To demonstrate the calculations for Wei’s SV correction facto
Pressure-Volume
Transonic Scisense Technical Note
cardiac cycle (End-Systole and End-Diastole as determined by
A. Hentonand
andtherefore
F. Konecnyunique to any st
Wei’s SV correction is dynamic
March,
2013
variables used above in Baan’s SV correction
will apply:
Transonic
Transonic Scisense
Scisense Technical
Technical Note
Note
L = 4.5 mm
A mathematical review of SV correction factors employed in Baan’s
ρ = 1.2 Ohm·m
equation and Wei’s equation:
Wei’s SV Correction:
Scisense
PV Technical
Note
Wei’s SV Correction:
Transonic Scisense Technical Note
A. Henton
F. Konecny echocardiogra
SVreference = 32uL (as derived
fromand
hi-resolution
March, 2013
To
demonstrate
the calculations
for
Wei’s SV
correction facto
To
demonstrate
calculations
for
To
demonstrate
the
calculations
for Wei’s
Wei’s SV
SV correction
correction facto
facto
Gb-ED
= 855 uS =the
0.855
mS
cardiac
cycle
(End-Systole
and
End-Diastole
as
determined
by
cardiac
cycle
(End-Systole
and
End-Diastole
as
determined
cardiac cycle (End-Systole and End-Diastole as determined by
by
Baan’s equation:
Where:
Wei’s
SV
correction
is
dynamic
and
therefore
unique
to
any
st
Gb-ES
=
465
uS
=
0.465
mS
A mathematical review of SVρ =correction
factors
employed
in
Baan’s
Wei’s
SV
correction
is
dynamic
and
therefore
unique
to
any
st
blood resistivityWei’s SV correction is dynamic and therefore unique to any st
variables
used
above
in
Baan’s
SV
correction
will
apply:
variables
used
in
SV
will
variables
used above
above
in Baan’s
Baan’s
SV correction
correction
will apply:
apply:
L = measuring electrodes
distance
Transonic
Scisense
Technical Note
equation and Wei’s equation:
How Wei’s Equation Improves Volume Measurement
Using Gamma Correction Factor
𝑆𝑆𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
The conversion of blood conductance to volume
LL == 4.5
α = SV correction VARIABLES
factor
= mm
4.5
mm
1
−𝑏𝑏 ±√𝑏𝑏2 −4𝑎𝑎𝑎𝑎
L
=
4.5
mm
𝐺𝐺
can be achieve by2employing a conversion equation
𝑏𝑏𝑆𝑆𝑆𝑆𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑉𝑉𝑉𝑉𝑉𝑉
=
𝜌𝜌𝜌𝜌
(𝐺𝐺
−G.
)
�1
−
�
,
𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒
γ
=
𝑥𝑥 or Wei’s
𝑝𝑝 equation.
ρ = blood
resistivity
Gx The
= measured TOTAL
such as Baan’s
𝛾𝛾Ohm·m
Therefore, we can compare
𝛼𝛼 equation
2𝑎𝑎 SV correction process between B
ρ
== conductance
1.2
ρ
1.2
Ohm·m
ρ
=
1.2
Ohm·m
primary difference in these equations is how
the
=
parallel/muscle
conductance
L
=
measuring
electrode
distance
Gp
Baan’s
equation:
Where:
𝑆𝑆𝑆𝑆
stroke
volume
(SV) correction factor is treated.
(assumed to be removed
by hypertonic
saline
injection)
==SV
32uL
(as
derived
from
echocardiograp
αSV
= reference
Baan’s
correction
factor
= hi-resolution
( 𝑆𝑆𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
) VS
32uL
(as
derived
from
hi-resolution
echocardiograp
reference
SV
(as
derived
from
hi-resolution
echocardiograp
ρ = blood resistivitySV
reference = 32uL
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
2 (𝐺𝐺
2
)
𝑎𝑎
=
𝑆𝑆𝑆𝑆
−
𝜌𝜌𝐿𝐿
−
𝐺𝐺

32
−
(1.2)(4.5)
(0.8
Gx = measured
Total
conductance
𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸
L = measuring electrodes
distance
Baan’s Equation
Gb-ED
=
855
uS
=
0.855
mS
Gb-ED
=
855
uS
=
0.855
mS
we must recognize
that Baan’s ‘alpha’ correction i
= 855
uSBlood
=However,
0.855
mS
𝑆𝑆𝑆𝑆
𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
GGb-ED
conductance
(separated
b = measured
α = SV correction factor
=
(𝐺𝐺
)
dynamic
and
defined
by
the
following:
a non-linear
+
𝐺𝐺
𝑏𝑏
=
−𝑆𝑆𝑆𝑆
·
−32(0.855
+ 0.465)
=1
𝑆𝑆𝑆𝑆
𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸
Note: for the purpose
this document we will not use a hypertonic
saline
bolus
process
to calculate
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
from
parallel/muscle
conductance
usinggamma,
Gb-ES
== 465
uS
==conductance
0.465
mS
𝑉𝑉𝑉𝑉𝑉𝑉 = 𝜌𝜌𝜌𝜌2 (𝐺𝐺𝑥𝑥of−G.
