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Pediatric Circulatory Support

Hemodynamic Guidelines for Design and Control of a Turbodynamic Pediatric Ventricular Assist Device

Uber, Bronwyn E.*; Webber, Steven A.; Morell, Victor O.; Antaki, James F.†‡

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doi: 10.1097/01.mat.0000227730.00085.36
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Abstract

The very limited options available to treat children with congenital and acquired heart diseases have recently motivated the development of a new generation of pediatric ventricular assist devices (Ped-VADs) that may support a young patient for up to 6 months.1 According to a 2005 NIH BAA2 (National Institute of Health Broad Agency Announcement), these systems are required to be appropriately sized but capable of providing adequate cardiac output for the infant or child, while avoiding complications associated with the patient's small size, such as vascular injury or thrombosis. However, the specific hemodynamic requirements for this patient population are ill defined. Limited clinical experience with Ped-VADs has restricted the collection of longitudinal data for designing these devices and treating these patients. There is also a dearth of data for healthy pediatric patients.

Extracorporeal membrane oxygenation (ECMO) is currently the most widely used means of mechanical circulatory support for pediatric patients. The limitations of ECMO3–5 and the success of VADs in adults have motivated the development of new devices specifically to treat this population.2 The advantages of VADs over ECMO include longer duration of support, improved quality of life with the ability for physical activity, fewer requirements for blood transfusion, and greater cost-effectiveness.3 Second-generation implantable Ped-VADs currently under development promise new opportunities for treatment and rehabilitation of the unique and high-risk population of children with congenital and acquired heart diseases. However, there is a lack of consensus regarding the range of flows that Ped-VADs must accommodate.

For a given pump design, the hemodynamic range is constrained by two factors: biocompatibility and capacity. Biocompatibility limits the operating range due to the necessity to avoid blood trauma, thrombosis, and thermal damage. The capacity of a given pump to develop a desired pressure at a given rate of flow is governed by principles of physics related to the pump size, speed, rate, and so forth, of the particular pump design. For example, a turbodynamic blood pump typically produces pressure and flow characterized by a monotonically decreasing relation (Figure 1). The hemodynamic demand of the circulation, however, requires an increasing relation; therefore, the speed of the pump must be increased with increasing demand. However, speed may not be increased indefinitely because of risk of blood damage and physical constraints of the motor. Furthermore, the size of the pump places an upper limit to the pressure that can be developed at high flow. The latter motivates the design of a relatively large pump with correspondingly high optimal flow point (indicated by BEP, best efficiency point, in Figure 1). Unfortunately, the optimal flow point also affects the biocompatibility at low flow. This is illustrated in Figure 2, which provides the visualization of flow within a centrifugal blood pump at the optimal and at low-flow condition. Whereas the flow streamlines are well behaved and laminar at the optimal condition, the streamlines at the low-flow condition are clearly disturbed, presenting recirculation that will inevitably promote deposition and risk of thrombosis. This in turn has clinical implications relating to the freedom from anticoagulation.

Figure 1.
Figure 1.:
Relation of hemodynamic capacity to physiological demand of a turbodynamic pump. Typical quasi-static pressure capacity decreases with increasing flow. BEP, Best efficiency point.
Figure 2.
Figure 2.:
Flow visualization of centrifugal blood pump at optimal flow (left) and low flow (right) condition. (Courtesy of Z. Wu.)

This study, therefore, was undertaken to derive guidelines for specifying the operating limits for designing future Ped-VADs. The source data were compiled from hemodynamic studies on healthy and unhealthy pediatric patients and registries for ECMO and heart transplants.

Defining Operating Range

Figure 3 illustrates a proposed algorithm for prospectively establishing the operating range for designing a pediatric circulatory device. It is based on the limited range of operation of a turbodynamic pump defined by the deviation from its optimal (best efficiency) point. The optimal utility will be achieved by choosing the upper and lower limits of flow to accommodate the greatest population of potential patients. The upper limit is assumed to be 80% above the BEP, based on fluid dynamic restrictions described above. The lower limit is assumed to be 50% below the BEP defined empirically according to flow stability.6 In other words, a VAD designed for a nominal operating point of 1.0 lpm would be typically labeled for a range from 0.5 to 1.8 l/min.

