Computer simulation of human breath-hold diving: cardiovascular adjustments

Abstract

The world record for a sled-assisted human breath-hold dive has surpassed 200 m. Lung compression during descent draws blood from the peripheral circulation into the thorax causing engorgement of pulmonary vessels that might impose a physiological limitation due to capillary stress failure. A computer model was developed to investigate cardiopulmonary interactions during immersion, apnea, and compression to elucidate hemodynamic responses and estimate vascular stresses in deep human breath-hold diving. The model simulates active and passive cardiovascular adjustments involving blood volumes, flows, and pressures during apnea at diving depths up to 200 m. Redistribution of blood volume from peripheral to central compartments increases with depth. Pulmonary capillary transmural pressures in the model exceed 50 mm Hg at record depth, producing stresses in the range known to cause alveolar capillary damage in animals. Capillary pressures are partially attenuated by blood redistribution to compliant extra-pulmonary vascular compartments. The capillary pressure differential is due mainly to a large drop in alveolar air pressure from outward elastic chest wall recoil. Autonomic diving reflexes are shown to influence systemic blood pressures, but have relatively little effect on pulmonary vascular pressures. Increases in pulmonary capillary stresses are gradual beyond record depth.

Appendix

Thoraco-abdominal mechanics

The three compartment pressures in Fig. 1 are derived from static equilibrium of the springs using the compliance curves in Fig. 2 based on standard curves (Agostoni and Rahn 1960). Pleural pressure P _PL at the chest centroid h ₁ is the sum of external hydrostatic pressure γ_W h ₁, relative to the neck, and transthoracic pressure across the rib cage, dependent on chest compliance K _W and total chest volume. Abdominal pressure P _AB is the sum of pleural pressure, inspiratory diaphragmatic pressure P _DI, and static pressure of the abdominal wall fit to an exponential function of lung volume V _L. Alveolar pressure P _A relative to pleural pressure depends on the volume-dependent compliance. Compartment volumes are updated by their respective differentials δV at each time step, accounting for blood shifts δV _TX and δV _AX.

PPL =  γWh1 +  1 / KW ln[(VL +  VTB +  VDI −VR)/(VV − VR)]	Pleural pressure
PAB =  γWh2 +  PDI +  PPL +  30 exp[−(VL − 0.4)/0.6]	Abdominal pressure
PA =  PPL − 1/KL ln [(VM − VL)/(VM − VO)]	Alveolar pressure
δV DI =  (−δP DI +  δP AB − δP RC − K W δV L)/(K W +  K DI +  K AB)	Diaphragm volume change
δV TX =  δV L + δV DI +  δV H + δV GV	Chest wall volume change
δV AB =  −δV DI +  δV AX	Abdominal volume change

Pulmonary vascular pressures

Pulmonary capillary pressure P _PC relative to alveolar pressure is given by the compliance curve in Fig. 7. P _X and P _Y are the inlet and outlet pressures of the capillary bed, obtained from the analogous voltage-divider circuit according to network resistances shown in Fig. 7. Effective resistances R _2A and R _3A of the pulmonary artery and vein are represented by curvilinear functions simplified from a spreadsheet model of a more complex network (Zhuang et al. 1983) adapted to humans. R _2B and R _3B are the lumped resistances of the capillary sheet (Fung and Sobin 1972). Sheet thickness tapers from H _X to H _Y , and collapses if P _A exceeds P _PC at any point along its length.

PPC =  PA +  (VPC − VPCO)/(α APC)	Pulmonary capillary pressure
PPC =  PA if PPC <  PA	Capillary sheet compressed
PX =  PPA − R2A/(R2A +  R2B) (PPA − PPC)	Pulmonary capillary pressure (inlet)
PY =  PPV +  R3A/(R3A +  R3B) (PPC − PPV)	Pulmonary capillary pressure (outlet)
R2A =  0.10 exp[−(0.5 (PPA +  PX) − PPL)/20]	Pulmonary capillary resistance (inlet)
R3A =  0.05 exp[−(0.5 (PPV +  PY) − PPL)/20]	Pulmonary capillary resistance (outlet)
HX =  Ho +  α (PX − PA) if HX >  Ho	Capillary sheet thickness (inlet)
HL =  Ho +  α (PPC − PA if HX >  Ho	Capillary sheet thickness (central)
HY =  Ho +  α (PY − PA) if HX >  Ho	Capillary sheet thickness (outlet)
R2B =  40/(H 3X +  H 2X HL +  HXH 2L +  H 3L )	Capillary sheet resistance (inlet)
R3B =  40/(H 3Y +  H 2Y HL +  HYH 2L +  H 3L )	Capillary sheet resistance (outlet)
RP =  R2B + R3B	Pulmonary capillary resistance (total)

