joints, modify the structure of the model to eliminate wasted space and increase its portability, close the circuit and add fluidic flow, and improve the anatomical representation of the interior of the

8 http://www.delta.com/traveling_checkin/baggage/carryon/index.jsp

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9/16'' 7/16''

Figure 5. Schematic of connector to interface silicon tubing from pump to the acrylic tubing from the model.

heart. Finally, we sought an aesthetic, professional model that would be well regarded during presentations.

Water Retention

In order to develop a tubing system that did not leak, we began with studying materials and considering several adhesives. We first discussed some options with a silicone tubing distributor and learned that silicone glue could only be melded if at the same ratio and material that it’s being glued to. Following this, in discussions with John Fellenstein at the Vanderbilt machine shop, we were informed that acrylic could be sealed to other acrylic pieces using dichloroethylene or an acrylic cement. Dichloroethylene is a very strong acrylic adhesive as it welds two neighboring acrylic parts together by melting the plastic structures together. However, the adjoining pieces must have a very flat surface interface. The acrylic cement on the other hand would more properly join acrylic pieces at machined surfaces. It was therefore primarily used but the dichloroethylene was used supplementary to ensure complete water tightness. In addition to gluing acrylic parts to each other, we designed a Y-connector, which represents the inferior vena cava bifurcation, by using double o-rings to prevent leaking at those joints. This type of o-ring connection also contributed to the modularity of the model and the ability to exchange the limbs representing the femoral veins.

In order to connect the pump to the rest of the acrylic circuit, flexible silicon tubing (½'' inner diameter , ¾" outer diameter) was used. In a push on fashion the flexible tubing was sealed over the

pump input and output connectors which had a ½'' outer diameter. This provided a proper seal at the pump interface as but was unsuitable for interfacing with the ¾'' outer diameter tubing of the model. Therefore two tubular connectors were manufactured: one for the input to the model from the pump and one for the output from the heart to the pump (Figure 5). One end of these connectors was tapered with a maximum outer diameter slightly under ½'' so that it

would slide into the ½'' inner diameter of the model. The other end had an outer diameter slightly over ½'' so that the flexible silicon tubing would form a water tight seal after being pushed over this end. To further ensure proper sealing metal tube clamps were used over the silicon tubing pressed over the larger diameter end of the connector. The smaller diameter end was glued into the ½'' inner diameter tubing prevalent in the model. It is important to note that one connector was constructed from acrylic tubing while the other was constructed from aluminum tubing. The acrylic connector was an inch long and connected to a two inch segment of ½'' inner diameter tubing. This tubing was then pushed into the bottom Y-connector. The aluminum tubing was three inches long to allow for more overlap between the connector and the silicon tubing in an attempt to prevent leaks. It was constructed from aluminum to give it more structural integrity which allowed for the tube clamp to be sealed much tighter and further reduce the potential for leaking.

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To prevent leaking from the heart, where the two halves were bolted together, a material was chosen for the septum that was slightly flexible to allow compression, but firm enough to withstand the pressures created by the pump. Finally, in order to capture any liquid that might leak during use of the cardiovascular model, a rectangular acrylic base was constructed for the model to rest on while in use, and was equipped with 1” high acrylic walls around the edge that were glued using acrylic bonding cement.

Closed Circuit & Flow Dynamic

In order to create a closed circuit, part of the rigid acrylic tubing needed to be bent into a semi-circle. We decided that if we heated the tubing, we may be able to bend it. Using a heat gun, we experimented using high and medium heat, as well as bending the tube faster or slower. Throughout all bending experiments, we kept the tubing flat on the table so as to be sure that all bending was occurring in one plane and that no twisting occurred. We found that if the tubing got too hot or if we bent it too fast, it would result in kinks. We also experimented with putting sand into the tube to help reduce the amount of kinking and maintain the same inner diameter of the tube throughout the bending process. This however, ended with sand being engrained in the part of the tubing that was heated, causing a decrease in the clarity. The best results occurred when we attempted slower heating over a 1”-1.5” length of tubing and allowed for some cooling before bending. In order to ensure a standard bending radius for the final bent tubes, we used a metal cylinder to bend the tubes around. The cylinder was coated in acrylic glue to prevent the heated tube from sticking to the metal during bending. This grease did not leave any residue engrained in the tubing after cooling of the acrylic tube.