Figure 3.
Figure 3.:
Conceptual diagram for determining hemodynamic requirements. Exercise capacity will be restricted at the upper limit of Ped-VAD capacity, which can be accommodated, if desired, by conversion to a larger VAD for toddlers (TVAD).

The estimation of optimal range for a Ped-VAD according to this algorithm is achieved in three steps: first, by identifying potential patient population by deriving prevalence of the diagnoses for which such a device would be indicated according to a patient parameter, preferably weight or BSA (body surface area); second, the required cardiac output (CO) is determined for the target population according to the same patient parameter; and, third, the number of prospective patients—based on device-specific constraints—is mathematically maximized. The great range of required flow rates spanning from smallest patients at rest to the largest patients at exercise, will inevitably necessitate two sizes of pumps, such as depicted in Figure 3: a Pediatric VAD (Ped-VAD) and a Toddler VAD (T-VAD).

Estimating the Intended Patient Population for Pediatric VAD

When defining the flow ranges of a Ped-VAD, the actual number of estimated patients is not as important as the distribution of patients according to BSA, weight, or age. Due to the limited clinical experience of VADs for pediatric patients, it is difficult to define the patient population who could potentially benefit from a chronic, implantable VAD. However, an estimate may be derived from the experience with heart transplantation and ECMO. The most inclusive and specific sources of these data are available from the extracorporeal life support (ECLS) Registry,5,8 the United Network of Organ Sharing (UNOS) heart transplant waiting list,10 and the North American Pediatric Heart Transplant Study (PHTS).9,10 Although not as preferable as BSA or weight, Table 1 compiles the prevalence of children listed for a heart transplant according to age from the latter study for patients under 12 years of age. The range of 0 to 1 year old is the most prominent group (57% of the total). This population may be used to estimate the potential subpopulation of patients who would have benefited from a VAD if one were available. It may be safely assumed that most of those who died while waiting for a transplant would have benefited from a VAD as well as a subset of children who only just survived to transplant and therefore would have benefited from a Ped-VAD. Additionally, it may be argued that a class of patients who were never listed because of their poor prognosis may also be added to the pool of potential VAD recipients. Although it is difficult to predict the exact number of patients in this category, it seems clear that when this device is available, there will be patients implanted with the pump who otherwise would have had no treatment options. Recall that the exact number estimated is not crucial to this calculation; the distribution of patients is more important. For the sake of an estimate, the potential patient population was assumed to be 25% of all of the children on the heart transplant waiting list.12Figure 4 is a graphical representation of the estimated Ped-VAD population according to age in months.

Table 1
Table 1:
Distribution of Age of Children (<12 Years of Age) at the Time of Listing for Heart Transplant, Based on Compilation of Data From December 1993 to December 2002 (N = 1563)
Figure 4.
Figure 4.:
Estimated potential Ped-VAD population per year, broken down by age in months. Estimate is based on 25% of children on the heart transplant waiting list.11

The graph in Figure 5 can also be used to predict the potential Ped-VAD patient population. This graph is a snapshot of the number of patients 0–6 years old, according to UNOS, who were waiting on a particular date (April 1, 2005).13 It is valuable because the prevalence is broken down in terms of weight instead of age. The minimum weight is 2.0 kg, and 75% of the patients weighed 10 kg or less.

Figure 5.
Figure 5.:
Distribution according to weight of children (0 to 6 years old) on the UNOS Heart Transplant Waiting list on April 1, 2005.12

The extracorporeal life support registry,5 which has been compiling yearly comprehensive data from ECMO patients since 1987, can offer additional insights about the potential VAD population (Figure 6). The preponderance of patients supported for cardiac causes are treated after the repair of a congenital heart defect, and more than 65% of these patients are under 1 year old. The majority of all ECMO patients treated for cardiac causes over the past 15 years are in the age group from newborn to 30 days old—almost 40% of all cases. In 2003, there were 237 patients in this age group, 117 patients between 30 days and 1 year old and 135 patients from 1 year to 16 years old.5 These data further emphasize the particular necessity for a VAD to accommodate the youngest children.

