The primary challenge of thoracic artificial lung (TAL) design is to create a device with an impedance equal to or less than that of the natural lungs. Thoracic artificial lungs are attached to the pulmonary circulation, and blood flow is driven by the right ventricle. Right ventricular (RV) function is highly dependent on pulmonary system impedance, with acute increases in impedance leading to significant reductions in blood flow output. Under normal physiology, pulmonary system impedance is primarily determined by the impedance of the natural lung. During TAL attachment, however, the pulmonary system impedance is dependent on the impedance of the combined artificial and natural lung system, which is a function of TAL impedance, natural lung impedance, TAL attachment mode, and the blood flow rates to the artificial and natural lungs. Elevated TAL impedance increases pulmonary system impedance and the power the right ventricle must expend to maintain any given flow rate. This elevated workload can lead to reduced cardiac output. For this reason, the TAL must be designed to have a low impedance.

Impedance is typically expressed as a spectrum, with each frequency having its own impedance modulus. Vascular hemodynamics are affected most significantly by the lower harmonic frequencies, with the harmonics equal to integer multiples of the heart rate. The vast majority of physiologic blood flow, blood pressure, and, thus, right ventricular power output exists within the lower harmonics.^{1} The two most significant impedances are *Z*_{0} and *Z*_{1}, the zeroth and first harmonic impedances. The zeroth harmonic impedance is the opposition to the constant, steady component of blood flow and is more commonly known as the resistance. The first harmonic impedance is the opposition to blood flow at a frequency equal to the heart rate. Ideally a TAL should have low *Z*_{0} and *Z*_{1} to avoid overloading the right ventricle.

The TAL impedance is a function of TAL resistance, compliance, and inertia. This *in vitro* study focuses on the effect of compliance and seeks to determine the TAL compliance that minimizes *Z*_{0}, *Z*_{1}, and RV output power when used with the MC3 BiolungÂ®. In addition, this study seeks to determine how effectively an expandable polyurethane compliance chamber functions. Ultimately, this work should lead to compliance chamber designs that maximize RV function during TAL attachment.

## Materials and Methods

### Test Circuit

A recirculation circuit was constructed of a pulsatile pump (Harvard Apparatus, Dover, MA), a compliance chamber, and a reservoir that is open to the atmosphere (Figure 1). Two types of compliance chambers were used: (1) a piston-cylinder (PC), spring-controlled, variable compliance chamber, or (2) a polyurethane compliance chamber (see following descriptions). Fluid flows from the pulsatile pump to the compliance chamber, artificial lung, and reservoir and then back to the pump. The reservoir was elevated to maintain a nearly constant TAL outlet pressure of 10 mm Hg. Noncompliant, 5/8" ID, polyvinyl chloride tubing connected each of the elements.

The PC compliance chamber (Figure 2) was designed according to Woodruff *et al*.^{2} and consists of a flexible, rolling diaphragm (Bellofram, Inc; Newell, WV) fixed to a piston within a solid cylinder. An exchangeable coil spring sits upon the piston and controls the force necessary to expand the diaphragm. Thus, the diaphragm compliance could be changed by varying the stiffness of the spring. The polyurethane compliance chamber (Figure 3) was designed by MC3 (Ann Arbor, MI) such that it relies both on unfurling and stretching for its compliance. At lower pressures, the compliance chamber expands with minimal material stretching to achieve a higher compliance. At higher pressures, the compliance chamber is fully unfurled, relies on stretching for its compliance, and thus has a smaller compliance. The PC chamber compliance is constant for any spring regardless of pressure. The compliance of the polyurethane chamber, however, is pressure dependent (Figure 4). Compliance for this chamber is approximately 0.8 ml/mm Hg at pressures â‰¤ 10 mm Hg and decreases with increasing pressures above 10 mm Hg. Methods for determining each chamberâ€™s compliance are contained in the Appendix.

A 3.0 cP glycerol solution was pumped through the test circuit at average flow rates, *Q*_{0}, of 1.8, 3.0, and 5.0 l/min. Pump rates (HR) of 60, 75, and 100 bpm were tested at *Q*_{0} = 3.0 and 5.0 l/min, whereas only 60 and 75 bpm were tested at *Q*_{0} = 1.8 l/min. Thus, stroke volumes, *V*_{s} = *Q*_{0}/HR, ranging from 24 to 83 ml were tested. At each flow and heart rate combination, compliances of 0.5, 1, 2, 3, 4, 5, 10, 15, and 20 ml/mm Hg were tested by changing the chamber spring. The same flow rate conditions were also tested with the polyurethane compliance chamber. Lastly, a zero-compliance control case was tested by replacing the compliance chamber with 5/8" ID, relatively noncompliant, polyvinyl chloride tubing.