)
measured throughout the cardiac cycle. There
Gb-ES
465
uS
0.465
mS
𝑝𝑝
Gb-ES
=
465
uS
=
0.465
mS
admittance
phase measurement)
= measured
TOTAL
conductance
𝛼𝛼 Vp to satisfy Baan’s equation.GxInstead
the average
we will
employ
the admittance
correction
process
two
processes
it is best∙ to
use a sample
data set a
𝑐𝑐
=
𝑆𝑆𝑆𝑆
·
𝐺𝐺
· 𝐺𝐺correction
32(0.855
0.465)
= 12.7224
𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸 conductance
=
parallel/muscle
conductance
Gp this we canGbetter
=
Baan’s
parallel/muscle
(assumed
reliant
on
phase
shift
measurement.
By
doing
compare
resulting
volume
p
For the purpose of this document we will not use
The saline
following
guideline shows
how
to compare the SV corre
toby
behypertonic
removed
by hypertonic
saline
injection)
(assumed to be removed
injection)
2
derived
each Baan’s
and
Wei’s
of each
unique SV
a measurements
hypertonic saline
bolusbyprocess
to calculate
theequations and 𝐺𝐺understand the effect
−𝑏𝑏
±√𝑏𝑏
−4𝑎𝑎𝑎𝑎
2
𝑏𝑏
𝐺𝐺
−𝑏𝑏 ±√𝑏𝑏
±√𝑏𝑏2 −4𝑎𝑎𝑎𝑎
−4𝑎𝑎𝑎𝑎
In
Wei’s
𝐺𝐺𝑏𝑏
�1
−
��can
,, 𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒
γγ == −𝑏𝑏
average
Gp factor.
to satisfy
Baan’s equation.
Instead
𝑏𝑏equation:
correction
Therefore,
after satisfying
Vpwe
by admittance
we
understand
Baan’s2𝑎𝑎
equation as:
�1
−
𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒
𝛾𝛾
�1
−
�
,
𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒
γ
=
𝛾𝛾
2𝑎𝑎
will employ the admittance correction process
𝛾𝛾
2𝑎𝑎baseline data2set
Step 1: Select
stable
−𝑏𝑏 ±√𝑏𝑏2 −4𝑎𝑎𝑎𝑎
42.24
±�−42.24 −4(22.5230 ∙ 12.7
reliant on phase shift measurement. By doing
γ
=

Note: for 1
the purpose of this document we will not use a hypertonic saline bolus process to calculate
2(22.5230)
this we can better2compare resulting volume
2𝑎𝑎
𝑉𝑉𝑉𝑉𝑉𝑉
= Vp
𝜌𝜌𝜌𝜌
(𝐺𝐺𝑏𝑏by
)Baan’s
the average
to satisfy
equation.