Figure 6.
Figure 6.:
Data from the past 15 years of ECMO patients treated for cardiac failure.5

Further useful information from the ECMO experience is the minimum weight of a pediatric patient. A weight of below 2.0 kg is a commonly accepted contraindication for ECMO, although, in rare instances, centers will place patients on ECMO who are 1.8 to 1.9 kg.12–14

As stated previously, many children who will require mechanical circulatory support are likely to be below the mean weight for their age. Therefore weight (or BSA) should be preferred over age to predict the appropriate CO for VAD. Unfortunately, most of the data provided by UNOS includes only age, not weight or BSA. The data from the PHTS, which provided BSA of transplant recipients, was used in this study. The minimum BSA was 0.17 m2, and the preponderance of children receiving cardiac transplant had a BSA between 0.17 and approximately 0.38 m2.10 This range can also be depicted in terms of weight, approximately 2.3 to 7.9 kg.

Although children as small as 2.0 kg are placed on ECMO and on the heart transplant waiting list, that minimum does not necessarily extend to Ped-VAD implantations. The cannulation of the smaller children presents an added obstacle because cannulation is affected by the size of the child, the heart condition (whether the heart is enlarged), and the size of the ports on the pump. Determining the appropriate cannula size is beyond the scope of this paper. Speculating that a 5-mm ports will be used, the minimum weight of a child implanted with the pump would most likely be 3.0 kg. In most cases, it would be difficult to cannulate a smaller child. Therefore, in this paper, 3.0 kg was taken as the minimum weight of the potential patient population.

Ranges of Cardiac Output for Pediatric VAD

An assumption is made that the resting CO of normal healthy children is the ultimate goal for a patient of the same weight or BSA who is on a VAD. There are some patients who, immediately after implant, may require lower flow due to limited right ventricular function. This inability to achieve “low normal” flow in the operating room due to inadequate performance would constitute an indication for simultaneous right ventricular support. Therefore, these low flows (significantly below normal) will not be included when determining the necessary pump range.

Allometry, the study of size of living things, can be used to define rules that can be applied across the entire patient population. This concept, dating back to the 19th century,15–17 provides correlations within mammalian biology for CO, weight, and BSA. These are typically described in the form of a power function Y = αxβ, relating two size measures, x and Y, where α and β are constants.

According to Reiss18 a power law relation for oxygen requirement versus weight can be applied across the mammalian species, with β = 3/4. In this paper, it is assumed that oxygen requirement can represent CO because hematocrit is constant across individuals in a species, hence19:

CO can also be related to BSA by using a power law, with β = 9/8.18

It should be pointed out that this relation is not valid for some categories of adults, particularly obese patients.16 This issue, however, is not relevant to the ped-VAD population. Equations 1 and 2 indicate that the relation of BSA to CO is more linear (β = 1.125) than the relation of weight to CO (β = 0.75). As a result, this study chose BSA to normalize CO.

It is difficult to obtain CO data on healthy children because these measurements typically involve invasive procedures that are not usually performed. Therefore, CO range for the patient population was derived on the basis of two standard cardiac indices CIs—upper and lower limits—which were constant over different BSAs and distribution of BSA and/or weight. For reference, Table 2 provides the average weight and BSA for normal children of different ages, obtained from a pediatric dosage handbook.7

Table 2
Table 2:
Standard Values for BSA and Weight of Healthy Children at Particular Ages

Previous data from Abolmaali et al.21 have shown that CI, based on BSA, is reasonably constant for healthy subjects between 3 and 17 years old. The maximum and minimum CI (CO/BSA) for the children between the ages of 3 and 6 are 2.8 and 5.5 l/min per m2, respectively. The entire group of subjects falls between 2.8 and 6.5 l/min per m2. Poutanen et al.21 also measured CO of healthy children with BSA between 0.5 and 1.0 m2 by using echocardiography. The resulting CI values overlap and are consistent with those of the Abolmaali study. See Table 3. A further corroboration of the constancy of CI is provided by data from adults. Table 4 is compiled from data of two independent studies of CI in healthy adults.22,23