At each flow rate condition, circuit inlet pressure, *p*, was measured at the outlet of the pump immediately before the compliance chamber, with fluid coupled pressure transducers (Abbot Critical Care Systems, Chicago, IL) connected to a Marquette series 7000 patient monitor (Marquette, Milwaukee, WI). Fluid flow rate was measured at the same point using a 5/8" ID tubing, clamp-on, ultrasonic flow probe and flow meter (Transonic, Ithaca, NY), which was calibrated for use with glycerol. Instantaneous pressures and flow rates were digitally acquired under each test condition at 250 Hz for 10 seconds using Labview (National Instruments, Austin, TX). Five TALs were tested with the PC chamber, and four TALs were tested with the polyurethane chamber.

### Data Analysis

Excel (Microsoft, Redmond, WA) was used to perform Fourier transforms on pressure and flow data and thus determine circuit input impedance. Fourier transforms decompose periodic signals into a series of component sinusoids. The Fourier series for pressure, *p*, and flow, *Q*, are represented mathematically as:

and

in which *p*_{0} is the constant, steady component of pressure, *Ï‰*_{i} is the *i*th frequency, *p*_{i} is the amplitude or modulus at the *i*th harmonic frequency, *Ï†*_{p,i} is the *i*th harmonic frequency phase shift for pressure, *Q*_{0} is the constant, steady component of flow rate, *Q*_{i} is the amplitude or modulus at the *i*th harmonic frequency, and *Ï†*_{Q,i} is the *i*th harmonic frequency phase shift for flow rate. The *p*_{0} and *Q*_{0} are equivalent to the average pressure and flow rate, respectively.

Only the sinusoids at the harmonic frequencies have significant amplitudes, and thus only these frequencies are important in the physical system. For physiologic flows, the harmonic frequencies are integer multiples of the heart or pump rate, *HR*. Furthermore, in these flows, flow rate amplitudes decrease as the frequency of the harmonic increases. Therefore, our analysis was limited to the zeroth harmonic frequency, or the steady component, and the first harmonic frequency, equal to the heart rate. The zeroth and first harmonic input impedance moduli, *Z*_{0} and *Z*_{1}, were calculated according to the formulas:

and

respectively.

Output power was also broken down into its steady and pulsatile components. The steady component, *P*_{s}, was calculated as the product of steady pressure and flow, or *p*_{0}Q_{0}. The pulsatile component of power, *P*_{p}, was calculated as the difference between total and steady power, or *P*_{t}â€“*P*_{s}. The total pump output power is equal to the product of instantaneous pressure and flow rate integrated over time and divided by the duration of the integral:

The total pump output power was thus calculated using trapezoidal numerical integration. Lastly, stroke volume, *V*_{s}, was calculated as described above.

### Statistical Analysis

Statistical analysis was performed to answer three questions: (1) What is the role of *C*, *Q*_{0}, and *V*_{s} in determining *Z*_{0}, *Z*_{1}, *P*_{s}, and *P*_{p} in the PC chamber?, 2) What is the role of *Q*_{0} and *V*_{s} in determining *Z*_{0}, *Z*_{1}, *P*_{s}, and *P*_{p} in the polyurethane chamber?, and (3) How do *Z*_{0}, *Z*_{1}, *P*_{s}, and *P*_{p} with the polyurethane chamber compare to those using the PC chamber at compliances between 0 and 1 ml/mm Hg? Mixed model analysis was thus used within SPSS to determine if *C*, *Q*_{0}, or *V*_{s} affect *Z*_{0}, *Z*_{1}, *P*_{s}, and *P*_{p} for PC chamber compliances between 0 and 20 ml/mm Hg. In brief, the model used *C*, *Q*_{0}, and *HR* as repeated measures and *C*, *Q*_{0}, and *V*_{s} as fixed factors for analysis. In addition, *C*(*Q*_{0}), and *C*(*V*_{s}) were used as nested factors to account for the different effects of compliance at different flow rates and stroke volumes. Lastly, Bonferroni-adjusted post hoc tests were conducted that compared every compliance value pairwise.