the
admittance
correction
process
2
2
measurements
derived
each Baan’s
and Instead
Wei’s we will 𝑎𝑎employ
)) 
2
2
=
𝑆𝑆𝑆𝑆
−
𝜌𝜌𝐿𝐿
−
𝐺𝐺
32
−
(1.2)(4.5)
2 (𝐺𝐺
𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸
2 (0.8
𝛼𝛼
(𝐺𝐺
𝑎𝑎
=
𝑆𝑆𝑆𝑆
−
𝜌𝜌𝐿𝐿
−
𝐺𝐺

32
−
(1.2)(4.5)
(0.8
(𝐺𝐺
)
𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸
𝑎𝑎
=
𝑆𝑆𝑆𝑆
−
𝜌𝜌𝐿𝐿
−
𝐺𝐺

32
−
(1.2)(4.5)
(0.8
𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸
equations
and
understand
the
effect
of
each
reliant on phase shift measurement. By doing this we can Note:
better compare
resulting
volume
Wei’s equation always uses the larger postive solu
unique SV correction factor. Therefore, after
measurements derived by each Baan’s and Wei’s equations
and
understand
the+
of)
each
unique SV +
𝐺𝐺
𝑏𝑏
= −𝑆𝑆𝑆𝑆
· (𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸
−32(0.855
)
+effect
𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏
−32(0.855
+ 0.465)
0.465) == -(𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸
satisfying Gp by admittance we can understand
𝑏𝑏 =
= −𝑆𝑆𝑆𝑆
−𝑆𝑆𝑆𝑆 ·· (𝐺𝐺
𝑏𝑏−𝐸𝐸𝐸𝐸 + 𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸 ) −32(0.855 + 0.465) = correction
factor.
Therefore,
after
satisfying
Vp
by
admittance
we
can
understand
Baan’s
equation
as:
Baan’s equation as:
𝑐𝑐𝑐𝑐 =
𝑆𝑆𝑆𝑆 ·· 𝐺𝐺
·· 𝐺𝐺
 32(0.855
32(0.855 ∙∙ 0.465)
0.465) == 12.7224
Wei’s Equation:
Where:
𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸

12.7224
𝑏𝑏−𝐸𝐸𝐸𝐸
𝑐𝑐 =
= 𝑆𝑆𝑆𝑆
𝑆𝑆𝑆𝑆 · 𝐺𝐺
𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸 · 𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸  32(0.855 ∙ 0.465) = 12.7224
1 2
ρ = blood resistivity
𝑉𝑉𝑉𝑉𝑉𝑉 = 𝜌𝜌𝜌𝜌 (𝐺𝐺𝑏𝑏 )
L = measuring electrodes
distance
However,
we must recognize that Baan’s ‘alpha’
𝛼𝛼
correction
is a constant, while Wei’s correction
conductance
Gb = measured BLOOD
2
2 −4(22.5230 ∙ 12.7
−𝑏𝑏
±√𝑏𝑏
2
42.24
±�−42.24
2
is
dynamic
and
defined
by
the
2 −4𝑎𝑎𝑎𝑎
−𝑏𝑏
±√𝑏𝑏
−4𝑎𝑎𝑎𝑎
2 −4(22.5230
42.24
±�−42.24
(calculated usingfactor
admittance
process,
involving
removal
of following:
−𝑏𝑏 ±√𝑏𝑏
−4𝑎𝑎𝑎𝑎
42.24
±�−42.24
−4(22.5230 ∙∙ 12.7
12.7
γ
=

γ
=

gamma,
a
non-linear
constant
and
G
,
the
unique
=
2(22.5230)
2𝑎𝑎
Wei’s Equation
b 2(22.5230)
parallel/muscle conductance 2𝑎𝑎
using
phase
measurement)
2(22.5230)
2𝑎𝑎 conductance measured throughout
value of blood
2 −4𝑎𝑎𝑎𝑎
−𝑏𝑏
±√𝑏𝑏
Wei’s Equation:
Where:
the cardiac cycle. Therefore, it is our opinion that
1
2
γ=
Note:
Wei’s
equation
always
uses
the
larger
postive
solu
𝑉𝑉𝑉𝑉𝑉𝑉 =
compare
these
two correction
processes
it is best
Note:
Wei’s
equation
always
the
postive
2𝑎𝑎 to
ρ = blood resistivity
𝐺𝐺𝑏𝑏 𝜌𝜌𝜌𝜌 (𝐺𝐺𝑏𝑏 )
Note:
Wei’s
equation
always uses
uses
the larger
larger
postive solu
solu
(1− )
to use a distance
sample data set and follow the process of
L = measuring electrodes
𝛾𝛾
where,
each equation.
