Measuring and testing – Volume or rate of flow – By measuring transit time of tracer or tag
Reexamination Certificate
2001-01-30
2004-01-06
Lefkowitz, Edward (Department: 2855)
Measuring and testing
Volume or rate of flow
By measuring transit time of tracer or tag
C073S861950
Reexamination Certificate
active
06672172
ABSTRACT:
BACKGROUND OF THE INVENTION
Devices and methods of flow measurements are disclosed in U.S. Ser. Nos. 09/073,061, 09/117,416, all assigned to Radi Medical Systems AB, Sweden.
In particular Ser. No. 09/073,061 relates to a method of flow measurements by thermo-dilution, wherein the time measurements are triggered by a pressure pulse detected as a result of the injection of a bolus dose of saline. The general theory described therein fully applies to the present invention, and therefore the entire disclosure thereof is incorporated herein.
Nevertheless, the discussion therein is repeated below for ease of understanding.
Application of the thermodilution principle in the coronary sinus was introduced by Ganz (Ganz et al, ”Measurement of coronary sinus blood flow by continuous thermodilution in man,
Circulation
44:181-195, 1971). A small catheter is introduced deeply into the coronary sinus and cold saline is delivered at its tip. Theoretically, flow can be calculated from the changes in blood temperature, registered by a thermistor close to the outlet of the coronary sinus. An advantage of this method is that only right heart catheterization is required.
The principle of thermo-dilution involves injecting a known amount of cooled liquid, e.g. physiological saline in a blood vessel. After injection the temperature is continuously recorded with a temperature sensor attached to the tip of a guide wire that is inserted in the vessel. A temperature change due to the cold liquid passing the measurement site, i.e. the location of the sensor, will be a function of the flow.
There are various methods of evaluating the temperature signal for diagnostic purposes. Either one may attempt to calculate the volume flow, or one may use a relative measure, where the flow in a “rest condition” is compared with a “work condition”, induced by medicaments.
The latter is the simpler way, and may be carried out by measuring the width at half height of the temperature change profile in the two situations indicated, and forming a ratio between these quantities.
Another way of obtaining a ratio would be to measure the transit time from injection and until the cold liquid passes the sensor, in rest condition and in work condition respectively.
The former method, i.e. the utilization of the volume flow parameter as such, requires integration of the temperature profile over time in accordance with the equations given below
(
1
)
Q
r
e
s
t
=
V
/
∫
t
1
t
0
(
T
r
,
m
/
T
r
,
l
)
ⅆ
t
∝
V
/
∫
t
1
t
0
(
T
r
,
0
-
T
r
,
m
)
ⅆ
t
(
3.1
)
(
2
)
Q
w
o
r
k
=
V
/
∫
t
1
t
0
(
T
w
,
m
/
T
w
,
l
)
ⅆ
t
∝
V
/
∫
t
1
t
0
(
T
w
,
0
-
T
w
,
m
)
ⅆ
t
(
3.2
)
wherein
V is the volume of injected liquid
T
r,m
is the measured temperature at rest condition
T
r,1
is the temperature of injected liquid at rest condition
T
0
is the temperature of the blood, i.e. 37° C.
T
w,m
is the measured temperature at work condition
T
w,1
is the temperature of injected liquid at work condition
Q is the volume flow
These quantities may then be used directly for assessment of the condition of the coronary vessels and the myocardium of the patient, or they may be ratioed as previously discussed to obtain a CFR, i.e. CFR=Q
work
/Q
rest
.
The latter method, i.e. determination of the transit time requires an accurate time measurement, in view of the relatively small distances in question, about 10 cm or less from injection to measurement site.
To obtain a correct measurement, the time has to be measured with some accuracy. Using a simple stop watch, which is a common means of timing, is far too inaccurate for obtaining reliable transit times.
The flow F may be obtained as follows, which is a derivation for a similar technique, namely the indicator dilution technique. This is based on a rapidly injected amount of some kind of indicator, the concentration of which is measured.
Suppose that the flow through a branching vascular bed is constant and equals F, and that a certain well-known amount M of indicator is injected into this bed at site A (see FIG.
7
). After some time, the first particles of indicator will arrive at the measuring site B. The concentration of indicator at B, called c(t), will increase for some time, reach a peak and decrease again. The graphic representation of indicator concentration as a function of time is called the indicator dilution curve.
Consider M as a large number of indicator particles (or molecules). The number of particles passing at B during the time interval &Dgr;t, between t
i
and t
i+1
, equals the number of particles per unit time multiplied by the length of the time interval, in other words: c(t
i
)·F·&Dgr;t (FIG.
8
).
Because all particles pass at B between t=0 and t=∞, this means that:
M
=
lim
Δ
t
→
0
∑
i
=
0
∞
(
c
(
t
i
)
·
F
·
Δ
t
)
or
M
=
∫
∞
0
c
(
t
)
·
F
·
ⅆ
t
or
F
=
M
∫
∞
0
c
(
t
)
·
ⅆ
t
(
3.3
)
and it is the last expression which is used in most methods to calculate systemic flow as outlined above. Essential features of this approach is that the amount M of injected indicator should be known whereas no knowledge about the volume of the vascular compartment is needed.
The calculation of volume is more complex. For this purpose, the function h(t) is introduced which is the fraction of indicator, passing per unit of time at a measurement site at time t. In other words, h(t) is the distribution function of transit times of the indicator particles. If it is assumed that the flow of the indicator is representative for flow of the total fluid (complete mixing), h(t) is also the distribution function of transit times of all fluid particles. Suppose the total volume of fluid is made up of a very large number of volume elements dV
i
which are defined in such a way that dV
i
contains all fluid particles present in the system at t=0, with transit times between t
i
and t
i+1
. The fraction of fluid particles requiring times between t
i
and t
i+1
to pass the measurement site, is h(t
i
)·&Dgr;t by definition. Because the rate at which the fluid particles pass at the measurement site, equals F, the rate at which the particles making up dV
i
pass at the measurement site is F·h(t
i
)·&Dgr;t. The total volume of dV
i
equals the time t
i
required for all particles segments in dV
i
to pass at the measurement site multiplied by the rate at which they leave. In other words:
dV
i
=t
i
·F·h
(
t
i
)·&Dgr;
t
(3.4)
and by integration:
V
=
F
∫
∞
0
t
·
h
(
t
)
ⅆ
t
(
3.5
)
The integral in the equation above represents the mean transit time T
mn
, which is the average time needed by one particle to travel from an injection site to a measurement site. Therefore:
V=F·T
mn
(3.6)
or:
F=V/T
mn
; T
mn
=V/F
(3.7)
which states the fundamental fact that flow equals volume divided by mean transit time.
The mean transit time (T
mn
) can now be calculated easily from the indicator or thermo dilution curve in the following way. When looking at the hatched rectangle in
FIG. 8
, it can be seen that the number of indicator particles passing between t
i
and t
i+1
, equals the number of
Smith Leif
Tulkki Sauli
Foley & Lardner
Lefkowitz Edward
Mack Corey D.
Radi Medical Systems AB
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