Computer models in bedside physiology - Chapter 2: Optimal cardiopulmonary resuscitation as identified by computer modeling

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Computer models in bedside physiology

Zhang, Y.

Publication date

2013

Link to publication

Citation for published version (APA):

Zhang, Y. (2013). Computer models in bedside physiology.

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Chapter 2 Optimal Cardiopulmonary Resuscitation as Identified by Computer

Modeling

Yanru Zhang, Xiaoming Wu, Hengxin Yuan, Lin Xu and John M.Karemaker Most of the work in this chapter has been the subject of 2 congress papers (2009 and 2010) on one of which Ms. Zhang was co‐author; moreover a full paper was published: Xu, L, Wu, X, Zhang, Y and Yuan, H.: The Optimization Study on Time Sequence of Enhanced External Counter‐Pulsation in AEI‐CPR. J. Computers 4; 1243‐1248 (2009) In view of this publication history and the fact that chapter 3 originated from the study reported here (as a warning not to ‘overdo’ the combination of abdominal and chest compression) an extensive discussion of the findings has been deferred to chapter 3. The appendix of chapter 2 (modeling details) applies to both the chapters 2 and 3.

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Abstract

Objective and Design: We aimed to find the optimal mode of cardiopulmonary resuscitation (CPR) in a computer model of the circulation. At least four variants of the simple compression of the heart between sternum and spine exist. For several reasons the efficacy of these modes is difficult to compare in clinical trials. In order to identify the optimal mode we conducted in silico experiments. Setting and Interventions: A Matlab® computer model of the circulation was developed. At simulated cardiac arrest the model was subjected to the various modeled CPR‐variants. The effects on cardiac output and perfusion of critical organs were compared. Measurements and Main Results: We compared Chest Only CPR (CO‐CPR), Active Compression‐Decompression CPR (ACD‐CPR), Interposed Abdominal Compression CPR (IAC‐CPR), thoracic‐abdominal compression‐decompression CPR (Lifestick‐CPR) and chest compression assisted with Enhanced External Counterpulsation on the legs and abdomen (EECP‐CPR). They were combined with the action of an Impedance Threshold Valve (ITV) to support venous return in the chest decompression phase. The three techniques that involve abdominal compression were at least twice as effective as the two that only apply force to the chest, independent of which parameter was used to quantify the result. Compression of the abdominal veins played a more important role than arterial compression in generating cardiac output and organ perfusion. Conclusions: In this in silico study Lifestick‐CPR was the most effective of the CPR techniques tested.

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Introduction

Sudden cardiac arrest is the most critical manifestation of cardiac disease, requiring immediate action to save the patient’s life. Outside a hospital this will mostly be done by cardiopulmonary resuscitation (CPR). This aims to keep the perfusion of heart, brain and lungs going while the heart is in arrest. Since the introduction of closed‐chest CPR several improvements to the classical, or Chest Only CPR (CO‐CPR) have been proposed (5, 11, 12, 19). These have in common that they either require the availability of equipment, or the presence of a second person assisting the one that delivers CPR. Therefore, the application of improved CPR is normally limited to a medical setting such as an ambulance or emergency room. The first variant is the combination of chest compression with Interposed Abdominal Compression (IAC‐CPR) (11). This involves the application of abdominal pressure during the relaxation phase of chest compression in otherwise classical CO‐CPR. This requires the presence of a second rescuer or a dedicated machine. In a second variant, chest compression is combined with active thorax expansion by the Active Compression‐Decompression CPR (ACD‐CPR) (5). This variant uses a suction device to actively compress and decompress the chest. A third variant involves machine‐driven, phased thoracic‐abdominal compression–decompression CPR (Lifestick‐CPR) (17). Lifestick‐CPR combines IAC and ACD‐CPR by alternately compressing and decompressing the chest and the abdomen through adhesive pads. And finally, a G‐suit like device has been designed to ‘milk’ the venous blood by inflatable cuffs wrapped around legs and buttocks. This variant is knows as Enhanced External Counterpulsation (EECP‐CPR) (8, 21). An inspiratory impedance threshold valve (ITV) has been proven as a beneficial adjunct (15). The valve closes the airways while the chest is being decompressed, with the objective to improve venous return due to the enhanced subatmospheric intrathoracic pressure during the recoil phase of chest compression. In our modeling ITV is combined with the aforementioned five CPR variants (Fig. 1) mentioned. At present there is no decisive evidence which one of the alternative CPR‐techniques is superior to Chest Only CPR (10, 20). In 2010 International Consensus on Cardiopulmonary Resuscitation and Emergency Cardiovascular Care Science with Treatment Recommendations emphasizes CO‐CPR as the only accepted resuscitation method (7). Clinical evidence is lacking

