An Arteriovenous Mock Circulatory Loop and Accompanying Bond Graph Model For In Vitro Study Of Peripheral Intravascular Bioartificial Organs

Abstract

Background:

Silicon nanopore membrane-based implantable bioartificial organs are dependent upon arteriovenous implantation of a mechanically robust and biocompatible hemofilter. The hemofilter acts as a low-resistance, high-flow network, with blood flow physiology similar to arteriovenous shunts commonly created for hemodialysis access. A mock circulatory loop (MCL) that mimics shunt physiology is an essential tool for refinement and durability testing of arteriovenous implantable bioartificial organs and silicon blood-interfacing membranes. We sought to develop a compact and cost-effective MCL to replicate flow conditions through an arteriovenous shunt and used data from the MCL and swine to inform a bond graph mathematical model of the physical setup.

Methods:

Flow physiology through bioartificial organ prototypes was obtained in the MCL and during extracorporeal attachment to swine for biologic comparison. The MCL was tested for stability over-time by measuring pressure-wave variability over a 48-hour period. Data obtained in vitro and extracorporeally informed creation of a bond graph model of the MCL.

Results:

The arteriovenous MCL was a cost-effective, portable system that reproduced flow rates and pressures consistent with a pulsatile arteriovenous shunt as measured in swine. MCL performance was stable over prolonged use, providing an important medium for enhanced testing of peripherally implanted bioartificial organ prototypes. The corresponding bond graph model recapitulates MCL and animal physiology, offering a tool for further refinement of the MCL system.

Graphical Abstract

Mock circulatory loops (MCL) and mathematical models are essential tools for developing arteriovenous implantable bioartificial organs (IBO) containing silicon nanopore membranes. An MCL was constructed to replicate experimental flow conditions through arteriovenous IBO prototypes and to inform a bond graph model of the MCL. The MCL reproduces flow rates and pressures consistent with pulsatile arteriovenous IBO prototypes, and the corresponding bond graph model recapitulates MCL and animal physiology.

Background

Advances in organ-assist and organ-replacement technology have provided great benefit to patients over several decades and are a mainstay of treatment of the failing heart. Ongoing innovation of biomechanical devices continues to offer promise for treatment of the failing heart, lung, liver, kidney and pancreas^1–8. Mock circulatory loops (MCL) and associated mathematical models designed to replicate specific components of the systemic and/or pulmonary arterial circulation have proven indispensable for enhanced in vitro testing, prototyping, and refinement of cardiovascular devices prior to in vivo trials^9–11. Given the complexity, expense, and safety concerns associated with pre-clinical animal testing and clinical studies in humans, MCL serve a vital role in informing prototype design and evaluating device performance over time in an environment that replicates the pressure and flow conditions of the cardiovascular system.

Our team is developing a new class of implantable bioartificial organs (IBO) for renal and pancreatic replacement therapies (Figure 1)^12,13. The unifying principle is convective oxygen and nutrient delivery by immunoprotective hemofiltration across high efficiency silicon nanopore membranes (SNM)^7,14–17. We have previously described a SNM-based hemofilter for renal replacement therapy, demonstrating diffusive solute clearance across SNM and gross device patency up to 30 days when implanted in arteriovenous (AV) fashion in large animals^12,18,19. SNM also offer a promising platform for immunoprivileged tissue transplantation, creating a microencapsulation environment that relies on convective mass transfer to deliver oxygen and nutrients to transplanted cells, while blocking the local host immune response^7,15.

Figure 1:

Conceptual illustrations of implantable bioartificial kidney (A) and pancreas (B) devices that utilize hemofiltration through silicon nanopore membranes (SNM). Device development requires optimization of blood flow path using 3D printed prototypes (C & D).

Peripherally implanted SNM bioartificial organs differ from other blood-contacting artificial organs, such as ventricular assist devices (VAD), in that they do not provide a pump function and instead rely on the arteriovenous pressure gradient for function. Once implanted, IBO prototypes are fixed within a newly created arteriovenous shunt, with low inherent device resistance interacting with the cardiovascular system to enable rapid blood flow and gradual pressure drop across the arteriovenous IBO. Accordingly, while some MCL previously described for VAD development could be adapted to enable IBO prototyping and testing, we sought to develop a simple, compact and cost-effective MCL containing only the critical components for enhanced peripherally implanted IBO prototype design and testing.