The polyurethane chamber *Z*_{0}, *Z*_{1}, *P*_{s}, and *P*_{p} data were compared to those of the PC compliances closest to its pressure-compliance function, 0 through 1 ml/mm Hg. The purpose of these comparisons was to determine if the polyurethane compliance chamber improves impedance and power results over no compliance at all and, if so, how it compares to the PC compliance chamber. In brief, the SPSS model used *C* (polyurethane or PC 0, 0.5, or 1 ml/mm Hg), *Q*_{0}, and *HR* as repeated measures and *C*, *Q*_{0}, and *V*_{s} as fixed factors for analysis. In addition, *C*(*Q*_{0}), and *C*(*V*_{s}) were used as nested factors as above, and Bonferroni-adjusted post hoc tests compared the polyurethane chamber to the each of the three PC compliances.

## Results

### Piston-Cylinder Compliance Chamber

Figure 5 presents the zeroth harmonic impedance, *Z*_{0}, versus compliance, *C*, for the piston-cylinder (PC) compliance chamber. In general, *Z*_{0} decreased significantly with increasing *C* (*p* < 10^{â€“6}). When compliance was less than one, furthermore, *Z*_{0} was slightly larger if flow rate or stroke volumes were large. The effects of *Q*_{0} and *V*_{s}, however, were statistically insignificant when considering all compliances. Post hoc, pairwise analysis of compliance indicated that increasing *C* ceased to decrease *Z*_{0} significantly at C > 1 ml/mm Hg. Thus, *Z*_{0} was minimized statistically at *C* â‰¥ 1 ml/mm Hg.

Figure 6 presents the first harmonic impedance, *Z*_{1}, versus *C*. In general, *Z*_{1} decreased significantly with increasing *C* (*p* < 10^{â€“100}) and *Q*_{0} (*p* < 10^{â€“20}) and decreasing stroke volumes, *V*_{S} (*p* < 10^{â€“14}). In three cases, *Z*_{1} was smaller without a compliance chamber (*C* = 0) than with *C* = 0.5 ml/mm Hg. These cases occurred at *HR* = 60 bpm with *Q*_{0} = 1.8 or 3 l/min and *HR* = 75 bpm with *Q*_{0} = 1.8 l/min. Post hoc analysis of compliance indicates that, at *C* > 5 ml/mm Hg, increasing *C* ceases to decrease *Z*_{1} significantly. The *Z*_{1}, therefore, was minimized statistically at *C* â‰¥ 5 ml/mm Hg.

Figure 7 presents the steady component of power, *P*_{s}, versus *C*. The *P*_{s} decreased significantly with increasing *C* (*p* < 0.05) and decreasing *Q*_{0} (*p* < 10^{â€“25}) and *V*_{S} (*p* < 0.01). The effects of *C* and *V*_{s}, however, are small compared to that of *Q*_{0} when *C* â‰¥ 0.5 ml/mm Hg. Post hoc analysis of compliance indicates that, at *C* > 0.5 ml/mm Hg, increasing *C* ceases to decrease *P*_{s} significantly. The *P*_{s}, therefore, was minimized statistically at *C* â‰¥ 0.5 ml/mm Hg.

Figure 8 presents the pulsatile component of power, *P*_{p}, versus *C*. The *P*_{p} decreased significantly with increasing *C* (*p* < 10^{â€“24}) and decreasing *Q*_{0} (*p* < 10^{â€“86}) and *V*_{s} (*p* < 10^{â€“33}). Post hoc analysis of *C* indicates that, at *C* > 4 ml/mm Hg, increasing *C* ceases to decrease *P*_{p} significantly. The *P*_{p}, therefore, was minimized statistically at *C* â‰¥ 4 ml/mm Hg.

### Polyurethane Compliance Chamber

Figures 9 and 10 present *Z*_{0} and *Z*_{1}, respectively, versus *Q*_{0} for the polyurethane compliance chamber. The *Z*_{0} increased with increasing *Q*_{0} (*p* < 10^{â€“6}) and *V*_{s} (*p* < 10^{â€“5}) unlike the PC compliance chamber results. The *Z*_{1} also varied significantly with *Q*_{0} (*p* < 0.01) and *V*_{s} (*p* < 10^{â€“3}), and the relationship between the variables also differed from that of the PC compliance chamber. Unlike the PC chamber, the polyurethane chamber *Z*_{1} was smallest at intermediate values of *Q*_{0} (3.0 l/min) or *V*_{s} (30â€“50 ml). The polyurethane *Z*_{1}, furthermore, was the smallest at *HR* = 100 bpm. Figures 11 and 12 present *P*_{s} and *P*_{p}, respectively, versus *Q*_{0} for the polyurethane compliance chamber. Both *P*_{s} and *P*_{p} increased significantly with increasing *Q*_{0} (*p* < 10^{â€“10} and *p* < 10^{â€“3}, respectively) and increasing *V*_{s} (*p* < 10^{â€“6} and *p* < 10^{â€“12}, respectively).

