Venous congestion and the geometry of Guyton

Background

Balan and colleagues have published an intriguing, post-hoc investigation of patients following elective coronary artery bypass grafting in Annals of Intensive Care [1]. They studied the interaction between a Doppler ultrasound marker of venous congestion (portal vein pulsatility index, PVPI), echocardiographic measures of right ventricular (RV) function and a surrogate of volume state, the mean systemic pressure analogue (P_MSA). Included patients had no venous congestion (i.e., PVPI < 50%) at baseline. The experimental protocol is shown in Fig. 1A and 65% were preload responsive (PR) while 35% were preload unresponsive (PUR).

Fig. 1.

A Experimental protocol. Preload responsive patients were defined by a ≥ 12% increase in left ventricular outflow tract velocity time integral (LVOT VTI) during passive leg raise (PLR). Right ventricular (RV) parameters studied were 1. RV to left ventricular (LV) end-diastolic area ratio (RVEDA/LVEDA), 2. tricuspid lateral annular systolic velocity (RV S’), 3. RV fractional area change (RVFAC), 4. pulmonary acceleration time (PAT) and 5. right myocardial performance index (RIMP). B The Geometrical model showing effect of change in P_MSF on operating point (OP₁ to OP₂) between a preload responsive (left) and unresponsive (right) patient. P_RA−plat is the right atrial pressure at which the cardiac function curve plateaus C Using Eqs. 1 and 2, this is a graphical simulation showing effect of increasing P_MSF on P_RA (i.e., PVPI) between preload responsive and unresponsive patients assuming an R_VR:R_CARDIAC ratio of 2.5 and P_RA−plat of 2 mmHg. PVPI portal vein pulsatility index; LVEF left ventricular ejection fraction; P_MSA mean systemic pressure analogue; P_MSF mean systemic filling pressure; Q is blood flow in liters per minute; mmHg millimeters of mercury; LR Lactated Ringer’s solution

At baseline (T1), multivariable regression found that three measures of RV function (RVEDA/LVEDA, RV S’ and RIMP) associated with PVPI while P_MSA did not. However, for all patients across T1-T3 there was a significant correlation between P_MSA and PVPI. Lastly, in the subset of PR patients studied at T1, T4 and T5, P_MSA associated with PVPI as did the three significant RV parameters from T1.

We think that a recently proposed ‘Geometrical model’ of the circulation elaborates the findings of Balan and colleagues [2, 3]. We argue that (1) there are subtle mathematical differences in the P_MSA-to-PVPI relation in preload responsive versus unresponsive patients and that (2) the ratio between the resistance to venous return (R_VR) and cardiac function (i.e., cardiac resistance, R_CARDIAC) as a measure of ‘veno-cardiac coupling’ modulates the relation between PVPI and P_MSA.

Synopsis of geometrical model

The Geometrical model reaffirms Guyton’s own words [4] that: “… right atrial pressure is not one of the primary determinants of cardiac output but, instead, is itself determined simultaneously along with cardiac output.” What, then, are the independent variables that determine right atrial pressure (P_RA) and blood flow (Q)? The Geometrical model proposes that there are four: 1. The mean systemic filling pressure (P_MSF), 2.) the resistance to venous return (R_VR), 3.) the pressure surrounding the right atrium (i.e., the pericardial pressure, P_PC), and 4.) cardiac resistance (R_CARDIAC). Furthermore, the model specifies that the independent variables alter the P_RA and Q by different magnitudes contingent upon whether the patient is PR or PUR (Fig. 1B).

Because the Geometrical model asserts that both Q and P_RA are concurrently determined by the system of independent variables above, the model reconciles debate between the experimental approaches of Guyton and Levy [5]. Guyton altered the height of a collapsible tube, effectively using gravity to change the transmural pressure of the right atrium, analogous to changing the P_PC; then he varied pump function (R_CARDIAC) to return the tube wall to a trans-mural pressure of approximately zero, in which state the height of the collapsed tube was equivalent to the P_RA. With this, Guyton iteratively generated a series of unique P_RA-Q relationships plotted as a venous return curve. Levy, on the other hand, changed only R_CARDIAC to produce P_RA-Q relationships. Regardless, neither P_RA nor Q in either experiment were independent variables.