Table 3
Table 3:
Data From the Poutanen Study of Healthy Children
Table 4
Table 4:
Data About Cardiac Index in Healthy Adults

Because these reports did not study the very youngest patients, these data were concatenated from three data sets: Walther et al.24; Kusaka et al.25; and Pauli et al.26 Walther and colleagues recorded CI for healthy premature (n = 59) and term newborn infants (n = 62), using range-gated, pulsed Doppler velocimetry, and M-mode echocardiography. The average CI for each weight range from this study is reproduced in Figure 7. The study concluded that 325 ml/min per kilogram and 200 ml/min per kilogram can be used as the upper and lower limits of normal.24 These data further demonstrate consistency of CI with (birth) weight. Also depicted in Figure 7 are data from a study by Kusaka et al. of CI of newborn infants in the neonatal intensive care unit. The data from unhealthy children can be used as a comparison to the normal values.25 The cardiac indices of this group are much more scattered than those for healthy normal subjects. The majority are below normal.

Figure 7.
Figure 7.:
Cardiac index (CI), based on weight of healthy premature and term newborn infants24 (solid diamonds) and premature and term newborn infants in the neonatal intensive care unit (open squares).25

A highly relevant group of children are those who have undergone cardiac surgery and/or catheterization. Although their diagnosis varied, all of these patients were seriously ill and were placed in a pediatric cardiac intensive care unit. Figure 8 provides a summary of results from Pauli et al.,26 who measured CI by thermodilution (range: 4.3 to 88 kg) after surgery and during catheterization procedures. The postoperative data are similar to healthy values; however, catheterization data are also systematically lower. (Note that the units in Figure 8 [l/min per m2] are different than those in Figure 7 [l/min per kilogram] and therefore must be converted for direct comparison.)

Figure 8.
Figure 8.:
Cardiac indices (CI), based on body surface area from children after surgery or during cardiac catheterization.26

ECMO data are not presented here for comparison because the flows are set by the technicians and are not automatically a gold standard of what is necessary to maintain end organ function. Furthermore, these patients are heavily sedated, unlike the Ped-VAD patients, and often their hearts are still pumping, which means the pump flow is not the total CO.

Figure 9 summarizes the maximum and minimum CI from all of the studies discussed above, categorized by subpopulation. Standard deviation cannot be given because some data only provided averages instead of each individual data point. All data provided as l/min per kilogram were converted to l/min per m2, using Equation 2. Three studies (hatched bars) depict data for unhealthy children. The lower and upper limits of normal were taken as 2.8 l/min per m2 and 5.5 l/min per m2, respectively. From this summary, the minimum value for CI for children in a critical care environment is as low at 1.0. The CI of 2.0, which was typical for children in the critical care environment, was chosen to all for comparison with the flows in healthy children.

Figure 9.
Figure 9.:
Summary of maximum and minimum values for CI from multiple studies.20,21,24–27 Solid bars indicate healthy children; hatched bars indicate pediatric cardiac patients. Horizontal dotted lines indicate maximum and minimum values for healthy subjects and the average value found in a critical care environment.

The maximum pump output depends on the maximum size of patient to be supported, the anticipated level of activity, and patient growth while on the pump. Older children and adults, for example, may experience a 4- to 6-fold increase in CO while exercising at maximal levels.28 This study assumes, however, that the activity of ped-VAD patients will be limited to moderate levels. This assumption is justified due to the relative brevity of VAD support (2 to 4 months), since these patients will not be candidates for the VAD as a destination therapy. As a result, to account for the increase demand due to normal activities, the pump should accommodate a 50% increase in CO.

Based on the forgoing assumptions, three different levels of predicted CO can be defined to aid in determining the most appropriate flow ranges for the pump design. The first two are based on the lower portion of normal CO (CI = 3.0) and a 50% increase in that value to account for mild exercise. These can be used to define the maximum pump output necessary and a possible option for the minimum. The third is based on the CO, which captures the majority of patients in a critical care environment (CI = 2.0). This value can be used as a comparison, and it may be necessary to define the minimum CI in between the lower limit of normal and the average found in a critical care environment.

where BSA is given in units of m2.