In selecting a pump to create flow throughout the cardiovascular model, we consulted with Dr. David Merryman, an assistant professor in the Departments of Biomedical Engineering, Medicine and Pediatrics. On his advice we explored using a bellows metering pump to generate a pulsatile flow similar to that found in the venous system. A Gorman Rupp Industries bellows pump was selected for its suitable flow requirements and compact size. The pump used was an adjustable Compact Bellows Metering Pump with a 2” bellows size, a motor RPM of 90 at 60 Hz, a maximum flow rate of 1620 mL/min, and a ½” inner diameter input and output.9

Catheter Insertion Points

Unlike the previous prototype, this cardiovascular model was designed to be a closed circuit to allow for flow from the femoral veins through the heart. Accordingly catheter access holes need to be created in the tubing. This was accomplished by drilling holes into the tubing representing the femoral veins. The holes were drilled at a 45 degree angle to prevent the catheters from needing to bend at an extreme angle when inserted into the model. Moreover, the largest hole possible was drilled (a ½” hole into a ½” inner diameter tube) in order to allow the largest feasible device to be inserted into the model. To accommodate for smaller catheters, rubber stoppers were inserted into the catheter access holes. These rubber stoppers were then drilled to create a more appropriately sized catheter insertion

9 Gorman Rupp Industries. Compact Bellows Pump Selection Guide. [Internet] ©2009. Available from: http://www.gripumps.com/upload/products/CompactBellowsPumpSelectionGuide0310.pdf

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point. These smaller holes were sealed with a catheter sheath with a one way valve that prevented water from squirting out. The diameter of these holes could be adjusted between stoppers to accommodate the various sizes of the catheters. However, because the catheter insertion hole was drilled at an angle, a normal rubber stopper was not able to properly seal the hole. To accommodate for this, an endmill was used on one end of another ½” inner diameter, ¾” outer diameter acrylic tube at 45 degrees so that it would line up exactly with the hole drilled into the femoral vein tube (Figure 6). This angled tube was then glued onto the femoral vein tube and since it terminated in a circle a rubber stopper created a proper seal.

Figure 6. Side profile of bent acrylic tubing representing femoral vein complete with catheter insertion point.

Size & Portability

Our overall goal for the size of the model was that it could be small enough to fit inside of a standard carry-on suitcase in order for it to be able to travel safely and easily. The most significant way in which we decreased the size of the old model was by eliminating all of the tubing representative of the veins superior to the heart. Weight considerations of materials remained a priority for all parts of the cardiovascular model as well. While a prime candidate for effectively sealing joints, hard acrylic tubing was heavier than the soft plastic used in the previous model. However, because the acrylic is relatively light, and because the leaking issue and poor clarity at joints was a key problem with the previous design, this trade off was acceptable. We further minimized the size of the model by reducing the bend radius of the tubing representing the femoral veins. This was the limiting factor to the model height and after establishing this radius the exterior heart size and pump location were designed accordingly.

Another feature of our cardiovascular model that helped increase its portability was the use of o-rings at the Y-connector which simulated the inferior vena cava bifurcation. Because the parts of the model are not glued at this juncture, the limbs representing the femoral veins are removable from the upper half of the model and can be stored separately during travel. This allows the model to be disassembled into parts which are 13'' x 6 '' X 6 '' at the largest. This feature also allows for the

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ID: OD:

Figure 7. Top view of final cardiovascular model resting on blue acrylic surface.

interchange of different sized limbs representing the femoral veins. This exchange permits the distance between the insertion point and heart to be easily changed if need be.

Heart Design Improvements

Initially we explored materials and methods for casting a model of the heart. Machining acrylic leaves a slightly hazy finish which we hoped to eliminate all together by constructing the heart from clear casting materials. We experimented with two shore hardness ratings of clear polyurethane casting compound (70A, 80D). After attempting several casts we noticed that the polyurethane had numerous bubbles and was also hazy. We came to learn however, by contacting the manufacturing company, that the polyurethane was rated at clear only up to ¼'' thickness. Furthermore, we struggled with releasing the mold as well with what to make the mold out of and which materials to use. Eventually we deemed that casting the heart was unfeasible given our objectives and difficulty achieving success with the geometry and clarity. We finally decided on making a machined acrylic model of the heart which would mimic the shapes and volumes of the right atrium and ventricle. By taking this approach we were able to generate a model of the heart with ovular/ellipsoid chambers of relative similarity to the actual heart while also devising a way for the chambers to contact the septum. For the purposes of our model we concerned ourselves only with the right side of the heart. We wanted an input from the modeled inferior vena cava coming directly into the right atrium and an output returning to the rest of the model exiting from the right ventricle. This was due to the need to model only inferior venous catheterizations.