Geometrical model and venous congestion

The Geometrical model can be solved for P_RA. To better understand the findings of Balan et al., and to simplify the analysis, we set P_PC to atmospheric pressure such that P_RA is the right atrial transmural pressure as a surrogate for PVPI. This is reasonable because increasing PVPI is partly due to greater retrograde a-waves at end-diastole, reflecting right atrial congestion into the hepatic circulation. Different equations apply for the PR and PUR states (1 and 2 respectively; see Appendix).

1

2

First, there is a direct relationship between P_MSF (or P_MSA) and PVPI, but also an indirect relationship between PVPI and the ratio of the R_VR to R_CARDIAC. Decreasing R_VR and/or increasing the R_CARDIAC raises P_RA (and therefore PVPI) for any given P_MSF (and vice versa). The R_VR:R_CARDIAC ratio is analogous to ventriculoarterial coupling (i.e., the E_A:E_ES ratio) and could partly explain the lack of association between PVPI and P_MSA at baseline. Consequently, the PVPI-P_MSA relationship must be understood in terms of ‘veno-cardiac coupling’.

Second, in PR patients, the R_VR:R_CARDIAC ratio is the multiplicative inverse of PVPI while in PUR patients the ratio is the arithmetic inverse. Thus, when P_MSF is increased (e.g., during PLR or crystalloid infusion) the PVPI (and therefore P_RA) is predicted to change more in PUR patients (Fig. 1C); conceptually this is because the venous return curve shifts right along a flat portion of the cardiac function curve (Fig. 1B).

Limitations and conclusions

The transmural P_RA, by itself, does not fully explain PVPI. Retrograde a-waves reflected into the hepatic and portal venous systems due to right atrial congestion is one determinant. Additionally, vascular compliance, valve function, damping properties of the hepatic venous outflow, organ compliance, perihepatic pressure, autonomic tone and reflexes such as the hepatic buffer arterial response also mediate this dynamic, waveform-based index.

We congratulate Balan and colleagues for their excellent work linking venous congestion, preload responsiveness and Guytonian principles. Though hypothesis-generating, the simplified Geometrical model connecting venous return (P_MSF, R_VR) and cardiac function (P_PC, R_CARDIAC) helps predict P_RA and, theoretically, venous Doppler patterns. Increased R_CARDIAC (i.e., impaired cardiac function) augments P_RA at any volume state (i.e., P_MSF); this relationship is amplified when the patient is preload unresponsive. While not perfectly related, rising P_RA contributes to venous congestion and PVPI. We believe that the ability to distinguish dependent (e.g., P_RA) from independent (e.g., R_CARDIAC) hemodynamic variables is relevant for proper bedside therapeutic decision-making.

Abbreviations

PVPI

Portal vein pulsatility index

RV

Right ventricle

P_MSA

Mean systemic pressure analogue

PR

Preload responsive

PUR

Preload unresponsive

T1–5

Time 1–5

RVEDA

Right ventricular end diastolic area

LVEDA

Left ventricular end diastolic area

RV S’

Tricuspid lateral annular systolic velocity

RVFAC

RV fractional area change

PAT

Pulmonary acceleration time

RIMP

Right myocardial performance index

LVOT VTI

Left ventricular outflow tract velocity time integral

LVEF

Left ventricular ejection fraction

LR

Lactated Ringer's solution

OP

Operating point

R_VR

Resistance to venous return

R_CARDIAC

Cardiac resistance or cardiac function

P_RA

Right atrial pressure

Q

Blood flow - cardiac output or venous return

P_MSF

Mean systemic filling pressure

P_PC

Pericardial pressure

P_RA−plat

Right atrial pressure when cardiac function curve forms plateau (i.e., flattens)

E_A:E_ES

Arterial elastance to end-systolic elastance

PLR

Passive leg raise

Appendix

These equations assume two adjacent right triangles [2]: the y-axis is blood flow (Q), the x-axis is pressure (P), and the slope relating flow over pressure is 1/Resistance.

Preload responsive state:

Preload unresponsive state:

Authors contributions

JESK initial drafting; PWM critical revisions.

Funding

Not applicable.

Data availability

Not applicable.

Declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

JESK is the co-founder and chief medical officer of Flosonics Medical.