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since for obvious reasons, it is not feasible to compare the various CPR techniques under the same condition. We therefore turned to computer models of the circulation. Otto Frank’s computational model of cardiac function in conjunction to the Windkessel concept conceived in the late 19th century (13), paved the way for the current era. In our time, with ever increasing calculation speed, computer modeling of circulation has shaped a new avenue of research to investigate medical problems (6, 16). A computer model may avoid the major disadvantages of animal and clinical experiments such as ethical issues, high costs, complexity, influence of external factors and operator‐dependent effects. Furthermore, it overcomes time and space limitations. We argue that to conquer the difficulties inherent to finding ‘evidence‐based’ best practice in an emergency situation like CPR, computer modeling is an obvious choice. This approach can quantify and evaluate the effects of the different components of the various CPR‐techniques to help decide which ones are effective and which are of little consequence. In this paper a circulatory model has been used as an experimental platform to test the five CPR techniques. In silico experiments do not put a critically ill patient at risk, and allow comparison of the various CPR techniques under highly‐defined conditions. We extended the model developed by Charles F. Babbs (1‐3) to simulate CO‐CPR, ACD‐CPR, IAC‐CPR, Lifestick CPR and EECP‐CPR. In all experiments we assumed that an ITV was in place. We focused on their hemodynamic effects to identify the optimal CPR technique. Here we report that Lifestick‐CPR is the most effective of the five CPR techniques.

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Methods

Model description The model we adopted for this study is largely based on the work of Babbs et al. (1‐3). The model is an electrical equivalent circuit and has sufficient details to allow simulation of the five CPR techniques except for the initial blood volumes immediately after the cardiac arrest (CA). These blood volumes were estimated by us (Table 1). The model has 14 compartments, including four heart chambers, the pulmonary circulation, the thoracic aorta feeding an upper body and an abdominal compartment (Fig. 2). The structure of each lumped artery and vein compartment is the same, including a resistance followed by a capacitance (compliance). The peripheral circulation for each compartment is a simple resistance. Each ventricle has two valves. Each vein outside the trunk has one valve to ensure unidirectional blood flow. In view of the low blood velocity in CPR, inertial effects were neglected. The initial pressure of all systemic compartments in simulated CA is set to 5 mmHg, and to 8mmHg in the pulmonary part. Finally, it was assumed that coronary perfusion stopped during the compression phase. Figure 2 Top: structure of the circulatory model. Details of chest pump: next page

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Figure 2. Bottom (detail): model of the chest pump including heart and pulmonary circulation.

Relevant parameter values of the model are listed in the appendix. To help understand Fig. 2 a list of symbols and subscripts is given in Table 1

Table 1. Symbols and subscripts used in Fig. 2

Symbol Electrical Mechanical

C capacitor Compliance (i.e. compliant compartment)

i current (blood) flow

R resistance resistance to flow

Subscript Definition Subscript Definition

aa abdominal aorta la left atrium and central pulmonary

ao thoracic aorta lv left ventricle

c / car carotid arteries mv mitral valve

cppa central to peripheral pulm aa. pa pulmonary arteries cppv peripheral to central pulm vv. pc pulmonary capillary