Beyond physical modeling of the cardiovascular system, mathematical modeling has also proved invaluable in implantable organ development. Bond graph modeling is a method developed in the 1960s to model complex dynamic systems, such as aircraft, land vehicles, hydraulic/pneumatic systems, and mechatronic systems^20–24. A Bond graph model represents the system using a set of ordinary or partial differential equations, which are solved simultaneously to produce a Bond Graph that enables obtaining hemodynamic parameters such as pressure. Bond graph models have only recently been used for the cardiovascular system, and present a valuable opportunity to incorporate mathematical modeling for assessing in vitro and in vivo scenarios^25–27.

Here, we present the development of an arteriovenous MCL and an accompanying bond graph model. Fluid pressure and flow data measured through IBO prototypes in the MCL were compared to values obtained in an acute animal study employing arteriovenous attachment of IBO prototypes in swine. MCL and in vivo data then informed creation of the bond graph model. Finally, the MCL was run with IBO prototypes for 48 hours to ensure physiologic stability during SNM fatigue testing.

Methods

Mock Circulatory Loop:

The required design parameters for our AV MCL were: 1) a pulsatile pump with controllable cycling rate and systolic duration; 2) an arterial system with an adjustable systolic/diastolic pressure range to match values obtained in healthy preclinical or clinical subjects; 3) a high compliance venous system with mean central venous pressure matching values obtained in healthy subjects, with an anticipated range of 1–10 mmHg; 4) the ability to connect IBO prototypes between the arterial and venous limbs; and 5) a flow rate through the AV IBO prototype that mimics flow rates through the device when implanted in AV fashion in vivo. Additionally, we sought to replicate a physiologic arterial pressure-time waveform as a secondary goal. A schematic of the MCL system is shown in Figure 2. To satisfy these requirements, the MCL consists of four components: 1) a pneumatic pulsatile pump mimicking the left ventricle; 2) an arterial circulation; 3) a low-pressure venous system; 4) a continuous venous pump to return circulating fluid to an atrial collecting chamber (Figure 3). To construct the left heart, two three-foot long vinyl tubes with two-inch inner diameter are placed vertically to create the left ventricular chamber and left atrial chamber. Two ¾-inch brass one-way check valves are attached between the ventricular and atrial chambers, and at the outflow of the ventricle to replicate the mitral valve and the aortic valve, respectively. The check valves are attached to horizontally oriented ¾-inch vinyl tubing using ¾-inch threaded T’s and ¾-inch threaded to barb adapters.

Figure 2.

Schematic of the arteriovenous mock circulation system (AV MCL) to assess flow parameters in artificial organ devices. Key components are: 1) a pneumatic pulsatile pump to mimic the left ventricle, controlled by a solenoid switch valve; 2) an arterial circulatory system; 3) a low-pressure venous system; 4) a continuous venous pump to return circulating fluid to an atrial collecting chamber. Blood viscosity can be mimicked using a 10% glycerol solution.

Figure 3.

Photograph of AV MCL set up. The left heart component (encircled by dashed lines on the right) consists of vinyl tubing, compressed air controlled by a solenoid switch valve, and check valves. The solenoid valve is connected to a compressed air source and controlled using an on/off relay set by microcontroller. The arterial and venous circulatory systems (encircled by dashed lines on the left) consist of vinyl tubing, a compliance chamber, flow reducers, a vertical venous collection chamber, and a peristaltic pump to return blood to the heart and regulate venous pressure by maintaining a fixed column height.

An SMC^® solenoid valve (SMC Corp. of America, Indianapolis, IN) is connected to an air pressure source and placed on top of the otherwise sealed ventricular chamber. Activating the valve allows high pressure air into the ventricular chamber to produce a systolic phase, while deactivating the solenoid allows compressed air to escape to atmosphere, producing the diastolic phase. The solenoid cycling rate and duration of each phase are controlled by an Arduino^® microcontroller and are thus adjustable. The open and close signals from the Arduino are amplified by a TIP120-based amplification circuit, powered by an external power source set to output 12 V at 290 mA. The pressure is controlled by regulating the pressure of the compressed air entering the chamber.

The peripheral arterial circulatory system is built upon ¾-inch vinyl tubing attached to the brass check valve simulating the aortic valve. The compliance of the arterial circulatory system is replicated by sealing air in a vertical two-inch diameter vinyl tube to create a compliance chamber, and a 10-inch segment of 1-inch diameter latex tubing set within a 2-inch vinyl tube to prevent ballooning. Reduced vinyl tubing and two ¾ inch to ¼ inch reducers reproduce arterial resistance.

