Cardiopulmonary Resuscitation Modeling and Optimization
Sudden Cardiac Death

Sudden cardiac death remains the main cause of out-of-hospital death in United States. In fact according to a joint report by American Heart Association (AHA) and Center for Disease Control and Presentation of the National Institute of Health (NIH), cardiovascular disease was responsible for 30.6\% of total number of death in US from 1998 to 2008. In 2010, overall rate of death attributable to cardiovascular diseases was 23.5\% and coronary heart disease alone caused approximately 1 of every 6 deaths in the United States in 2010. Cardiopulmonary resuscitation procedure (CPR) is performed in emergency conditions on patients suffering from cardiac arrest to maintain blood flow and oxygen delivery to the brain and other vital organs until further treatments are performed on the patient is the only hope of survival these patients. CPR procedure involves chest compression and artificial respiration. Chest compressions help to pump blood from the heart to restore blood circulation in the body and artificial ventilation provides manual respiration.

Since 1966 the AHA has been developing and implementing guidelines for step by step procedures of CPR. The developed guidelines have been saving many lives by emphasizing early recognition, activation and defibrillation; in addition, they have shown the importance of early access to emergency medical care. The prospect of saving lives demonstrates the importance of resuscitation research and clinical translation. However, there has not been a fundamental change in CPR procedure since its introduction. In spite of CPR's relative success, survival rates for in-hospital patients was very low, generally 5-10\% in 2001 and now it is up to 23\%. Low survival rates demonstrate the fact that the current state of the art methods in resuscitation are far from optimized and CPR is still an open research area. Consequently, the main goal of resuscitation research remains to be an appropriate modification of the CPR procedure to improve survival rate.

CPR Mechanism

During the chest compression phase of the CPR, the rescuer pushes the chest to create the desired blood pressure and circulation in the body. Although studies have shown that increasing chest compression depth and, consequently, force, will increase blood flow during the CPR, the exact mechanism which is responsible for generating blood flow from chest compression is yet to be understood. There have been two mechanism hypothesized. These mechanisms are (i) thoracic pump and (ii) cardiac pump. The cardiac pump theory hypothesizes that compressing the heart between the sternum and the spine pushes the blood in the heart to the rest of the body. Releasing the pressure allows the heart chambers and other blood vessels to refill. The thoracic pump theory hypothesizes that the chest compressions induce pressure on the whole chest to circulate blood. In other words, the heart acts primarily as a passageway for the blood. Both of these theories have shown to be valid to some extent, however the exact relationship between chest compression and produced blood flow is not yet understood.

CPR Modeling

Figure~(1) represents a schematic of our chest model during the CPR procedure. $F$ represents the force which is applied to the chest by the rescuer and the compression depth $X$ represents the chest deflection due to the applied force.

To develop the essential elements of the model, we first start by looking at a sample of the collected data (the experiment will be described in detail later). For instance, Figure~(2) shows the real collected data of the force plotted against displacement for consecutive compression-release cycles during CPR. Note the hysteresis loop that is clearly evident. Hysteresis, or material damping, is caused by internal friction, is frequency dependent, and causes energy dissipation. We believe that this hysteresis effect (never documented before to our knowledge) is an important feature for characterizing the mechanical properties of the chest.

An additional aspect of the model is nonlinearity in elasticity and damping. Previously developed models fail to capture the complex nature of different phenomena happening during CPR, such as structural damping or hysteresis. We believe that these phenomena need to be addressed by the model for a better representation of the real data. Moreover,these models make an assumption that the ribs are intact and not broken during the CPR event which is not true in many CPR cases. In fact, ribs break about 3\% of the time during pediatric CPR and about 10-20\% of the time during adult CPR. Also sternal fracture occurs about 5\% of the time in good quality adult CPR. To address the problem of fracture during CPR, we need to analyze changes in the CPR parameters over time. More important is the fact that, even in the cases when ribs do not break, the chest properties change during the time that CPR is administered due to various structural changes that happen in the chest, most of which have been observed, but are not clearly understood. Regardless of this lack of detailed understanding, we believe that these changes should, and can indeed be captured in a sound model.

In order to make a better analysis of the proposed model and to decrease uncertainties associated with estimating the model parameters we have nondimensionalized the proposed model. Nondimensionalization will enable a parametric study of the nonlinear model; even more significantly, also, it provides a clear and easy way to compare the magnitudes of the vairous coefficients by creating dimensionless parameters. The non-dimensional model has been presented in:

The data for the current study was collected at our pig lab at CHOP. The predefined experimental protocol was approved by The University of Pennsylvania Institutional Animal Care and Use Committee. 15 healthy 3-month-old female domestic swine (32.4 Kg) were anesthetized and mechanically ventilated using a Datex Ohmeda anesthesia machine (Modulus SE) on a mixture of room air and titrated isoflurane ( 1.0 - 2.5\%) .

