Editor:
A recent investigation by Cheong and colleagues should pique the interest of all clinicians
who employ sonography during resuscitation [1]. In their report, a novel method of
measuring the left common carotid artery, maximum velocity time integral (VTIMAX-CA)
was described and its value was related to the left ventricular outflow tract VTI
(VTILVOT). Absolute VTI measurements (in centimeters) were made in critically-ill
patients, though the population studied was relatively stable, seemingly not on vasoactive
medications and with normal cardiac function. Importantly, there was no provocative
(i.e., dynamic) maneuver carried out during their investigation.
As anticipated, Cheong and colleagues observed a stronger relationship between total
(i.e., systolic plus diastolic) VTIMAX-CA and VTILVOT than between only the systolic
portion of the VTIMAX-CA and the VTILVOT. Of most interest, however, was the near
parity between VTIMAX-CA and VTILVOT in absolute value. Based on their regression
equation, the VTIMAX-CA overestimated the VTILVOT less than 10%. Considering why this
might be so elaborates some caveats to their approach.
The maximum-to-centroid velocity ratio
What escapes some clinical sonographers is that the VTI of hemodynamic interest is
not the maximum VTI, but rather the ‘centroid’ VTI (VTICENT). The centroid velocity
is a ‘power weighted,’ average velocity across the vessel lumen [2–4]. Importantly,
the relationship between VTICENT and the maximum VTI (VTIMAX) depends upon the velocity
profile within the vessel [2, 3]. In ‘plug flow’ conditions (e.g., LVOT, ascending
aorta), the velocity profile is flat such that maximum and centroid velocities are
nearly identical [5]. Accordingly, the maximum-to-centroid ratio is roughly 1.0 at
the LVOT. By contrast, ‘parabolic flow’ is characterized by a maximum velocity double
that of the centroid velocity (i.e., a max-to-centroid ratio of 2.0) [2]. This occurs
in smaller-diameter vessels where the centerline red blood cell (RBC) velocity is
greatest and there is progressive slowing of the RBCs towards the lumen periphery;
however, few vessels in the body are characterized by fully-developed, parabolic flow
[5]. The velocity profile of the carotid artery, for instance, is characterized as
‘blunted parabolic,’ with a max-to-centroid ratio approximately mid-way between 1.0
and 2.0 [4]. Given the above, we can express the following relationship as Eq. (1).
1
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\begin{document}$$ K = \frac{{VTI_{MAX} }}{{VTI_{CENT} }} $$\end{document}
K
=
V
T
I
MAX
V
T
I
CENT
where K = 1.0 in plug flow; K = 2.0 in parabolic flow and K
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\begin{document}$$\approx$$\end{document}
≈
1.5 in blunted parabolic flow.
Using the wireless, wearable Doppler system developed by our group [6–10], we have
observed that in resting, healthy volunteers, the common carotid artery max-to-centroid
ratio falls between 1.5 and 1.7 over the entire cardiac cycle. Thus, for simplicity
we assume that the VTIMAX-CA is 1.6 times the carotid artery centroid VTI (VTICENT-CA);
that is, K = 1.6 and we express Eq. (2):
2
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\begin{document}$$ VTI_{MAX - CA} = 1.6 \; \times \;VTI_{CENT - CA} . $$\end{document}
V
T
I
M
A
X
-
C
A
=
1.6
×
V
T
I
C
E
N
T
-
C
A
.
Furthermore, we assume that the velocity profile in the left ventricular outflow tract
is plug; thus, Eq. 3:
3
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\begin{document}$$ VTI_{MAX - LVOT} = 1.0 \times VTI_{CENT - LVOT} . $$\end{document}
V
T
I
M
A
X
-
L
V
O
T
=
1.0
×
V
T
I
C
E
N
T
-
L
V
O
T
.
In other words, the LVOT maximal velocity is used interchangeably with the LVOT centroid
velocity.
Relationship between LVOT and carotid artery VTI
The stroke volume (in mL or cm3) is calculated with ultrasound by multiplying the
cross-sectional area (CSA) of the LVOT (in cm2) by the VTILVOT (in cm) (Eq. 4) [11]:
4
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\begin{document}$$ SV = CSA_{LVOT} \; \times \;VTI_{LVOT} . $$\end{document}
S
V
=
C
S
A
LVOT
×
V
T
I
LVOT
.
The volume of the SV that moves up a carotid artery, the carotid beat volume (CBV),
can be generally expressed as the fraction of the SV distributed to one carotid artery
(CAFLOWFRAC). The CBV can also be calculated analogously to the SV, by multiplying
the CSA of the carotid artery (CSACA) by the VTICENT-CA. Therefore, we arrive at Eq. (5):
5
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\begin{document}$$ CBV = CSA_{CA} \times VTI_{CENT - CA} = CA_{FLOWFRAC} \times
SV. $$\end{document}
C
B
V
=
C
S
A
CA
×
V
T
I
C
E
N
T
-
C
A
=
C
A
FLOWFRAC
×
S
V
.