The peripheral venous circulatory system receives flow from the arterial system after passing through flow reducers and the IBO prototype. To produce a high compliance venous system with a pressure of 5–10 mmHg, fluid passes into a vertical, two-inch diameter vinyl tube open to the atmosphere. To regulate the venous pressure, a venous return peristaltic pump is set to evacuate fluid once it rises above a threshold set by the user, in our case 10 cm H₂O. Venous circulatory fluid is then returned to the atrial chamber, to produce a closed circulatory system. To test flow through IBO, the prototype is attached to the MCL between the arterial and venous limbs.

To measure pressure within the MCL, Transpac^® IV disposable pressure sensors (ICU Medical, Inc. San Clemente, CA, USA) are connected via ¼-inch vinyl tubing at various locations in the MCL, enabling measurement of systemic arterial, systemic venous, and arteriovenous shunt (before and after the device) pressures. The sensed pressures are sent to an HP^® CMS 24 Omnicare patient operating room (OR) monitor for visualization and recording. The pressures sensed by the OR monitor are then transferred and digitally recorded using an Arduino^® microcontroller. Flow rates were recorded digitally by an Uxcell Hall Effect flow sensor attached in-line to the arterial circulation, and cross referenced by adjusting the peristaltic venous pump rate to reach equilibrium in the venous chamber.

Durability and Fatigue Testing of AV MCL

Stability of the AV MCL system over prolonged use is vital to enable IBO device fatigue testing. Accordingly, the AV MCL was run continuously for 48 hours with an IBO prototype attached. The arteriovenous graft pressure-time waveform was recorded continuously for 5 minutes, once per hour over the 48-hour test to assess pressure variation in the system. Data recorded by a serial data logger through an Arduino and then plotted in MATLAB (Mathworks, Natick, MA, USA) as an overlay plot for each arterial systole-diastole cycle recorded.

When run continuously over 48 hours, the AV MCL provided consistent arterial pressure waveforms. For each systole-diastole cycle recorded, there was a maximum variation of 3 mmHg (range 43–46 mmHg) in the systolic peak, and maximum variation of 8 mmHg (range 20–28 mmHg) in the diastolic trough (Figure 4).

Figure 4.

Overlay plot segment of arteriovenous graft pressure-time waveform collected continuously over 5 minutes each hour for 48 consecutive hours. The maximum systolic peak difference was 3 mmHg, while the maximum diastolic trough difference was 8 mmHg.

In Vitro Testing of Intravascular Bioartificial Organ Prototypes

Our team has previously reported on the design and development of IBO prototypes after extensive computational modeling and platelet-focused thrombogenic flow analyses for serpentine and parallel designs¹³. These two IBO prototypes for renal replacement therapies were attached between the arterial and venous limbs of the MCL. Once attached, 10% glycerol in water was circulated at room temperature by activating the ventricular (roller) pump. The pump rate was set at various rates, between 80–150 cycles per minute. The pressure was monitored continuously and recorded at four locations along the MCL: 1) the proximal arterial tubing; 2) the AV conduit attaching the IBO to the arterial limb; 3) the AV conduit attaching the IBO to the venous limb; and 4) the venous tubing. Flow rate was measured through the IBO by flow sensor, and by adjusting the venous return pump rate to achieve equilibrium with the arterial pump, reflected by stable height of the venous fluid chamber.

MCL Comparison to In Vivo Flow Parameters

To assess the MCL’s fulfillment of the design parameters, we performed an ex vivo experiment using two unique IBO prototypes in swine, and recorded arterial, AV shunt and venous pressures, as well as flow rate through the device and attached ePTFE vascular grafts. Animal studies were reviewed and approved by an Institutional Animal Care and Use Committee prior to being performed at an AAALAC-accredited animal research facility (LabCorp Drug Development, formerly PMI Preclinical, San Carlos, CA). In a 42 kg Yucatan minipig, ePTFE grafts were anastomosed to the common carotid artery and external jugular vein. The IBO prototypes were then attached to the grafts to establish an arteriovenous shunt through the IBO. Blood was allowed to circulate for 10 minutes to reach stable cardiovascular and AV shunt physiology. After 10 minutes, blood pressure was transduced using HP^® CMS 24 omni care patient OR monitor via catheters at four locations: 1) common femoral artery; 2) the graft attaching the IBO to the carotid artery; 3) the graft attaching the IBO to the jugular vein; and 4) and central venous catheter with the tip placed at the cavoatrial junction. Flow rate was measured using Duplex Ultrasonography (General Electric Vivid IQ). Heart rate was recorded via the arterial blood pressure transducer. Flow parameters were recorded for 3 minutes for each IBO prototype.