To guide and record the CPR data, a Philips Heart Start MRx defibrillator with Q-CPR option was deployed. The chest depth, acceleration and applied force on the chest were recorded using Laerdal technology. Each defibrillator in the experiment has an oval pad that has been placed on the lower part of the sternum. The oval pad is equipped with an accelerometer and a force sensor to measure the chest compression, acceleration and force during each CPR cycle. This method has been previously validated with compression depth data accurate to within 1.6 mm. To ensure the consistency of the results and to remove artifacts from the data, two criteria have been applied for the inclusion of cycles. These two criteria are compression depth minimum and compression frequency minimum. Cycles with the compression depth of less than 30 mm and more than 55 mm have been removed from the analysis. Additionally, cycles which are shorter than 0.4 s (150 cycles/min) or longer than 1 s (60 cycles/min) have been excluded from the analysis. A total of 14,693 cycles from 15 pigs have met the two criteria and have been included in the analysis.

Modeling Results

As we know, the CPR procedure is a dynamic procedure, meaning that the characteristics of the thorax are time dependent. There have been studies focused on thorax changes during CPR as time progresses. However, the varying mechanical properties of the thorax during chest compression have not yet been the subject of much study. Recently, showed that the chest stiffness (which they simply defined as force divided by displacement), will change during the CPR delivery; however, this analysis needs to be improved since the definition of stiffness is overly simplified and does not completely capture the really complex and nonlinear nature of the chest during CPR.

To track the changes in the mechanical properties of the chest during CPR which stems from potential rib breakage or change in the shape and geometry of the chest, we have divided the CPR cycles into two time periods. These two time periods are time periods before and after 10 minutes from the start of CPR. We call these two time periods, early and late time periods. We then estimate the parameters for each time period separately. This separation allows us to analyze the changes in the mechanical properties of the chest over time. The analysis of the changes in chest parameters helps us understand the changes that are happening to the chest during the CPR and how these changes may affect the delivery and the efficacy of CPR. As mentioned earlier, a total of 14,693 cycles from 15 adolescent 30 Kg swine have been included in the analysis. Among these cycles, 10,273 cycles belong to the early time period and the remaining 4,420 cycles belong to the the late time period. The estimated parameters of the model for the two time periods are presented in Table (1). We use these sets of parameters to estimate the force for all cycles and then we calculate the RMSE for each cycle. The calculated RSME values mean for the two time periods are 0.12 and 0.09 for each time period respectively.

Table (1) reveals interesting information regarding the mechanical properties of the chest during the CPR: there is a very strong nonlinearity in the elastic part of the model, particularly the third, fourth and fifth order components. Although we could have gone to higher orders for the elasticity, we did not do so in order to prevent over-fitting. It would also be an unnecessary complication of the proposed model especially since the RMSE values are very good. Results also show a relatively strong nonlinearity in the damper. The results presented here show that the current CPR manikins which are based on the linear viscoelastic model are not fully representative of the sternum during the CPR and consequently fail to mimic real conditions. Very small p-values for hysteresis coefficients display strong correlation between hysteresis force and measured force. Moreover, the results show that the hysteresis force decreases in later stages of the CPR. It is a very interesting finding which shows that, with progression of time, more energy is dissipated in viscous damping and the role of hysteresis damping starts to decrease. This may be due to the fact that the shape of the sternum changes ("molding" as the critical care physicians call it) as CPR continues.

Figure (3) represents a plot of the estimated versus measured nondimensional forces for 10 consecutive cycles in the early time period as an example of the results. As can be seen from the figure this is a very good estimation especially considering the fact that the force amplitude varies cycle by cycle. Furthermore, another interesting observation from this plot is that although the proposed model is smooth and continuous, the estimated force shows some sharp changes, particularly in the resting state. By the resting state, we mean time that the force is close to zero which represents the beginning of a new cycle. We suspect that these unexpected changes are mainly caused by sharp changes in acceleration for which there is no clear explanation. Since no explanation for this behavior can be found in the literature, we believe we need a more sophisticated model in the future to fully address this problem.

The plots of energy distributions for two different time periods have been presented in Figure~(4). This is a box plot of the calculated energies for each cycle based on the estimated parameters. The middle line in each box is the mean of the respective group, the bottom and top lines of the box represent the $25\%$ and $75\%$ quartiles respectively and the whispers represent $5\%$ and $95\%$ quartiles. A very interesting observation from Figure~(4) is that as CPR progress, the energy needed to push the chest increases; an even more interesting fact is that this increase in energy is mostly used to overcome viscous damping as elastic and kinetic energies remain almost constant. Figure~(4) presents the mean energy distribution during the two stages of CPR. The figure shows that although at the beginning of the CPR procedure, the elastic energy is responsible for 75\% of total consumed energy, it drops to 64\% of total consumed energy due to increase in the viscous energy dissipation.

Sample Publications
  1. A Jalali, Vinay M Nadkarni, C Nataraj, Modeling mechanical properties of the chest during the cardiopulmonary resuscitation procedure , Computing in Cardiology, (41) 13-16, 2014.