fa femoral arteries ppa peripheral pulmonary arteries

fv femoral veins ppv peripheral pulmonary veins

h head vasculature pv pulmonary valve

ht heart (coronary) ra right atrium

iv iliac veins rv right ventricle

ivc / v inferior vena cava s splanchnic

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CPR description CPR chest compression theoretically has two mechanically distinct effects on the central circulation. In the thoracic pump mechanism compression of lungs and mediastinal organs, including atria and great vessels (pulmonary trunk, ‐ arteries and aorta) causes blood to flow. In the cardiac pump mechanism compression of the heart causes blood to flow. Which one of the two mechanisms prevails remains controversial (18). In our model we left the controversy alone. Like in Babb’s model (2) we defined a factor ftp (0 ≤ ftp ≤ 1) to allocate the relative contribution of both mechanisms: ftp = 0 denotes pure cardiac pump mechanism, ftp = 1 denotes pure thoracic pump mechanism. Values between 0 and 1 denote a mixture of the two mechanisms. Every CPR technique involves chest compression. In our in silico experiments chest compression is modeled as described earlier (2, 4). Briefly, the resistance of the chest to external compression is represented by a simple spring and damper system defined by spring constant k and damping µ. During chest compression the force applied, F(t), leads to downward movement of both sternum and anterior chest wall over a distance x1 (cm). The reactive force due to damping depends on the speed of movement (x´1). We can now define F(t) as follows ' 1 1

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A

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₍₂₎ The mechanical effects of chest compression are translated in equivalent electrical events and applied to our model. The equations are presented in the appendix. For example, in IAC‐CPR, Lifestick CPR when the abdomen is compressed, the pressure to the abdomen is taken as a voltage source in series with the appropriate compliances (Civc and Caa in Fig.2). In EECP‐CPR the lower body and abdomen are compressed ‘sequentially’.

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allows positive pressure ventilation but prevents inspiration caused by subatmospheric airway pressures. Following the 2010 International Consensus on CPR and ECC Science with Treatment Recommendations (14), the compression frequency was set to 100 times/min. As compression/decompression waveforms we adopted sine waves or rather half‐sine waves as suggested by Babbs (2005) and Noordergraaf et al. (2005) (2, 9); the pressure patterns for the various CPR‐techniques are shown in Fig. 3A‐E. The model was solved using MAT LAB/Simulink. The solver was ODE4. To make the model reach steady state in a convenient time frame, step size was set at 0.0001s; simulation time was 40 s. The model reached a steady state after 8 seconds.

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Figure 3 Pressure waveforms: A: CO‐CPR; chest compression only; B: ACD‐CPR; chest compression and decompression combined; C: IAC‐CPR; chest compression and abdomen compression combined (abdomen: red dashed line); D: Lifestick CPR; chest compression and decompression, combined with abdomen compression and decompression. E: EECP‐CPR; chest compression and decompression, combined with abdomen and lower body compression (green line). Peak values for thorax (de‐)compression: +400 & ‐200 N; for abdomen (Pabd): +100 & ‐20 mmHg, for

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Results

Comparison of the five CPR techniques To compare the relative effects of CO‐CPR, ACD‐CPR, IAC‐CPR, Lifestick CPR and EECP‐CPR (combined with ITV), we chose to present Cardiac Output (CO), carotid artery flow (Qcar) and myocardial flow (Qheart). Qcar reflects global cerebral perfusion, while Qheart reflects coronary perfusion. The results are summarized in Fig. 4. Figure 4 Comparison of the five different CPR techniques: A: CO cardiac output (L/min). B: Qcar average carotid blood flow and Qheart average coronary blood flow (ml/s). These three parameters are considered the most important parameters for CPR. The effects of IAC‐CPR, LIFESTICK CPR and EECP‐CPR give great improvement over CO‐CPR and ACD‐CPR Compared to CO‐CPR and ACD‐CPR, the three techniques that involve abdominal and/or lower body compression (IAC‐CPR, LIFESTICK CPR and EECP‐CPR) produce at least a two times higher CO. The same holds for Qcar and Qheart which are at least doubled compared to CO‐CPR and ACD‐CPR. Of the three superior variants Lifestick CPR has the best efficacy in terms of cardiac output and cerebral perfusion. Finally, in our model, ACD‐CPR is only slightly better than CO‐CPR. The aforementioned experiments were conducted with ftp = 0.75. To test for the sensitivity of our results for ftp we repeated the in silico experiments with ftp = 0, which represents the

