Method of calibrating a radiological system and of measuring the equivalent thickness of an object

The calibration method consists in measuring the efficiency D of a detector cell placed behind the object as a function of various phantom thicknesses E.sub.p and various X-ray tube supply voltages V.sub.m. These measurements enable an analytic model D=f(V.sub.m, E.sub.p) to be determined describing the resulting curves. The inverse function of this analytic model can be used for calculating thickness E.sub.p as a function of the measured efficiency D and the known supply voltage V.sub.m.

FIELD OF THE INVENTION 
This invention relates to radiological systems for examining objects, and 
more particularly, in such systems, the invention relates to a method of 
calibrating a radiological system and of measuring the equivalent 
thickness of an object to be examined. 
BACKGROUND OF THE INVENTION 
A radiological system essentially comprises an X-ray tube and a detector of 
such rays with an object to be examined such as the portion of the body of 
the patient being interposed therebetween. The detector (which may be 
constituted by a film-screen pair, for example), provides an image of the 
object after being exposed for an appropriate length of time and after the 
film has been developed. The quality of the image depends both on the 
characteristics of the object and on the parameters of the radiological 
system. 
The radiological properties of an object are given by its thickness and by 
its composition, and these properties vary firstly from one patient to 
another and secondly from one part of the body to another. It is difficult 
to determine these characteristics accurately: in particular, it is 
difficult or even impossible to determine the composition of an object 
merely by means of a physical examination. The notion of equivalent 
thickness, as known in radiology, serves to reduce knowledge about these 
two variables to a problem in one dimension. 
The equivalent thickness of an object is defined relative to a reference 
substance such as plexiglass or a substance simulating the absorption of 
an organ of given composition. Under accurate radiological conditions, 
i.e. with fixed configuration and exposure parameters, the equivalent 
thickness of an object placed in the radiation field is represented by the 
thickness of the reference substance that would provide the same quantity 
of energy at the detector, i.e. the same optical density when the detector 
is a film. 
A doctor can make use of knowledge about the equivalent thickness of an 
object, for example, as a medical indication or for establishing 
statistics about patients. 
The equivalent thickness of an object also depends on parameters of the 
radiological system. These parameters are generally classified in two 
categories: 
"radiological" parameters such as the voltage V of the X-ray tube, the 
current I taken by the tube, the exposure time S, and the product 
I.times.S which defines the quantity of energy emitted; and 
"configuration" parameters which are all of the parameters other than the 
radiological parameters that have an effect on the quality of the incident 
radiation on the detector, and not including the object. 
For example, these configuration parameters may be: 
a) the selected track of the rotary anode in the X-ray tube; 
b) the selected size of the focus in the X-ray tube; 
c) the selected filter interposed on the path of the beam of X-rays; 
d) the selected magnification; 
e) the selected distance between the focus and the image receiver; 
f) the selected image receiver; and 
g) the selected types of accessory present in the beam of X-rays, e.g. a 
compression pad, an anti-diffusion screen, etc. 
SUMMARY OF THE INVENTION 
An object of the present invention is to implement a method of calibrating 
a radiological system making it possible to determine the relationships 
between the radiological parameters of the system, the object to be 
X-rayed, and a magnitude characteristic of the radiation spectrum that has 
passed through the object. 
Another object of the invention is to implement a method of measuring the 
equivalent thickness of an object. 
The invention provides a method of calibrating a radiological system 
designed to examine an object, the system comprising: an X-ray tube whose 
supply voltage V can take up various different values V.sub.m, varying 
either continuously or discretely, the tube emitting a beam of X-rays in 
the form of bursts of variable duration S; and a detector cell for 
detecting X-rays that have passed through the object to be examined and 
serving to convert a physical magnitude characteristic of the beam of 
X-rays into a measurement signal M such as an electrical signal; the 
method being characterized in that it comprises the following operations: 
(a) selecting a physical magnitude A characteristic of the object to be 
observed; 
(b) choosing a class of reference objects comprising n objects or phantoms 
for which the physical magnitude takes up n known values; 
(c) selecting j values V.sub.m of the supply voltage for the X-ray tube at 
which calibration is to be performed; 
(d) selecting the value of the product I.times.S of the anode current taken 
by the X-ray tube during the exposure time S for each phantom associated 
with each value of the supply voltage V.sub.m ; 
(e) installing a phantom on the path of the X-rays, adjusting the supply 
voltage to a value V.sub.m, and integrating the radiation that passes 
through the phantom as detected by the detector cell between the beginning 
of measurement and the instant at which the product I.times.S is equal to 
the value selected in operation (d), thereby obtaining a measurement M; 
(f) calculating the efficiency D as given by the ratio M/I.times.S; 
(g) reiterating operations (e) and (f) for the same phantom but for the 
(j-1) other values of the supply voltage V.sub.m ; 
(h) reiterating operations (e), (f), and (g) for the (n-1) other phantoms; 
(i) using a conventional estimation method to determine the analytic model 
D=f(V.sub.m,A) relating the values of efficiency D to the values of the 
physical magnitude A and of the voltage V.sub.m ; and 
(j) determining the inverse function of f(V.sub.m,A), written g(V.sub.m,D) 
enabling A to be determined given V.sub.m and D. 