Based on the forgoing assumptions, quadratic polynomials were used to regress the predicted CO demand versus weight (these equations only apply to weights under 18 kg):

where W is weight (in kg). Figure 10 and Figure 11 show graphs of these equations. The CO predictions in terms of BSA and weight are also provided in tabular form (Table 5).

Figure 10.
Figure 10.:
Three different levels of predicted CO as a function of BSA to help determine target output for Ped-VAD. Max lower limit of normal (upper line); lower limit of normal (middle line); critical care values (dashed lower line.)
Figure 11.
Figure 11.:
Three different levels of predicted CO as a function of weight to help determine target output for Ped-VAD. Max lower limit of normal (upper line); lower limit of normal (middle line); critical care values (dashed lower line.)
Table 5
Table 5:
Tabular Form of Equations 3 Through 8 , Predicting CO for a Given Weight or BSA

The polynomial relation between output and age is shown below. Remember that the previous two relations should be used preferentially (these equations are valid for children up to 5 years old):

where x is age (in years.)

The accuracy of Equations 6 and 7 was further validated by comparison to unpublished data obtained from patients receiving a Berlin Heart at Children's Hospital of Pittsburgh. Data from four patients given implants between 2004 and 2005 are provided in Table 6, along with the predicted flows according to weight. The recorded mean flow of one patient (No. 2) was within the range provided by the prediction. The model, however, slightly overpredicted the lower range of flow in two patients (Nos. 3 and 4) and underpredicted the upper limit of flow of one patient (No. 3). On the basis of these limited data, it appears that the minimum range (based on CI = 3.0), may not be sufficient; however, the absolute minimum (based on CI = 2.0, average CI found in a critical care environment) appears to be lower than necessary. An alternate absolute minimum could be based on the average of these two, CI = 2.5 l/min per m2, which would capture the average flow for all of the Berlin heart patients.

Table 6
Table 6:
Information Based on Unpublished Data From Berlin Heart Patients at Children's Hospital of Pittsburgh

Range of Pump Operation

The ultimate objective of this study was to determine specifications for the design of a ped-VAD that may provide the optimal utility. The utility function described previously may be formulated in terms of the following integral:

which aims to maximize the number of patients, N, that may be accommodated by a VAD with nominal flow Q, assuming an upper and lower limit of flow capacity equal to 180% and 50%, respectively. Because the lower bound of flow is defined according to risk of thrombosis, the function also includes a weighting function w(Q) that may subjectively convey the desire to avoid anticoagulation at the lowest flow. The function for demand according to flow, N(Q), was derived from Table 1, using Equations 9 and 10 and presuming a uniform fraction of patients of each age group who would be implanted with a VAD. (Without loss of generality, this was assumed to be 50%.) Figure 12 depicts the estimated distribution of CO requirements based on the forgoing assumptions. Since the majority of patients are under 1 year old, there is a clear weighting to the lowest range of flow.

Figure 12.
Figure 12.:
Estimated distribution of cardiac output demand of prospective pediatric patients requiring VAD. Solid line is based on data obtained from ECMO; dashed line represents upper range of normal healthy patients of the same ages. (Assumes the distribution, for children 6 years and younger, shown in Table 1. Critical care assumed to have CI = 2.0; normal to lower range assumed to have CI = 3.0; normal to upper range assumed to have CI = 4.5.)

With an equal weighting value, w = 1, and assuming a nominal value of CI = 2.8 yields a nominal flow of Q = 1.4 lpm, implying minimum and maximum flow capacity of 0.7 and 2.5 lpm, respectively. Using the same CI but weighting the lower flow range, that is, <1.0 lpm with w = 0.5, shifts the nominal flow point to Q̄ = 1.0 lpm, implying minimum and maximum flow of 0.95 and 3.4 lpm, respectively. In this latter case, anticoagulation may be indicated for applications below 0.95 lpm, including most newborn infants. Anticoagulation also depends on the device; therefore, flow is not the only determinant of the necessity of anticoagulation.