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pure cardiac pump mechanism, and ftp = 1 which represents the thoracic pump mechanism. The results are summarized in Fig. 5. Figure 5 Comparison of CO between pure cardiac pump (Ft=0) and pure thoracic pump (Ft=1. Compared to CO‐CPR, IAC‐CPR, LIFESTICK CPR and EECP‐CPR give a higher CO irrespective of ftp. Of the three superior variants Lifestick CPR again has the best efficacy in terms of cardiac output regardless of ftp. Furthermore, except for EECP‐CPR, CO is higher when a cardiac pump mechanism is operative. Another striking result is the large difference between cardiac pump mechanism CO and thoracic pump mechanism CO in CO‐CPR and ACD‐CPR but not the other three. Veins/ Arteries‐only compression in abdomen and limbs IAC‐CPR, LIFESTICK CPR and EECP‐CPR have abdominal compression during chest decompression in common. Next, we aimed to analyze which aspect of this maneuver is more important, compression of the abdominal veins or compression of the abdominal arteries. Such an analysis, of course, is only possible in computer models of the circulation. Venous compression pushes blood towards the heart, thus favoring a higher cardiac output. Arterial compression raises the resistance of the vessels and tends to trap blood in the proximal arteries. This mechanism resembles the action of a balloon pump. Arterial compression potentially limits the arterial pressure fall upon chest decompression in the phase of diastolic runoff. To address this question we first determined CO, Qcar and Qheart when both the arteries and veins were compressed (V + A)compr. Next we determined the same three parameters if only the veins are compressed (Vonly) or if only the arteries are compressed (Aonly). Finally we took the ratio of Vonly/(V + A)compr and that of Aonly/(V + A)compr. This procedure was

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Table 2. Ratios of veins‐ or arteries‐only compression to compression of both

IAC‐CPR LIFESTICK CPR EECP‐CPR

Veins‐ Arteries‐ Veins‐ Arteries‐ Veins‐ Arteries‐

CO (%) 94 52 93 43 89 46 Qcar (%) 91 45 94 41 92 41 Qheart (%) 71 86 76 67 57 93 Regardless of the CPR technique used, CO benefits most from venous compression. 89‐94% of the CO is preserved when only the veins are compressed. In contrast, CO halves (43 – 52%) when only the arteries are compressed. Similar observations were made for Qcar. Qheart, on the other hand, benefits most from arterial compression in IAC‐CPR and EECP‐CPR but not so much in Lifestick CPR. This follows directly from the assumption of stopped coronary flow during chest compression. These results explain to why IAC‐CPR, Lifestick CPR and EECP‐CPR are superior to CO‐CPR with regard to the resulting CO. The inferior vena cava (as simple model for the abdominal venous pool) is the largest vein in the body and a large amount of blood can be stored here. Compressing this vein restores a considerable venous return, thus favoring CO.

Discussion

In this paper CO‐CPR, ACD‐CPR, IAC‐CPR, Lifestick CPR and EECP‐CPR have been assessed using a computer model of the circulation. We reasoned that this model offers a uniform and unique platform to evaluate the different CPR techniques. We observed that abdominal and lower body compression in counter phase with thorax compression lead to substantially improved hemodynamic results and is therefore recommended. We concluded that Lifestick CPR gave the best effects in cardiac output, blood flow to brain and heart, EECP‐CPR increased mainly CO and Qcar. EECP‐CPR and Lifestick CPR produced better effects, but they are mechanical CPR techniques, which require the appliance at hand and trained professionals, which limits their use. IAC‐CPR can be performed just by hand, and the effects are tightly following EECP‐CPR and Lifestick CPR. If cardiac arrest happens in a public space, IAC‐CPR presumably is the best choice. Our model is restricted to the hemodynamic effects of CPR. Ventilation effects and oxygen

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compression pressure is set to fixed values, according to the recommendations of the Guidelines or clinical empirical setting. However, it is very likely that during actual resuscitation the compression pressure vary. Finally, our model is based on a ‘standard’ 70‐kg ‘textbook’ human subject, this potentially limits generalizability of our results.