### Polyurethane and Piston-Cylinder Compliance Chamber Comparison

The polyurethane chamber had a lower *Z*_{0} than with *C* = 0, 0.5, or 1 ml/mm Hg at all *V*_{s} â‰¤ 50 ml. At all *V*_{s} â‰¥ 66.7, the polyurethane chamber *Z*_{0} remains smaller than that at *C* = 0 and 0.5 ml/mm Hg but is larger than the *Z*_{0} at *C* = 1 ml/mm Hg. Statistical tests indicate that polyurethane chamber *Z*_{0} is significantly lower for *C* = 0 (*p* < 0.01) and 0.5 ml/mm Hg (*p* < 0.01) but not significantly different than *C* = 1 ml/mm Hg (*p* = 0.24). Overall, the polyurethane chamber *Z*_{1} is similar to the zero-compliance situation, which lies in between the *Z*_{1} for *C* = 0.5 and 1 ml/mm Hg. Statistically, the polyurethane *Z*_{1} is not significantly different than the *Z*_{1} at *C* = 0 (*p* = 1.0) but is significantly less than the *Z*_{1} at 0.5 ml/mm Hg (*p* < 0.05) and significantly greater than the *Z*_{1} at *C* = 1 ml/mm Hg (*p* < 0.0001).

Power output differences between the compliances were consistent across pump settings. The polyurethane chamber *P*_{s} is significantly less than the *P*_{s} at *C* = 0 (*p* < 0.0001), but not significantly different than the *P*_{s} at 0.5 (*p* = 1.0) and 1 ml/mm Hg (*p* = 1.0). The polyurethane chamber *P*_{p}, however, is not significantly different than the *P*_{p} at *C* = 0 (*p* = 0.47) and is significantly greater than the *P*_{p} at *C* = 0.5 (*p* < 0.01) and 1 ml/mm Hg (*p* < 10^{â€“19}).

## Discussion

Previous theoretical,^{3â€“6}*in vitro,*^{6} and *in vivo*^{7,8} research has demonstrated that TAL inlet compliance lowers pulmonary system impedance and improves RV function. No previous study, however, had sought to determine what value of compliance was ideal for improving TAL impedance and RV power output under a variety of heart rates and flow rates.

The normal role of compliance in the pulmonary circulation is to dampen the systolic flow pulse from the right ventricle before it reaches the resistance of the capillary bed. Due to the compliance, flow through this resistance is spread more evenly over the cardiac cycle, reducing peak flow rates, peak pressures, and RV work. The role of the TAL compliance is similar to that of pulmonary compliance, dampening the flow pulse through the artificial lung. The role of the compliance in this case, however, is even more crucial. In the pulmonary capillary bed, the resistance decreases with increasing flow rate, allowing the right ventricle to maintain relatively low rates of work even when cardiac output is elevated. The resistance of the TAL, on the other hand, includes so-called minor resistances that increase linearly with flow rate. These are primarily due to expansions, contractions, and changes in the direction of the flow field within the device. Because of these minor resistances, higher peak flow rates cause increased resistances and even greater RV work.

The effectiveness of the compliance chamber should, therefore, be a function of how well it dampens flow and limits peak flow rates in the system. A constant compliance chamber, like the PC chamber, was expected to decrease TAL impedance and power output with increasing compliance. Furthermore, it was expected that more compliance would be required to reduce impedance at larger stroke volumes, which increase peak flow rates and resistances during systole.

The results of these studies verify these hypotheses. The *Z*_{0}, *Z*_{1}, *P*_{s}, and *P*_{p} all decreased with increasing compliance. The *Z*_{1}, *P*_{s}, and *P*_{p}, furthermore, increased with increasing stroke volume. The compliance necessary to reach a statistical minimum of each factor varied. Factors that are predominantly defined by the steady, zeroth harmonic component of flow, *Z*_{0} and *P*_{s}, were minimized at smaller values of compliance, 1 and 0.5 ml/mm Hg, respectively. Factors that are predominantly defined by pulsatile portions of flow, *Z*_{1} and *P*_{p}, were minimized at larger values of compliance, 4 and 5 ml/mm Hg, respectively.