After obtaining physiologic ex vivo flow data, IBO were reattached to the MCL. The heart rate and systemic arterial pressure were set to match those obtained in the animal studies by adjusting the cycling rate of the solenoid valve, and the pneumatic pressure entering the ventricular chamber, respectively. Pressure and flow data were then measured at the three other locations (arterial and venous AV shunt conduits, and venous system) along the MCL flow circuit.

Bond Graph Model

We created a mathematical model of the AV MCL using a bond graph technique to predict the pressure-time waveform at various locations²⁸. Briefly, the first step is to create an analogy between each component in the AV MCL and a corresponding component in an electrical circuit (Figure 5). In this analogy, a compliance chamber behaves like a capacitor, a check valve like a diode, and the inertia of the fluid flow like an inductor. Similarly, flow reducers mimic resistors. After determining the analogues of each component, they are connected to others using port lines. The direction of flow of power between components is shown using half-arrows, while causality is indicated by short dash. Following a set of standard steps results in seven ODEs (Appendix A), which are solved using ODE45 numerical solver in MATLAB.

Figure 5.

Development of the AV MCL model using Bond graph method: Each component in the MCL is substituted with the corresponding electrical analog. Relationships between the components are illustrated using port lines. Energy transfer directions are shown using half-arrows at either side of the port line. The causality on each port line is indicated with a dash at either end of the port line. Components are connected using a 0 or 1 junction representing common pressure and common flow junctions, respectively.

Results

MCL and in vivo experiments

After successful construction of the MCL, we tested IBO prototypes to assess flow dynamics. Figure 6 shows representative waveforms obtained for the parallel and serpentine device designs. The maximal pressure required to drive flow (~ 45 mmHg) was lower in the parallel configuration compared to the serpentine configuration (~ 60 mmHg), on account of the differences in the fluid flow paths. The serpentine device had a flow ~ 1 L/min, which was approximately 20% lower than the parallel configuration device. These results matched closely with the in vivo experiments, shown in Figure 7 where both arterial (device inlet) and venous (device outlet) pressures are similar in the MCL and in vivo experiments for a device with parallel configuration. Table 1 shows the comparison of the in vitro and in vivo measured hemodynamic parameters that demonstrate that the in vitro MCL setup was able to replicate the in vivo conditions.

Figure 6.

Representative arteriovenous pressure-time waveforms collected at the arterial inflow and venous outflow of the AV conduit attached to IBO prototypes. Top: Parallel hemofilter prototype. Bottom: Serpentine hemofilter.

Figure 7.

Comparison of AV MCL and swine arteriovenous pressure-time waveforms measurements for a parallel flow configuration hemofilter prototype. Pressure was measured and recorded at the arterial inflow and venous outflow ends of the AV conduit in both scenarios.

Table 1.

Measured flow parameters across IBO in AV MCL and ex vivo conditions.

Device	Condition	Heart Rate (bpm)	Arterial Graft Pressure (mmHg)	Venous Graft Pressure (mmHg)	Flow Rate (mL/min)
1	Swine ex vivo	128	44/26 (35	16/12 (14)	1242
	MCL in vitro	128	45/26 (36)	14/11 (12)	1075
2	Swine ex vivo	94	78/60 (65)	40/30 (36)	1032
	MCL in vitro	90	75/59 (64)	37/33 (35)	950

Bond graph model

For MCL experiments, the bond graph model predictions of the MCL dynamics were used to verify and refine the operational parameters. After obtaining experimental ex vivo arteriovenous pressure data, the bond graph model components’ values were adjusted to replicate the pressure waveform measured in these experiments. Figure 8 presents the comparison of the pressures from the bond graph model and the ex vivo pressure measurements for the parallel hemofilter prototype. The parameters in the constructed MCL were then adjusted to recreate these pressure waveforms. The customized bond graph model was successfully able to replicate the in vivo experiments for both parallel and serpentine configurations. The values of all the parameters are presented in Table A.1 in the Appendix.