= measured
BLOOD conductance
GA.bHenton
Transonic Scisense Technical Note
and F. Konecny
March,
2013
(calculated
using
admittance process, involving removal of
2 (𝐺𝐺
SV Correction Factors
𝑎𝑎 = 𝑆𝑆𝑆𝑆 − 𝜌𝜌𝜌𝜌
𝑏𝑏𝑏𝐸𝐸𝐸𝐸 − 𝐺𝐺𝑏𝑏𝑏𝐸𝐸𝐸𝐸 )
parallel/muscle
conductance
using phase measurement)
We can compare SV correction process between
Therefore, we can compare
SV correction
process
between Baan’s
and following:
Wei’s equations
by±√𝑏𝑏
the
following:
2 −4𝑎𝑎𝑎𝑎
𝑏𝑏 =−𝑏𝑏
−𝑆𝑆𝑆𝑆
· (𝐺𝐺
Baan’s
and Wei’s
by the
𝑏𝑏𝑏𝐸𝐸𝐸𝐸 + 𝐺𝐺𝑏𝑏𝑏𝐸𝐸𝐸𝐸 )
1 equations
2
γ=
𝑉𝑉𝑉𝑉𝑉𝑉
=
𝐺𝐺 𝜌𝜌𝜌𝜌 (𝐺𝐺𝑏𝑏 )
𝐺𝐺𝑏𝑏 𝑐𝑐 = 𝑆𝑆𝑆𝑆 · 𝐺𝐺2𝑎𝑎
𝑆𝑆𝑆𝑆
𝑏𝑏𝑏𝐸𝐸𝐸𝐸 · 𝐺𝐺𝑏𝑏𝑏𝐸𝐸𝐸𝐸
(1− )𝑏𝑏 ) VS
( 𝑆𝑆𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
𝛾𝛾
𝛾𝛾
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
where,
(1 −
)
However, we must recognize that Baan’s ‘alpha’ correction is a constant, while Wei’s correction factor
is
𝑎𝑎 = 𝑆𝑆𝑆𝑆 − 𝜌𝜌𝜌𝜌2 (𝐺𝐺𝑏𝑏𝑏𝐸𝐸𝐸𝐸 − 𝐺𝐺𝑏𝑏𝑏𝐸𝐸𝐸𝐸 )
dynamic and defined by the following: gamma, a non-linear constant, and Gb, the unique value of blood
onductance measured throughout the cardiac cycle. Therefore, it is our opinion that to compare these
𝑏𝑏 = −𝑆𝑆𝑆𝑆 · (𝐺𝐺𝑏𝑏𝑏𝐸𝐸𝐸𝐸 + 𝐺𝐺𝑏𝑏𝑏𝐸𝐸𝐸𝐸 )
wo correction processes it is best to use a sample data set and follow the process of each equation.
RPV-1-tn Rev. A 6/13
= 𝑆𝑆𝑆𝑆 · 𝐺𝐺software.
The following guideline shows how to compare the SV correction processes using𝑐𝑐LabScribe2
𝑏𝑏𝑏𝐸𝐸𝐸𝐸 · 𝐺𝐺𝑏𝑏𝑏𝐸𝐸𝐸𝐸
Pressure-Volume
Wei’s Equation Gamma Correction Factor Cont.
The following guideline shows how to compare the SV correction processes using LabScribe2 software.
First select a stable baseline data set to provide the values for the equation comparison. Using the “Function”
tool, create a new channel for “Blood Conductance”
After selecting “Blood Conductance” a dialog box will appear (pictured below). Complete the “Settings” for
Magnitude, Phase, Species and Sigma/Epsilon, also referred to as ‘Heart Type’ in current ADV500/ADVantage
5.0 systems. In this file, the standard for healthy tissue was used (S/E = 800,000 units)
Pressure-Volume
Wei’s Equation Gamma Correction Factor Cont.
Using the “Function” tool on the Pressure Channel, create a new calculated channel for dP/dt.
In the “Analysis View”, use the vertical cursors to highlight maximum and minimum dP/dt points to determine
corresponding measurements Gb-ED and Gb-ES, respectively. Now that we have measured both Gb-ED and Gb-ES,
we can satisfy both SV correction formulas
(also using the common measurements for
electrode distance (L), blood resistivity (ρ),
and SVreference).
units
out):
ρ = cancel
1.2 Ohm·m
Pressure-Volume
L =SV
4.5
mm
reference = 32uL (as derived from hi-resolution echocardiography)
Transonic Scisense Technical Note
Transonic Scisense Technical Note
ρ =Gb-ED
1.2 Ohm·m
= 855 uS = 0.855 mS
SVGb-ES
32uLuS(as
derived
reference==465
= 0.465
mSfrom hi-resolution echocardiography)
A. Henton and F. Konecny
2013
A. Henton andMarch,
F. Konecny
March, 2013
Wei’s= 855
SV uS
Correction:
Gb-ED
= 0.855 mS
Wei’s SV Correction:
Wei’s
Equation
Gamma
Correction
Cont.