Heart and vascular pressures

Pericardial pressure P _PERI is approximated as a positive exponential function of heart volume above the unstretched volume of 500 ml. Each vascular compartment has a pressure P _i equal to its local external pressure (P _PL or P _AB). Heart chamber pressures are exponential functions of filling volume during diastole, and are increased by half-sine wave pressures proportional to contractility F _ci during systole. RV and LV pressures are further adjusted according to septal shift due to ventricular interdependence (Amoore and Santamore 1989) incorporated in the effective septal compliance factors F _PRV and F _PLV.

VH =  VRA +  VRV +  VLA +  VLV	Heart volume
VGV =  VIC +  VPA +  VPV +  VAO	Great vessel volume in chest
VTB =  VH +  VGV	Thoracic blood volume
PPERI =  1.2 {exp[0.01(VH − 500)] − 1} VH >  500 ml	Pericardial pressure
P i =  PPL +  C i (V i − Voi)	Intrathoracic vascular pressures
P i =  PAB +  C i (V i − Voi) +  γWh2	Intra-abdominal vascular pressures
P i =  C i (V i − Voi) +  γWh3	Peripheral vascular pressures
PPLV =  FPLV {exp[0.012 (VLV − 0)] − 1}	Passive diastolic LV pressure
PPRV =  FPRV {exp[0.008 (VRV − 0)] − 1}	Passive diastolic RV pressure
FPLV =  16.0 [1 +  0.03(VRV − 150)]	Reduction of LV filling due to RV
FPRV =  6.0 [1 +  0.01(VLV −100)]	Reduction of RV filling due to LV
PRA =  PP +  PPERI +  FPRAVRA +  FSRAVRAFC1(t)	Right atrial pressure
PLA =  PP +  PPERI +  FPLAVLA +  FSLAVLAFC2(t)	Left atrial pressure
PRV =  PP +  PPERI +  PPRV +  FSRVVRVFC3(t)	Right ventricular pressure
PLV =  PP +  PPERI +  PPLV +  FSLVVLVFC4(t)	Left ventricular pressure
Fci(t) =  F maxci sin(π t/TES) Fci (t) ≥  0	Systolic contractility of chamber i

Blood flows

Blood flows are linearly proportional to pressure difference according to Ohm’s law. Volume change is the integral of inflow rate minus outflow rate. Resistance of each peripheral vascular compartment is increased by a depth-dependent factor of F _J due to the diving reflex.

${\dot{{Q}}_{i} = ({P}_{i}-{P}_{i+1})/{R}_{i}}$	Vascular flow for vessel i = 1, ..., 14
${\dot{{Q}}_{i} = ({P}_{i}-{P}_{i+1})/({R}_{i} {F}_{\rm J})}$	Peripheral vascular flows i = 9, 11, 12
${\delta{V}_{i} = (\dot{{Q}}_{i}-\dot{{Q}}_{i+1}) \delta{t}}$	Vascular volume change

Diving reflex

The autonomic diving reflex modulates steady-state heart rate HR _SS as a function of depth. Actual HR is assumed to approach HR _SS with a first order time constant of τ_DR. Peripheral vascular resistance compartments are multiplied by a vasoconstriction factor F _J which changes with the same time constant.

FDR =  1 − exp(−D / 20)	Diving reflex factor, D = depth (m)
HRSS =  70 − 50 F DR	Steady state heart rate, min−1
δHR =  (HRSS − HR) / τDR δt	Change in heart rate
FJSS =  1 +  FDR	Steady state PVR factor
FJ =  FJ +  (FJSS − FJ) / τDR δt	Peripheral vascular resistance factor

Compartments

AA	Abdominal aorta
AO	Thoracic aorta
AR	Arterial
AS	Arterial splanchnic
IA	Inferior vena cava abdominal
IC	Inferior vena cava chest
LA	Left atrium
LV	Left ventricle
PA	Pulmonary artery
PC	Pulmonary capillary
PV	Pulmonary vein
RA	Right atrium
RV	Right ventricle
VN	Venous
VS	Venous splanchnic