Figure 8.

Comparison of the experimental (blue) and bond graph model arteriovenous pressure waveforms through the parallel flowpath IBO prototype. The components in the model are adjusted to recreate the pressure observed in the ex vivo experiments.

Discussion

We have described modeling, construction, and validation of an arteriovenous mock circulatory system to facilitate prototyping and testing of peripherally implanted arteriovenous bioartificial organs. This system offers similar arterial, venous and AV shunt pressures, heart cycling rates and blood/circulating media flow rates to those obtained in a swine model. Using data obtained on the benchtop and in vivo, we have constructed a corresponding bond graph model to facilitate further MCL development. While various MCL have been developed and improved using mathematical models, our approach utilizing a bond graph model offers several advantages. With the large number of components in the AV MCL, a bond graph model approach provides a simple and efficient model creation process. The model enables the user to directly create first-order differential equations. These resultant first-order differential equations (Appendix A) can be conveniently solved using ode45 function in MATLAB. Other modeling methods will result in the same outcome with more time and effort.

Our AV MCL and bond graph model benefit intravascular device innovation in ways inherent to all MCL, namely by offering high fidelity replacement of animal testing, prototype refinement prior to preclinical and clinical trials, and reduction of the number of animals required for device prototyping and development. However, a simple, portable and efficient system that is limited to essential elements – a low-pressure, high compliance venous system attached to a high-pressure pulsatile arterial limb driven by a consistent pump – provides a convenient platform for development of arteriovenous shunt devices and prosthetics. Such a platform is especially relevant to new classes of medical devices capitalizing on improved membrane technologies for implantable hemofiltration. These devices potentially apply to cell-replacement therapies, such as islet replacement in type 1 diabetes, and body water removal, as is required in end-stage renal disease and congestive heart failure. Our group recently described feasibility testing of early prototype silicon hemofilters for renal and pancreatic replacement therapies^7,12,17. Application of the AV MCL enables pulsatile AV hemodynamic testing, high fidelity device and membrane integrity and fatigue testing, and membrane fouling assessment under high flow and pulsatile pressure conditions.

Our team has considerable experience in evaluating the hemodynamics through the IBO designs using computational fluid dynamics simulations and platelet-level thrombogenic assessments¹³. The serpentine and parallel designs function differently from a hemodynamic perspective. The serpentine design, with its longer travel path, adds more flow resistance to the circuit, thereby resulting in an increased pressure drop and reduced flow rate, as seen in the results. In contrast, the parallel design consists of several parallel flow paths from the device inlet to the outlet, and does not present as much increased resistance to overall flow compared to the serpentine configuration. Thus, the pressure drop for the parallel design is lower than the serpentine design, and consequently results in allowing higher flow rates. These two designs were determined to provide more control over the clinically relevant hemodynamic parameters of pressure drop and flow rates. The overarching goal of investigating these designs is to enable tailoring these devices for individual patient needs.

The AV MCL is not meant to replace or improve upon MCL developed for application to cardiac assist devices. While adjustable across a wide physiologic range, our system allows rapid, precise adjustment only of cardiac rate and ventricular contractility (by adjusting gas pressure). As seen from Figure 8, the bond graph model represents the MCL closely. It is important to note that while the bond graph model itself can be further improved, the focus of the current work has been to leverage the combined advantages of the MCL and the bond graph model in a customizable, reliable and dependable framework that enables rigorous testing, which, in turn, may reduce the number of animal tests in developing and testing of IBO prototypes.

Limitations

The constructed prototype of the MCL is formed from several components. Small variations in these components can alter the pressure-time waveform. For example, elasticity of the vinyl tubing will change resistance and capacitance, variation of height of fluid in the towers will change the static pressure at the different locations of the AV MCL, and nonlinearity in the check valves will change the pressure waveforms. The small difference between the AV MCL bond graph model and experimental results are attributed to these non-ideal situations in the constructed AV MCL. Additionally, our system is susceptible to rapid pressure variations especially prominent in early systole, and likely a result of crude one-way check-valves slamming shut with rapid changes in fluid pressure. Adjustment of system resistance and compliance has minimized this effect, but has not removed it entirely.