References

1. Babbs CF. CPR techniques that combine chest and abdominal compression and decompression: hemodynamic insights from a spreadsheet model. Circulation 100: 2146‐2152, 1999. 2. Babbs CF. Effects of an impedance threshold valve upon hemodynamics in Standard CPR: studies in a refined computational model. Resuscitation 66: 335‐345, 2005. 3. Babbs CF. Efficacy of interposed abdominal compression‐cardiopulmonary resuscitation (CPR), active compression and decompression‐CPR, and Lifestick CPR: Basic physiology in a spreadsheet model. Crit Care Med 28, 2000. 4. Babbs CF, Weaver JC, Ralston SH, and Geddes LA. Cardiac, thoracic, and abdominal pump mechanisms in cardiopulmonary resuscitation: studies in an electrical model of the circulation. Am J Emerg Med 2: 299‐308, 1984. 5. Cohen TJ, Tucker KJ, Lurie KG, Redberg RF, Dutton JP, Dwyer KA, Schwab TM, Chin MC, Gelb AM, Scheinman MM, and . Active compression‐decompression. A new method of cardiopulmonary resuscitation. Cardiopulmonary Resuscitation Working Group. JAMA 267: 2916‐2923, 1992. 6. Guyton AC, Coleman TG, and Granger HJ. Circulation: overall regulation. Annu Rev Physiol 34:13‐46.: 13‐46, 1972. 7. Hazinski MF, Nolan JP, Billi JE, Bottiger BW, Bossaert L, de Caen AR, Deakin CD, Drajer S, Eigel B, Hickey RW, Jacobs I, Kleinman ME, Kloeck W, Koster RW, Lim SH, Mancini ME, Montgomery WH, Morley PT, Morrison LJ, Nadkarni VM, O'Connor RE, Okada K, Perlman JM, Sayre MR, Shuster M, Soar J, Sunde K, Travers AH, Wyllie J, and Zideman D. Part 1: Executive summary: 2010 International Consensus on Cardiopulmonary Resuscitation and Emergency Cardiovascular Care Science With Treatment Recommendations. Circulation 122: S250‐275, 2010. 8. Yuan HX, Zheng ZS, Zhong HF, Liao XX, Du ZM and Huang X. “Double Pump” Cardiopulmonary Resuscitation: The Hemodynamic Study of the Inflational VEST with External Counterpulsation (II). J of Jinan Univ (Nature Science & Medicine Edition): S1, 1997 9. Noordergraaf JG, Dijkema JT, Kortsmit WJPM., Schilders WHA, Scheffer GJ, and Noordergraaf A. Modeling in Cardiopulmonary Resuscitation: Pumping the Heart. Cardiovasc Eng 5: 105‐118, 2005. 10. Panzer W, Bretthauer M, Klingler H, Bahr J, Rathgeber J, and Kettler D. ACD versus

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11. Ralston SH, Babbs CF, and Niebauer MJ. Cardiopulmonary Resuscitation with Interposed Abdominal Compression in Dogs. Anesth Analg 61: 645‐651, 1982. 12. Safar P. Closed chest cardiac massage. Anesth Analg 40: 609‐613, 1961. 13. Sagawa K, Lie RK, and Schaefer J. Translation of Otto Frank's paper "Die Grundform des Arteriellen Pulses" Zeitschrift fur Biologie 37: 483‐526 (1899). J Mol Cell Cardiol 22: 253‐277, 1990. 14. Sayre MR, Koster RW, Botha M, Cave DM, Cudnik MT, Handley AJ, Hatanaka T, Hazinski MF, Jacobs I, Monsieurs K, Morley PT, Nolan JP, Travers AH, and Adult Basic Life Support Chapter C. Part 5: Adult basic life support: 2010 International Consensus on Cardiopulmonary Resuscitation and Emergency Cardiovascular Care Science With Treatment Recommendations. Circulation 122: S298‐324, 2010. 15. Shuster M, Lim SH, Deakin CD, Kleinman ME, Koster RW, Morrison LJ, Nolan JP, Sayre MR, Techniques CPR, and Devices C. Part 7: CPR techniques and devices: 2010 International Consensus on Cardiopulmonary Resuscitation and Emergency Cardiovascular Care Science With Treatment Recommendations. Circulation 122: S338‐344, 2010. 16. Snyder MF, Rideout VC, and Hillestad RJ. Computer modeling of the human systemic arterial tree. J Biomech 1: 341‐353, 1968. 17. Tang W, Weil MH, Schock RB, Sato Y, Lucas J, Sun S, and Bisera J. Phased chest and abdominal compression‐decompression. A new option for cardiopulmonary resuscitation. Circulation 95: 1335‐1340, 1997. 18. von Planta M and Trilló G. Closed chest compression: a review of mechanisms and alternatives. Resuscitation 27: 107‐115, 1994. 19. W.B.Kouwenhoven, R.Jude J, and Knickerbocker GG. Closed‐chest cardiac massage. JAMA 173: 1064‐1067, 1960. 20. Ward KR. Possible reasons for the variability of human responses to IAC‐CPR. Acad Emerg Med 1: 482‐489, 1994. 21. Yuan H, Zheng Z, and Jiang S. The Hemodynamic Study of The Chest Compression Assisted with Enhanced External Counterpulsation. Chinese J Emerg Med 4: 140‐144, 1995.