To demonstrate
the calculations
for Wei’s SV correction
factor, we will Factor
use two sample
points in the
Gb-ES
= 465 uS = 0.465
mS
2 is required
To
demonstrate
the calculations
for Wei’s
SVascorrection
we will
use twopoints).
sample This
points
in the as
cardiac
cycle (End-Systole
and(𝐺𝐺End-Diastole
determined
by(0.855−0.465)(1.2)(4.5)
dP/dt
inflection
𝑆𝑆𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
−𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸
)𝜌𝜌𝐿𝐿2 factor,
𝑏𝑏−𝐸𝐸𝐸𝐸
(
)

(
)

=
cardiac
(End-Systole
and End-Diastole
asunique
determined
dP/dt
required as
Wei’s𝑆𝑆𝑆𝑆
SVcycle
correction
is dynamic
and
to anybystage
ofinflection
the cardiac
cycle. This
The is
same
𝑆𝑆𝑆𝑆therefore
32 points).
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
Baan’s
SV
Correction
Wei’s
SV correction
dynamic
therefore will
unique
to any stage of the cardiac cycle. The same
variables
used aboveis in
Baan’s and
SV correction
apply:
0.2962
Transonic Scisense Technical
Note
2
2
variables
used above in Baan’s
SV correction
𝑆𝑆𝑆𝑆𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐
(𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸
−𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸will
)𝜌𝜌𝐿𝐿apply: (0.855−0.465)(1.2)(4.5)
Transonic
Scisense
Technical
Note
L
=
4.5
mm
0.2962
(
)(
)
=
𝑆𝑆𝑆𝑆
𝑆𝑆𝑆𝑆
32
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
L = 4.5 mm
ρ = 1.2 Ohm·m
0.2962
Referring
to Baan’s complete equation, the SV correction factor
Datafactor
Point 1 (End-Diastole):
VALUES
OF VARIABLES
ρ
= 1.2 Ohm·m
as follows:
isReferring
expressedto
asBaan’s
follows:complete equation, the SV correction
Data Pointis1expressed
(End-Diastole):
SVreference = 32uL
(as derived from hi-resolution echocardiography)
L = 4.5 mm
SV
=
32uL
(as
derived
from
hi-resolution
echocardiography)
Remembering
that
Wei’s SV correction factor is dynamic an
reference
1
1
= 1.2 Ohm·m
Remembering thatρ Wei’s
SV correction factor is dynamic an
Gb-ED
0.855
mS
3.376
= 855 uS = =
3.376
measurement
of
blood
conductance
(Gderived
b) during the cardiac
𝛼𝛼
0.2962
SV
= 32μL (as(G
from
Gb-ED = 855
uS = 0.855
mS
reference
Referring
to Baan’s
complete
equation, the SV correctionmeasurement
factor is expressed
as follows:
of blood
conductance
b) during the cardiac
specific
SV
correction
at
any
one
point
in
the
cardiac
cycle.
hi-resolution
echocardiography)
Gb-ES = 465 uS = 0.465 mS
specific
SV
correction
at any
one
point in the cardiac cycle.
Therefore,
every
measured
value
of
blood
conductance
during
the
cardiac
cycle
will
be
that would occur at
ED: = 855 μS = 0.855 mS
1Gb-ES = 465
1 uS = 0.465 mS
Gb-ED
Wei’s
 SV Correction
3.376
multiplied
by =
+3.376.
that would occur at ED:
Gb-ES = 465 μS = 0.465 mS
𝐺𝐺𝑏𝑏
0.855
To demonstrate the calculations
Wei’s SV correction factor,
−𝑏𝑏 ±√𝑏𝑏2for
−4𝑎𝑎𝑎𝑎
�

�1
−
= 0.4294
�1 − we
𝐺𝐺𝑏𝑏
𝐺𝐺
0.855 �Units
Note:
must be used as
𝑏𝑏
𝛾𝛾 �  �1 − 1.4984
will
use two
sample
points
invalue
the
cardiac
cycle
(End-Systoleduring
and
End�1 −
�
,
𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒
γ
=
�1
−
�
=tobe
0.4294
2
Therefore,
every
measured
of
blood
conductance
the
cardiac
cycle
will
−𝑏𝑏
±√𝑏𝑏
−4𝑎𝑎𝑎𝑎
𝛾𝛾𝑏𝑏
provided
properly cancel out.