In a system with a constant resistance, both *Z*_{0} and *P*_{s} would not be affected by compliance. In the BiolungÂ®, however, instantaneous resistance increases linearly with flow rate, leading to quadratic increases in pressure with flow rate. Therefore, the resistance averaged over a cardiac cycle, *Z*_{0}, increases with the pulsatility of the flow and stroke volume, as does *P*_{s}, the product of *Z*_{0} and *Q*_{0}. These results indicate that a small compliance is necessary to minimize the minor resistances in the system and the RV power output required by this resistance. A larger compliance, however, is required to dampen the flow pulse before it reaches the resistance of the artificial lung and generates high systolic pressure and large *Z*_{1} and *P*_{p}. If flow-dependent increases in resistance could be minimized via improved device design, the compliance required to dampen the flow pulse could also decrease. However, this reduction in resistance would also decrease the amount of damping in the system via reduction of the RC product. Thus, changes in the required compliance would likely be small.

Every compliance chamber also comes with some resistance of its own. For this reason, the benefit of the additional compliance must outweigh the negative effect of adding additional resistance. In most cases in this study, any compliance â‰¥ 0.5 ml/mm Hg has lower impedance than with zero compliance. However, the *Z*_{1} was smaller without a compliance chamber than with *C* = 0.5 ml/mm Hg for the cases in which *HR* = 60 bpm with *Q*_{0} = 1.8 or 3 l/min and *HR* = 75 bpm with *Q*_{0} = 1.8 l/min. In addition, there was minimal difference between the *Z*_{1} in the two compliance states when *HR* = 75 bpm with *Q*_{0} = 3 l/min. Together, this may indicate that no compliance is preferable to *C* = 0.5 ml/mm Hg if *Q*_{0} â‰¤ 3 l/min and *HR* is â‰¤ 75 bpm. These states, however, will be atypical for TAL use. It is expected that most TAL use will occur at flow rates > 3 l/min and heart rates > 75 bpm.

It should be noted, however, that the compliance necessary to minimize impedance or power actually depends on the stroke volume. A curve fit of *Z*_{1} for all PC compliances, for example, yields the equation (*R*^{2} = 0.91), demonstrating the opposing effects of increased compliance and stroke volume. Therefore, it requires a larger *C* to reach the minimum of any of these factors when *V*_{s} is large. This study sought to determine the compliance requirements in the clinical applications of a resting, adult patient, in which up to 5 l/min of TAL blood flow is required. In pediatric settings, less compliance would be required to reach minimum *Z*_{0}, *Z*_{1}, *P*_{s}, and *P*_{p}, whereas ambulatory adult settings would require more.

This study has also indicated that *Z*_{0} is minimized at a lower value of compliance than *Z*_{1}. The clinical compliance requirements of the device, therefore, depend on the relative effects of each on right ventricular function. Both are known to be significant contributors to RV power output,^{1} but their relative effect on cardiac output and long-term RV function is not well-studied. One previous *ex vivo* study examined the effects of compliance and resistance on short-term RV function in a pulmonary system model, indicating that both resistance and compliance play a significant role in determining cardiac output.^{9} That study, however, used isolated cat hearts pumping noncellular Tyrode solution under idealized conditions of constant perfusion pressure, heart rate, inotropy, and filling pressure. Thus, the relative effects of *Z*_{0} and *Z*_{1} on RV function under normal physiologic conditions remain unknown.

The ideal device compliance during *in vivo*, in series attachment may also be somewhat smaller because of the compliance of the proximal pulmonary artery. This compliance will cause blood flow entering the artificial lung to be slightly less pulsatile than that seen during these experiments, which used ventricular outflow waveforms. During *in vivo* use, therefore, a compliance less than 5 ml/mm Hg is expected to be the ideal to minimize device impedance. Future studies will be necessary, therefore, to determine the effect of device inlet compliance on the impedance of the combined natural/artificial lung pulmonary system and the relative importance of each harmonic impedance on right ventricular function. These *in vitro* results, however, indicate that the ideal device compliance is at least 1 ml/mm Hg and likely as high as 5 ml/mm Hg.

The current prototype, polyurethane, BiolungÂ® compliance chamber has a pressure dependent compliance that is 0.8 ml/mm Hg at pressures â‰¤ 10 mm Hg (see

Appendix), but decreases with increasing pressure. It performed in a statistically similar or superior fashion to the constant, 1 ml/mm Hg compliance when comparing *Z*_{0} and *P*_{s}, but was statistically inferior when comparing *Z*_{1} and *P*_{p}. The polyurethane compliance chamber, therefore, should be improved such that it has a larger compliance and greater reduction of *Z*_{1}.