Results

Our final model of the venous system consisted of clear, acrylic tubing and a heart fabricated from acrylic blocks. Each half of the heart was sealed with acrylic cement, as was the inferior vena cava – heart connection. The inferior vena cava bifurcation was created out of acrylic blocks and was sealed with double o-rings at each connection. The final bend radius of the acrylic tubing was 2”. The model rests on a blue acrylic base with 1” tall walls and flexible tubing connecting the venous circuit with a bellows metering pump (Figure 7).

The final heart model consists of 4 blocks of acrylic with hemi-elliptical shapes hollowed into them. Each half of the heart is formed from a bottom and top half. The two halves of each side of the heart are sealed together with acrylic cement. The right and left sides of the heart are bolted together but are separated by a cork gasket representing the septum. The atria are modeled by an ellipsoid with radius 0.7'' and height 0.75'', while the ventricles are represented by an ellipsoid with radius 0.75'' and

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height 1.2''. The top and bottom half of these shapes are hollowed out into the respective portions of the acrylic blocks. When sealed together these blocks created the chambers of the heart with a close representation to the anatomy of the heart, as shown in Figure 8. The septum was modeled by a cork gasket. Each chamber of the heart had direct access to the septum through an oval window created by cutting down the side of the ellipsoid shaped heart approximately 0.2'' from the side of the hollowed out heart. This cut was made after the top and bottom half of one side of the heart were glued together so as to provide more structural integrity during the cut. This process was akin to slicing through a bowling ball pin a few centimeters from the edge.

Our final cardiovascular model prototype successfully addressed the design objectives outlined. With the entire model assembled and filled with water, the model successfully retained all water after sitting for 72 hours. In addition, no leaking occurred while the pump was turned on for a continuous 30 minutes. To visually confirm that the water was flowing while the pump was turned on, a bolus of dye was injected into the model at one of the catheter insertion points. The dye was then observed to flow up the femoral vein limb, into the heart and pump, followed by return into each of the femoral vein limbs.

In addition to passing tests of water retention and simulated venous flow, the dimensions of our cardiovascular model were satisfactorily comparable to their corresponding anatomical values, as shown in Table 1 and Figure 9. Although the model was not anatomically exact the model was representative in the sense of depicting approximate physiology. The percent errors of the model dimensions hover between 20 and 30 % (Table 1) but this error was an acceptable trade off to helping to visualize catheter deliveries as requested by Dr. Barnett. The model furthermore is modular to pieces 13’’ x 6’’ x 6’’ or smaller. This fulfills the ability of the model to be stowed in carryon luggage if properly packed to prevent damage in travel. The only exception to this objective is the blue base which is 28’’ x 16’’. This however can be stored on checked baggage and would therefore still be portable.

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Figure 8. Top view of our computerized design of the two sides of the heart model (left), an electrocardiogram of a heart (middle), and our final acrylic heart (right).

10”

9”9”

6”6”

Figure 9. Overall layout of final model, with dimensions

1” ID

½” ID

Vein

Anatomical Value Tubing Value

Error

IVC Inner Diameter10 ~0.81” 1" 23%R/L Femoral Inner Diameter11 ~0.41” 0.5” 20%IVC Length12 ~14” (including SVC) 10” (not including SVC) 29%

Chamber Anatomical Volume Model Volume ErrorR/L Atrium13 ~2.37 in3 1.53 in3 35%R/L Ventricle14 ~3.60 in3 2.82 in3 22%

The proposed model is able to successfully demonstrate the use of various catheters and other intracardiac devices in a system that is anatomically representative of an average human. The model offers a competitive cost advantage over the models currently available. Further, the majority of the expense in building our model came from machining costs which would be lowered if the model were produced on a commercial scale. The ease of machining also allows for adaptations to the model as demanded by various users.

10 Prince, MR., Novelline, RA., et al. The Diameter of the Inferior Vena Cava and Its Implications for the Use of Vena Cava Filters. Radiology. 1983;149:687-689.11 Hertzberg, BS., Kliewer, MA., et al. Sonographic Assessment of Lower Limb Vein Diameters: Implications for the Diagnosis and Characterization of Deep Venous Thrombosis. American Journal of Roentgenology. 1997;168:1253-1257.12 Takayama, T., Hirai, S., et al. Measurement of the Vena Cava at Postmortem Examination, From the Upper End of the Superior Vena Cava Via the Right Atrium to the Lower End of the Inferior Vena Cava. Clinical Anatomy. 6:349-352 (1993).13 Wang, Y., Gutman, JM., et al. Atrial volume in a normal adult population by two-dimensional echocardiography. Chest. 1984;86:595-601.14 Nakagawa, Y., Fujimoto, A., et al. Assessment of the normal adult right ventricular diastolic function using M-mode echocardiographic measurement of tricuspid ring motion. International Journal of Cardiac Imaging. 1998;14:391-395.