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Appendix ‐ modeling details

Table 1A Definitions and values of resistances Definition R i t f S b l H /L/ carotid arteries Rc 60 head vasculature Rh 5520 jugular veins Rj 30 tricuspid valve Rtv 5 pulmonic valve Rpv 10 path from central to peripheral pulmonary arteries Rcppa 10 path from peripheral to central pulmonary veins Rcppv 5 mitral valve Rmv 5 aortic valve Rav 10 pulmonary capillary bed Rpc 105 coronary vessels (heart) Rht 15780 aorta Ra 25 inferior vena cava Rv 25 splanchnic vasculature Rs 1800 iliac arteries Ria 360 iliac veins Riv 180 leg vasculature Rl 8520 airways to ventilation Rairway 1.2

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Table 1B Definitions and values of compliances Definition Compliance of the ….. Symbol L/mmHg Initial volume (L) Unstressed volume (L) arrested right ventricle Crv 0.01600 0.150 0.070 large pulmonary arteries Cpa 0.00420 0.109 0.076 peripheral pulmonary arteries Cppa 0.00042 0.160 0.157 peripheral pulmonary veins Cppv 0.00128 0.300 0.290 central pulmonary veins and left atrium Cla 0.01280 0.250 0.148 arrested left ventricle Clv 0.00800 0.150 0.086 carotid arteries Ccar 0.00020 0.132 0.131 jugular veins Cjug 0.01200 0.216 0.156 thoracic aorta Cao 0.00080 0.078 0.074 right atrium and intrathoracic great veins Crh 0.00950 0.367 0.320 abdominal aorta Caa 0.00040 0.114 0.112 inferior vena cava Civc 0.02340 1.930 1.813 femoral arteries Cfa 0.00020 0.078 0.078 femoral veins Cfv 0.00470 0.267 0.244 combined lung‐chest wall Clung 0.15800 ‐ ‐ Initial conditions: 5 mmHg filling pressure in the systemic, 8 mmHg in the pulmonary circulation. Valves are supposed to be ideal, driven by pressure differences with the resistances as indicated, immediately closing when reverse flow would occur. Compliances are supposed to behave as follows: For positive pressures, volumes are increasing linearly above the unstressed volume as indicated by the index of compliance; for negative pressures volumes are supposed to be zero and the unstressed volume is emptied. For more details the reader is referred to: Koeken, Y, Aelen P, Noordergraaf GJ et al. The influence of nonlinear intra‐thoracic vascular behaviour and compression characteristics on cardiac output during CPR. Resuscitation 2011; 82: 538‐544.

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Table 2 Miscellaneous: Abbreviations and definitions

Abbreviation Definition

Value

Al Cross section area of lung squeezed by sternal compression 100 cm2

Ara Ala Arv Alv Cross section area of cardiac chambers in front to back 20 cm2

Frequency Number of cycle per minute for chest and abdominal pressure 100/min

Duty cycle Fraction of cycle time for chest compression 0.5 ftp Thoracic pump factor (0.75=adult, 0.25=child, 1.0=emphysema, 0=open chest) 0 ‐ 1.0 Pinit Initial equilibrium pressure of arrested circulation 5 mmHg Fmax_chest Maximum external force on sternum 400 N X0 Effective compression threshold 2 cm Table 3 Blood flow Abbreviations and definitions