Discussion

This study was undertaken to help predict the design requirements of a VAD for young children. It was intended to eliminate the need of iterative redesign, which is costly, time-consuming, and poses the risk of “missing the mark” for the intended population.

Because of the paucity of clinical data, several assumptions were necessary to complete this exercise. Consequently, there are several sources of error. The lack of specificity of age at the time of listing (Table 1) is one important source of error in regressing the equations for flow as a function of age or weight. The lack of data and relatively wide spread of CO values for the sample population also precluded statistical analysis of the upper and lower percentiles of prospective patients. This forced the use of either mean values or extreme upper and lower bounds in fitting the model equations.

Additional error is introduced by the assumptions of “safe” operating range of a turbodynamic VAD. The upper and lower limits of safe operation will depend on the particular design of the device as well as the condition of the patient. The use of 50% and 180% of nominal flow, however reasonable, should not be taken as an absolute standard.

The utility function itself bears a degree of subjectivity. It presumes that the optimal device is the one that serves the greatest population. This might be true from an economic perspective, but in reality the value to society is much more complicated. Indeed, from a safety perspective, it would be best to provide multiple devices with narrower bands of operation, allowing only for growth of the patient while on support. Multiple devices with overlapping ranges could be operated from the same controller, with only modest software modifications, since the controller electromechanics can cover a range much greater than that of the implantable part of the VAD.

It is possible to adopt a much simplified estimate of flow requirements, based on an educated guess. One might presume that the greatest demand exists for the youngest patients and therefore select the lower flow requirement, based on a child weighing 3 kg. This would correspond to a CO of approximately 0.54 l/min if a CI of 2.5 l/min per m2 is assumed. Therefore, the upper limit of flow, based on the guidelines given previously, would be 1.94 lpm. According to Equations 6 and 7, this would be suitable for a patient weighing 9 kg, who can sustain moderate activity, or a sedentary patient weighing 16 kg, without any native cardiac contribution to output. However, by using the absolute minimum (CI = 2.0), which allows children with lower CO to also be captured, as the minimum flow for the pump necessitates a flow of 0.34 for a child with a BSA of 0.17. This causes the upper limit of flow to significantly shift to 1.2 l/min, which only captures children up to 4 kg, if accounting for day-to-day activities.

The difficulty in choosing the minimum flow results because a subtle modification may have a great effect on the design of the VAD. For example, if 1.0 lpm is assumed as a lower operating flow, hence 3.6 lpm as the upper bound, this would correspond to an indicated population from birth to approximately 10 years of age. However, it would exclude the underweight children who are typical of the ECMO population. There is a trade-off. Based on all of the currently available data and information presented in this paper, 3 kg (0.214 m2) appears to be the best minimum weight and a CI of 2.5 l/min per m2 is the most appropriate minimum; therefore, the minimum flow necessary is 0.52 l/min. With the design constraints, the maximum flow will then be 1.92 l/min. This pump should capture the majority of the predicted pediatric patient population. Patients weighing 3 to 9 kg can be accommodated up to the upper limit of normal (which should allow for all normal daily activities), and patients weighing between 9 and 15 kg can also be supported; their activities, however, may be restricted.

Additional clinical experience will be needed to obtain the data necessarily to thoroughly optimize the model described herein. Ironically, these data can only be collected once a suitable Ped-VAD is brought to clinical readiness. If the first-generation design fails to accommodate the youngest or oldest intended patients, it may be prohibitively expensive to go back to the drawing board.

Acknowledgments

This work was partially supported by NIH Contract HHSN268200448192C (NO1-HV-48192), the National Science Foundation (ECS-0300097), and a Cardiovascular Bioengineering Training Grant, NIH Grant (T32-HL76124).

This work was also partially supported by Health Resources and Services Administration contract 231-00-0115. The content is the responsibility of the authors alone and does not necessarily reflect the views of policies of the Department of Health and Human Services, nor does mention of trade names, commercial products, or organizations imply endorsement by the US Government.

A special thanks to Trevor Snyder and Tim Maul for their assistance.

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