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Model Total CostProposed $2,380 Mentice VIST $40,000 Dyanamic Med Peripheral Showcase $4,000 Dynamic Med Valve Replace. $8,000Table 2. Comparative table of current cardiovascular models.

Table 1. Comparison of Anatomical Sizes with Model Sizes

Conclusions

The prototype created successfully meets the specific device objectives. For proof of concept presentations or for use in clinical training, the model allows for clear visualization of catheterizations. Further, the model offers anatomically representative dimensions with an accurate venous flow gradient. Catheters of various diameters may be inserted with a maximum outer diameter catheter size of .5in. This size allowance meets the requirements for the optical scope proof of concept testing and demonstration. Access to the right atria and ventricle allows for use of Swan-Ganz catheters to measure intracardiac pressures. Access between the right and left atrium and ventricles and the presence of a biomemetic septum allows for testing catheters penetrating the septum.

Recommendations

Future work will involve establishing a means of casting the heart to achieve an anatomically correct exterior in addition to an anatomically correct interior. This casting will potentially involve plaster of paris and a cadaver heart. This construction will involve close work with Mr. Ray Booker and the Vanderbilt Simulation Center.

A second avenue of future work will involve adding a modular superior venous system as well as portions of the arterial system. Expanding the vasculature represented will allow for simulation of a larger number of processes and catheterizations. This could be done by adding on to the current model or by producing other models. Factors such as the size, portability and complexity will need to be considered to determine the best approach to accomplish these expansions. One possible use for an anatomically expanded device is detecting the introduction of air embolisms during catheterization. This avenue is of particular importance to the Simulation Center as Mr. Bookers has communicated a need for this training in the lab. His emphasis on the short comings of the Mentice VIST simulator and the demand for a system with clear visibility reiterates the value of our model and the future uses for our model.

Ethical issues will arise in casting the heart from a cadaver heart but this is a worthwhile avenue to pursue because of the advantages of our model and its demand. Otherwise, the model was constructed entirely of acrylic tubing and presents no other ethical concerns. Its uses will be limited entirely to in vitro demonstrations.

References

http://www.mentice.com/archive/pdf_products/Mentice_A4_broschyr_LR2.pdf

http://www.dynamicdemo.net

http://www.dynamicdemo.net

http://www.mecmesin.com/test-solutions/solutions-by-industry/medical-devices

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Appartus for Testing Prosthetic Heart Valve Hinge Mechanism. More RB et al., inventors. United States Patent US5531094. http://www.freepatentsonline.com/5531094.pdf accessed 12 Nov 2009

Durand LG, Garcia D, Sakr F, et al. A New Flow Model for Doppler Ultrasound Study of Prosthetic Heart Valves. Journal of Heart Valve Disease. [Internet] 2006 Nov 4 [cited 12 November 2009]; 17. Available from: http://www.icr-heart.com/journal/

Pantalos GM, Koenig SC, Gillar KJ, Giridharan GA, Ewert DL. Characterization of an adult mock circulation for testing cardiac support devices. ASAIO. Feb 2004; 50(1):37-46

http://www.delta.com/traveling_checkin/baggage/carryon/index.jsp

Gorman Rupp Industries. Compact Bellows Pump Selection Guide. [Internet] ©2009. Available from: http://www.gripumps.com/upload/products/CompactBellowsPumpSelectionGuide0310.pdf

Prince, MR., Novelline, RA., et al. The Diameter of the Inferior Vena Cava and Its Implications for the Use of Vena Cava Filters. Radiology. 1983;149:687-689.

Hertzberg, BS., Kliewer, MA., et al. Sonographic Assessment of Lower Limb Vein Diameters: Implications for the Diagnosis and Characterization of Deep Venous Thrombosis. American Journal of Roentgenology. 1997;168:1253-1257.

Takayama, T., Hirai, S., et al. Measurement of the Vena Cava at Postmortem Examination, From the Upper End of the Superior Vena Cava Via the Right Atrium to the Lower End of the Inferior Vena Cava. Clinical Anatomy. 6:349-352 (1993).

Wang, Y., Gutman, JM., et al. Atrial volume in a normal adult population by two-dimensional echocardiography. Chest. 1984;86:595-601.

Nakagawa, Y., Fujimoto, A., et al. Assessment of the normal adult right ventricular diastolic function using M-mode echocardiographic measurement of tricuspid ring motion. International Journal of Cardiac Imaging. 1998;14:391-395.

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