1.4984
𝛾𝛾
𝐺𝐺
2𝑎𝑎
Diastole
determined
�1 − 𝛾𝛾 �as,by
𝑤𝑤ℎ𝑒𝑒𝑒𝑒𝑒𝑒
γ = by dP/dt inflection points). This is required as
multiplied
+3.376.
Referring
Wei’s SV correction is dynamic2𝑎𝑎
and therefore unique to any
stage ofto Wei’s complete equation, the SV correction fac
Referring to Wei’s complete equation, the SV correction fac
the cardiac cycle.
1 − 0.465)1= 22.5230
𝑎𝑎 = 𝑆𝑆𝑆𝑆 − 𝜌𝜌𝐿𝐿2 (𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸 − 𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸 )  32 − (1.2)(4.5)2 (0.855
1𝐺𝐺 
1 = 2.329
𝑎𝑎 = 𝑆𝑆𝑆𝑆 − 𝜌𝜌𝐿𝐿2 (𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸 − 𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸 )  32 − (1.2)(4.5)2 (0.855
= 22.5230
 0.4294
= 2.329
� 0.465)
�1− 𝐺𝐺𝛾𝛾𝑏𝑏𝑏𝑏−
0.4294 A. Henton and F. Konecny
Transonic
Scisense
Technical
Note + 0.465) = �- 1−
�
(𝐺𝐺
)
+
𝐺𝐺
𝑏𝑏
=
−𝑆𝑆𝑆𝑆
·
−32(0.855
42.2400
𝑏𝑏−𝐸𝐸𝐸𝐸
𝑏𝑏−𝐸𝐸𝐸𝐸
𝛾𝛾
Transonic Scisense Technical Note
A. Henton and F. Konecny
2013
𝑏𝑏 = −𝑆𝑆𝑆𝑆 · (𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸 + 𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸 ) −32(0.855 + 0.465) = Therefore,
- 42.2400 the specific value ofMarch,
March,
blood2013
conductance at end-d
𝛼𝛼
0.2962
𝑐𝑐 = 𝑆𝑆𝑆𝑆 · 𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸 · 𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸  32(0.855 ∙ 0.465) = 12.7224Therefore, the specific value of blood conductance at end-d
by +2.329 to correct for the inherent SV underestimation at
𝑐𝑐 = 𝑆𝑆𝑆𝑆 · 𝐺𝐺
· 𝐺𝐺𝑏𝑏−𝐸𝐸𝐸𝐸  32(0.855 ∙ 0.465) = 12.7224
by +2.329 to correct for the inherent SV underestimation a
Data Point𝑏𝑏−𝐸𝐸𝐸𝐸
1 (End-Diastole):
cycle.
Data Point 1 (End-Diastole):
cycle.
Note: Wei’s equation
Remembering
that
Wei’s
SV
correction
factor
is
dynamic
and therefore unique to anyalways uses the larger
2
2 −4(22.5230 ∙ 12.7224)
−𝑏𝑏
±√𝑏𝑏
−4𝑎𝑎𝑎𝑎
42.24
±�−42.24
Remembering that Wei’s SV correction factor is dynamic and therefore unique to any
andand
0.3770
γ = −𝑏𝑏 ±√𝑏𝑏2 −4𝑎𝑎𝑎𝑎
 conductance
= 1.4984
1.4984
0.3770
measurement
blood
(G
during the ∙cardiac
must
calculate
the
positive
solution for
b2)−4(22.5230
42.24 ±�−42.24
12.7224)
Datacycle,
Point we
2 (End-Systole):
2(22.5230)
2𝑎𝑎 of
measurement
of
blood
conductance
(G
)
during
the
cardiac
cycle,
we
must
calculate
the
b
γspecific
=

=
1.4984
and
0.3770
gamma
(1.4984).