The operations (d) and (e) may be replaced by the following operations: 
(d') selecting the exposure time S for each phantom associated with each 
value of the voltage V.sub.m ; and 
(e') placing a phantom on the path of the X-ray, adjusting the supply 
voltage to a value V.sub.m, measuring the product I.times.S of the anode 
current taken by the X-ray tube for the exposure time S, and integrating 
the radiation that passes through the phantom as detected by the detector 
cell during the exposure time S as selected during operation (d'), thereby 
obtaining a measurement M. 
When the radiological system has several possible configuration parameters, 
the method includes an additional operation consisting in: 
(k) reiterating operations (e) or (e') to (j) for each value of the 
configuration parameters. 
When the configuration parameters can be grouped into classes, the various 
operations (e) or (e') to (j) are performed for a reference configuration 
of each class (C), and for each element of the class (C) a weighting 
coefficient is determined relative to the reference configuration by 
measuring the efficiency D at a voltage V.sub.m and for a given value of 
the physical magnitude A, and by defining the weighting coefficient of the 
configuration as the ratio between said measured efficiency D and the 
efficiency measured under analogous conditions using the reference 
configuration. In order to improve the accuracy of this coefficient, the 
value used may be the result of averaging efficiency ratios as defined 
above and as measured under various radiological conditions. 
In numerous radiological systems, the physical magnitude A will be the 
thickness of the phantom along the path of the X-rays. The calibration 
method of the invention can thus be used to determine the thickness 
E.sub.p of a phantom if V.sub.m and D are known. Thus, if the same values 
of V.sub.m and D are obtained for an object put in the place of the 
phantom, it will be deduced that the equivalent thickness of the object 
relative to the phantom is E.sub.p. Use can be made of this value by 
communicating it to the operator via an appropriate display device or by 
recording it for subsequent use. The above-described calibration method 
can thus be used for measuring the equivalent thickness of an object by 
means of a radiological system.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
A radiological system to which the calibration method of the invention 
applies comprises at least one X-ray source 11 and an X-ray detector cell 
12 disposed downstream from an object 13 in the propagation direction of 
the X-rays, as represented in FIG. 1 by a beam 14 of X-rays. 
The source 11 is associated with a power supply 15 which provides a 
variable high supply voltage V.sub.m for a variable length of time S 
referred to as the exposure time. During an exposure, the X-ray tube of 
the source 11 has an anode current I flowing therethrough. The detector 
cell 12 serves to convert a physical magnitude characteristic of the X-ray 
beam 14 such as its kerma or its energy fluance, into a measurement signal 
L, e.g. an electrical signal. The electrical signal L provided by the 
detector cell 12 is applied to a circuit 16 which integrates the 
electrical signal throughout the exposure time S. The result of the 
integration is a signal M which is a measurement of the radiation that has 
passed through the object 13 during the exposure time. 
The radiological system outlined briefly above does not make an image of 
the object. In order to make an image, a receiver 17 such as a sensitive 
film should be added, with the film being placed between the object 13 and 
the detector cell 12, or else downstream therefrom. In a third embodiment 
of the radiological system, the detector cell 12 may be incorporated in 
the receiver 17. The calibration method consists firstly in selecting a 
class of reference objects or phantoms and in performing radiation 
measurements, also called operating measurements, for each phantom and for 
various different values V.sub.m of the voltage supplied to the X-ray 
source 11. Within the class of reference objects, the variable may be, for 
example, the thickness E.sub.p of the phantom extending perpendicularly to 
the X radiation. This thickness E.sub.p constitutes the physical magnitude 
A which characterizes the object to be observed. The radiation measurement 
used is efficiency D which is defined as being the ratio between the value 
M provided by the circuit 16 and the product I.times.S. By choosing such a 
ratio to define the efficiency D, efficiency is independent of exposure 
time S and of various different values of tube current. 