Conclusions

We have successfully created of an arteriovenous mock circulatory loop and accompanying bond graph model to enable enhanced in vitro assessment and development of AV bioartificial organ prototypes. The AV MCL can be readily constructed in an academic laboratory setting, portable, and offers titration across a wide range of arterial and venous pressures, and cardiac cycling rates. The bond graph model provides a simplified method for modeling the multiple components of the AV MCL, and allows improved efficiency in AV MCL setup, adjustment of input parameters and future refinement. Implementation of the AV MCL may facilitate IBO development by replacing and reducing animal studies with a convenient high-fidelity in vitro testing system.

List of Acronyms

MCL

Mock circulatory loop

IBO

Implantable bioartificial organ

SNM

Silicon nanopore membranes

AV

Arteriovenous

VAD

Ventricular assist devices

OR

Operating room

Appendix

We present the model creation process for the MCL using bond graph method. Figure A illustrates the complete bond graph of the MCL. 0s and 1s illustrate the equal pressure and flow points in the MCL. Using this bond graph, a unified sets of first-order differential equations can be derived that governs the physics of the MCL.

Figure A.

Complete bond graph model of the AV MCL. Each portion of the model represent parts of the MCL. The port lines and the half arrows illustrate the direction of power between the components and sections of the MCL. The perpendicular lines at the end of each port line illustrate the causality of the port.

The equations governing the dynamics of the MCL are presented in the following equations:

$${\dot{q}}_2=\left(\frac{1}{L_1}\right)p_7+\left(\frac{1}{L_2}\right)p_{12}$$ (A.1)

$${\dot{q}}_9=\left(\frac{1}{L_1}\right)p_7$$ (A.2)

$${\dot{q}}_{17}=\left(\frac{1}{L_2}\right)p_{12}-\left(\frac{1}{L_3}\right)p_{22}$$ (A.3)

$${\dot{q}}_{20}=\left(\frac{1}{L_3}\right)p_{22}$$ (A.4)

$${\dot{q}}_{28}=\left(\frac{1}{L_3}\right)p_{22}$$

$${\dot{p}}_7=P_i(t)-P_1-\frac{1}{C_2}{q}_2-\frac{1}{C_1}{q}_9-R_2\left[\left(\frac{1}{L_1}\right)p_7+\left(\frac{1}{L_2}\right)p_{12}\right]-R_3\left[\left(\frac{1}{L_2}\right)p_{12}-\left(\frac{1}{L_3}\right)p_{22}\right]-D_1\left(\frac{1}{L_1}\right)p_7$$ (A.6)

$${\dot{p}}_{12}=P_i(t)-P_2-\frac{1}{C_2}{q}_2+\frac{1}{C_3}{q}_{17}-R_2{\left[\left(\frac{1}{L_1}\right)p_7+\left(\frac{1}{L_2}\right)p_{12}\right]}_1-R_3\left[\left(\frac{1}{L_2}\right)p_{12}-\left(\frac{1}{L_3}\right)p_{22}\right]-D_2\left(\frac{1}{L_2}\right)p_{12}$$ (A.7)

In these equations, R is a symbol used for flow resistors. Similarly, C is used for compliances and L for inductors (fluid inertia). p and q represent pressure and flow of the fluid, respectively. The subscripts of p and q show the corresponding port line. The subscripts of p and q correspond to the port line. P_i is the pressure controlled by the solenoid valve. Table A lists the values for each of the components used in the MCL model. The valves are simulated as a nonlinear component, to mimic physical valve operation. For opposite direction of the fluid flow through the valves they have a very large resistance and for fluid flow in the direction of the valve, they have a low measure of resistance.

Table A.

List of values used in the bond graph model.

Parameter	Value	Unit
L 1	1.78e+5	N.s2/m5
L 2	1.78e+5	N.s2/m5
L 5	8.91e+5	N.s2/m5
R 1	3.50e+6	N.s/m5
R 2	3.50e+6	N.s/m5
R 3	3.50e+6	N.s/m5
R 4	3.50e+7	N.s/m5
R 5	3.50e+7	N.s/m5
C 1	3.22e-8	m4/N
C 2	3.22e-8	m4/N
C 3	2.37e-9	m4/N
C 4	1.61e-7	m4/N
C 5	1.61e-7	m4/N
D 1	≈0 if f6 <0 3.5e+08 if f6 >0	N.s/m5
D 2	≈0 if f13 >0 3.5e+08 if f13 <0	N.s/m5