DataBelow
Pointis2 the
(End-Systole):
SV correction at any one point2(22.5230)
in the cardiac cycle.
specific SV correction
specific SV2𝑎𝑎
correction at any one point in the cardiac cycle. Below is the specific SV correction
Following
same principle, below is the specific SV correc
END-DIASTOLE
END-SYSTOLE
that
would
at ED:always uses the larger postive solution
Note:
Wei’soccur
equation
for γthe
(1.4984)
Following
the
same principle, below is the specific SV corre
that would occur at ED:
Note: Wei’s equation always uses the larger postive solution𝐺𝐺for γ (1.4984)
0.465
𝐺𝐺
0.855
�1 − 𝐺𝐺𝛾𝛾𝑏𝑏𝑏𝑏�  �1 − 1.4984
�1 − 𝐺𝐺𝛾𝛾𝑏𝑏𝑏𝑏�  �1 − 1.4984
0.465 � = 0.6897
0.855 � = 0.4294
�1 − 𝛾𝛾 �  �1 − 1.4984� = 0.6897
� = 0.4294
�1 − �  �1 −
𝛾𝛾
1.4984
Referring
to
Wei’scomplete
complete
equation,the
the SV correction fac
Referring
the
Wei’s
equation,
Referringto
toWei’s
Wei’scomplete
completeequation,
equation,
the SV correctionReferring
factor isto
expressed
as follows:
Referring
to Wei’s
equation,
the SV correction fac
Referring
to Wei’s
equation,
the SV correction
factor
is expressed
follows:
SV
correction
factorcomplete
is expressed
as follows:
SV
correction
factor complete
isas
expressed
as follows:
1
1
1
1
1𝐺𝐺𝑏𝑏 
1𝐺𝐺  1 = 2.329
1 = 1.450
2.329
1.450
= 2.329
�1− 𝐺𝐺𝛾𝛾𝑏𝑏�  0.6897 = 1.450
�1− 𝐺𝐺𝛾𝛾𝑏𝑏𝑏𝑏�  0.4294
0.6897
0.4294
�1− �
�1− �
𝛾𝛾
𝛾𝛾
Therefore, the
specificwill
measurement
of blood conductance
Therefore, the specific value of blood conductance at end-diastole
(0.855mS)
be multiplied
Therefore,
the
specific
measurement
of blood conductance
Therefore,
the
specific
value
of
blood
conductance
at
end-diastole
(0.855mS)
will
be
multiplied
As
from
finalfor
SV the
correction
factor
values Wei’s equation
multiplied
by +1.450.
by seen
+2.329
to the
correct
inherent
SV underestimation
at that specific
point of the cardiac
multiplied
by +1.450.
by +2.329variable
to correct
for(2.329
the inherent
SV underestimation
at that specific
point of the cardiac
produces
values
and 1.450)
depending on the
cycle.point in the cardiac cycle as compared with Baan’s equation
time
cycle.
which produces a single (and larger) value (3.376).
Data Point 2 (End-Systole):
Data Point 2 (End-Systole):
Pressure-Volume
The graph at right shows the resulting
volume calculations by Baan’s and Wei’s
equation vs. pressure for our sample
data set. As we can see, when a common
method of removing parallel/muscle
conductance is used (in this case the phase
measurement and admittance process), we
can isolate the effect of the SV correction
method unique to each equation.
Baan’s equation uses a linear correction
factor, alpha, to force the SV measurement
to fit a reference SV measurement.
Therefore, it does not account for the
dynamic electrical field properties and
resulting variable SV correction. Ultimately,
this leads to an over-estimation of true
volume (green PV loop).
In comparison, Wei’s equation uses a
dynamic correction factor defined by
gamma and the real-time measurement
of Gb. Gamma is a quadratic defined
by the SV reference, blood resistivity,
measurement field size, and specific
measurement of Gb-ED and Gb-ES unique
to the data set of interest. Ultimately this
process derives a much more accurate SV
correction throughout the cardiac cycle
as it takes into account dynamic electrical
properties. SV correction is therefore
smaller at end-systole and a gradually
increases as Gb approaches a maximum at
end-diastole. A more accurate derivation
of volume is shown using this correction
process (blue PV loops).
Pressue (mmHg)
Comparison of Baan’s & Wei’s Final Calculated Volumes
Volume (μL)
Wei’s equation produces the blue PV loops while Baan’s equation
produces the green PV loops with a larger volume.
Transonic Systems Inc. is a global manufacturer of innovative biomedical measurement
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