Abbreviation Definition

ic Blood flow in both carotid arteries ih Blood flow in the head vasculature ij Blood flow in both jugular veins ii The input blood flow to thoracic io The output blood flow from thoracic iht Blood flow in coronary vessels(heart) ia Blood flow in the aorta is Blood flow in residential systemic vasculature iv Blood flow in the inferior vena cava ifa Blood flow in both femoral arteries ifv Blood flow in both femoral veins i2 Blood flow in the pulmonary veins i3 Blood flow between central and peripheral pulmonary arteries i4 Blood flow in the pulmonary capillaries i5 Blood flow in between central and peripheral pulmonary veins i6 Blood flow in the left atrium

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Table 4 Volumes and pressures: Abbreviations and definitions

Abbreviation Definition

Blood volume Vaa Blood volume in the abdominal aorta Vivc Blood volume in the inferior vena cava Via Blood volume in both iliac arteries Vfa Blood volume in both femoral arteries Vfv Blood volume in both femoral veins Blood pressure Pao Blood pressure of thoracic aorta Paa Blood pressure of the abdominal aorta Pivc Blood pressure of the inferior vena cava Pfa Blood pressure of both femoral arteries Pra Blood pressure of the right atrium Pfv Blood pressure of the femoral veins Peecp Compression pressure to lower body

Pabd compression pressure to the abdomen

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There are 14 compartments in the model; there are 14 pairs of formulas to describe the relationship between pressure and volume. ‘P’ stands for pressure, ‘V’ stands for volume, and Subscripts indicate which compartment the formulas describe. ( ) [ ] car c h car jug ao car c h car car car V i i t P P P P t R R V P C       _        _     ₍₁₎ ( ) [ max(0, )] jug h j

car jug jug ra

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the pressure to the lungs. ‘ftp’ is thoracic pump factor; more information in references 2, 3. 1 1 ( ) 0 F t kx x_  ₍₃₎ 1 2 0

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4 5 ( ) [ ] ppv ppa ppv ppv la pc cppv ppv ppv lung ppv V i i t P P P P t R R V P P C       _ _       _       ₍₇₎ 1 0 ( ) [max(0, ) ] ao o c a ht lv ao ao car ao car ao ra av c a ht pa ao lung tp pa V i i i i t P P P P P P P P t R R R R V E P P f x t C d         _ _ _ _         _          ₍₈₎ 2 3 1 0 ( ) [max(0, ) ] pa rv pa pa ppa pv cppa pa pa lung tp pa V i i t P P P P t R R V E P P f x t C d       _ _       _          ₍₉₎ 1 0

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₍₁₀₎ 2 1 0 ( ) [max(0, ) max(0, )] ( ) rv i rv pa ra rv tv pv rv rv rv lung rv rv V i i t P P P P t R R V E V P P x t C d A       _ _       _ _           ₍₁₁₎ 5 6 1 0 ( ) [ max(0, )] ( ) la ppv la la lv cppv mv la la la lung tp la la V i i t P P P P t R R V E V P P f x t C d A       _ _  _ _ _    _ _          ₍₁₂₎

(23)

6 1 0

(

)

[max(0,

) max(0,

)]

(

)

lv o la lv lv ao mv av lv lv lv lung lv lv

V

i

t

P

t

R

V

E

V

P

x t

C

d

A





 





_













_

   



 





₍₁₃₎

When the abdomen is compressed in IAC-CPR, the abdominal aorta and inferior vena cava are directly exposed to the compression pressure.

( ) [ ] aa a s ia aa fa ao aa aa ivc a s ia aa aa abd aa V i i i t P P P P P P t R R R V P P C        _ _ _        _       ₍₁₄₎

(

)

[

) max(0,

)]

ivc s v fv fv ivc aa ivc ivc ra s v iv ivc ivc abd ivc

V

i

t

P

t

R

V

P

C





 























_



_

_{ }

_



₍₁₅₎

When the lower body is compressed in EECP-CPR, it undergoes the compression pressure directly. )] , 0 max( [ ) ( 1 ] [ ) ( 1 iv ivc fv l fv fa fv l fv l fv l fv l fv fa ia fa aa fa l l ia fa l fa R P P R P P C t P t i i C P P R P P R P P C t P t i i C P P                           (16)