By substituting Eq. (4) (for SV) into Eq. (5) above, and rearranging, we arrive at
Eq. (6):
6
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\begin{document}$$ VTI_{CENT - CA} = \frac{{CSA_{LVOT} }}{{CSA_{CA} }} \times
CA_{FLOWFRAC} \times VTI_{LVOT} $$\end{document}
V
T
I
C
E
N
T
-
C
A
=
C
S
A
LVOT
C
S
A
CA
×
C
A
FLOWFRAC
×
V
T
I
LVOT
And finally, to convert VTICENT-CA to VTIMAX-CA, which was the measurement obtained
by Cheong and colleagues, we derive Eq. (7):
7
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\begin{document}$$ VTI_{MAX - CA} = K \times \left[ { \frac{{CSA_{LVOT} }}{{CSA_{CA}
}} \times CA_{FLOWFRAC} \times VTI_{LVOT} } \right] $$\end{document}
V
T
I
M
A
X
-
C
A
=
K
×
C
S
A
LVOT
C
S
A
CA
×
C
A
FLOWFRAC
×
V
T
I
LVOT
where K = 1.6
Clinical implications
To make this more concrete, we might consider plugging in some typical anthropometric
values into Eq. (7). For example, if typical CSALVOT [12] and CSACA [13] values are
3.6 cm2 and 0.36 cm2, respectively, then the CSALVOT-to-CSACA ratio is roughly 10.
Curiously, a reasonable approximation of the CAFLOWFRAC is 0.10 [14], meaning that
the CSALVOT-to-CSACA ratio and CAFLOWFRAC reduce to 1.0. Nevertheless, as detailed
above, the maximum velocity in the carotid artery is greater than its centroid; thus,
we expect the VTIMAX-CA to be greater than the VTILVOT as a function of the velocity
profile (i.e., K = 1.6). One speculative explanation for the very slight overestimation
observed by Cheong and colleagues is their novel method of insonating the left carotid
artery. They ‘looked down’ from the supraclavicular fossa and may have insonated near
the bifurcation of the left common carotid artery from the aortic arch. Velocity profiles
at sharp bifurcations behave in complicated ways [2], but the profile can be flat
near the origin, especially if the mother vessel is large like the aorta. The profile
in the smaller vessel then evolves a parabolic morphology only after a distance known
as the ‘entrance length,’ which is estimated as roughly 10 cm for the carotid arteries
[2]. Thus, insonating near the origin of the left carotid artery may have reduced
K towards a ‘plug’ profile value (i.e., K = 1.1 or 1.2) which would make the VTIMAX-CA
closer in absolute value to the VTILVOT.
Regardless of the above, the clinical implications of Eq. (7) are probably greater
for something Cheong et al. did not do, that is, perform a hemodynamic intervention.
When doing so, the clinician is typically trying to infer change in the VTILVOT via
the VTIMAX-CA We see, however, that two variables in particular (i.e., the CSACA,
and CAFLOWFRAC) may co-vary during an intervention and thus dissociate the VTIMAX-CA
from the VTILVOT.
First, with provision of intravenous fluid, the CSACA can increase [15]. This may
be especially important in hypotensive patients in whom increased in mean arterial
pressure affects relatively large vessel distension [16]. Per Eq. (7), augmented CSACA
causes the VTIMAX-CA to underestimate the VTILVOT.
Second, an intervention that also changes the CAFLOWFRAC would also cause VTIMAX-CA
to diverge from the VTILVOT. Fundamentally, the CAFLOWFRAC is directly proportional
to the ratio of whole-body-to-head vascular impedance [6]. For example, lowering body-to-head
impedance diminishes CAFLOWFRAC. An illustration of this is exercise, where muscles
vasodilate and ‘siphon’ blood away from the head. This was shown in the study of Sato
and colleagues where baseline CAFLOWFRAC was about 0.14 and fell to about 0.06 at
peak exercise [17]. Ostensibly, inodilators have a similar effect; per Eq. (7), when
CAFLOWFRAC falls, VTIMAX-CA
underestimates VTILVOT. On the other hand, increased body-to-head vascular impedance
raises CAFLOWFRAC and causes the VTIMAX-CA to overestimate VTILVOT. Catecholamines,
which preferentially vasoconstrict ‘non-essential’ blood flow to maintain brain and
coronary perfusion have this effect. This was recently observed by Kim and colleagues
where carotid blood flow increased relative to cardiac output in response to norepinephrine
[18]. Though catecholamines are the most commonly employed intervention that raises
body-to-head impedance, mechanical therapies such as resuscitative endovascular balloon
occlusion of the aorta (i.e., REBOA) and intra-aortic counter-pulsation would have
similar hemodynamic effects.
Finally, within Eq. (7) we can reasonably assume constancy of the CSALVOT during most
interventions, though the value of K, in theory, might decrease with CSACA. This is
because the Womersley equation predicts flatter velocity profiles (i.e., decreasing
K) with increasing vessel diameter [19]. Thus, carotid artery vessel distention has
multiple mechanisms by which VTIMAX-CA
underestimates VTILVOT.
In summary, Cheong and colleagues are to be congratulated for their impressive clinical
work and their novel approach to carotid insonation. As shown in Eq. 7, there is a
direct relationship between VTILVOT and VTIMAX-CA. However, vessel distension, CAFLOWFRAC
and velocity profile will mediate this link and these covariates may be especially
important during hemodynamic interventions where the clinician performs pre-post VTI
calculations. Furthermore, the framework discussed above could be applied to peripheral
arteries other than the carotid. Novel means to infer real-time vessel diameter, body-to-head
impedance and velocity profile will better model the association between the left
ventricle and common carotid artery, especially in conjunction with other Doppler
measures such as the corrected flow time [6].