The efficiency D is calculated by means 18 which receive the signal M from 
the circuit 16 and which also receive information concerning the product 
I.times.S from the power supply 15. 
Of course, if the current I is not constant throughout the exposure time, 
then the product I.times.S should be replaced by the integral of the anode 
current taken over the exposure time. 
Similarly, the efficiency D could be measured over a fraction of the 
exposure time providing the signal M is obtained by integrating the signal 
L over the same integration period as is used for the anode current I. 
Thus, once the set of phantoms has been determined, the calibration method 
consists in measuring the efficiency for each phantom at specified supply 
voltages V.sub.m. 
More precisely, using a first phantom of thickness E.sub.1, the efficiency 
D.sub.1m is measured for each value V.sub.m of the supply voltage, with 
the different values V.sub.m constituting a determined set. These values 
of D.sub.1m as a function of voltage V.sub.m may be plotted on a graph in 
order to obtain points 21' in FIG. 2. 
The efficiency D is measured using a different phantom of thickness 
E.sub.2, thereby obtaining values D.sub.2m corresponding to points 22' in 
FIG. 2, and so on, thereby obtaining other series of points 23, 24, and 
25' corresponding respectively to efficiencies D.sub.3m, D.sub.4m, and 
D.sub.5m, and to thicknesses E.sub.3, E.sub.4, and E.sub.5. 
It should be observed that in FIG. 2, the efficiencies D.sub.pm are plotted 
up the Y axis using a logarithmic scale whereas the supply voltages are 
plotted along the X axis using a linear scale from 20 kilovolts to 44 
kilovolts. These series of points 21' to 25' are used to define the 
parameters of an analytic model which describes the behavior of the 
efficiency D as a function of the parameters V.sub.m and E.sub.p for a 
given configuration of the radiological system. This analytic model is 
written: 
EQU D=f(V.sub.m, E.sub.p) (1) 
The parameters of the analytic model may be adjusted using conventional 
estimation tools such as the least squares method. 
The curves 21 to 25 represent the values of the efficiency D given by the 
analytic model represented by the equation: 
EQU D=f(V.sub.m, E.sub.p)=exp[f.sub.1 (V.sub.m)+E.sub.p .times.f.sub.2 
(V.sub.m)] (2) 
in which f.sub.1 (V.sub.m) and f.sub.2 (V.sub.m) are second degree 
polynomials which can be written as follows: 
EQU f.sub.1 (V.sub.m)=A.sub.0 +A.sub.1 V.sub.m +A.sub.2 V.sub.m.sup.2 
EQU f.sub.2 (V.sub.m)=B.sub.0 +B.sub.1 V.sub.m +B.sub.2 V.sub.m.sup.2 
The inverse of the function expressed by equation (2) can be used for 
calculating E.sub.p if D and V.sub.m are known, by using the following 
equation (3): 
##EQU1## 
given that f.sub.2 (V.sub.m) cannot be zero for common values of V.sub.m 
since the efficiency D always depends on the thickness E.sub.p at the 
voltage V.sub.m under consideration. 
In other words, for each pair of values (E.sub.p, V.sub.m) there is a 
corresponding efficiency measurement D, thereby enabling E.sub.p to be 
determined as a function of V.sub.m and D. During radiological 
examination, a measured efficiency D performed with a given supply voltage 
V.sub.m can be used to determine an equivalent thickness expressed in the 
units used for E.sub.p. 
A preferred application consists in mammographic examinations, given the 
small variation in the composition of mammary tissue. 
To sum up, the method of calibrating a radiologic system consists in 
performing the following operations: 
(a) selecting a physical magnitude A which characterizes the object to be 
observed, e.g. the thickness E.sub.p of the object; 
(b) selecting n reference objects or phantoms for which the magnitude A 
(thickness E.sub.p) differs from one phantom to the next; 
(c) selecting j values V.sub.m of the supply voltage (circuit 15) applied 
to the X-ray tube for calibration purposes; 
(d) selecting the value of the product I.times.S of the current I taken by 
the X-ray tube during the exposure time S for each phantom associated with 
each voltage value V.sub.m ; 
(e) installing a phantom, adjusting the voltage to a value V.sub.m, and 
measuring M (circuit 16) when the product I.times.S is equal to the value 
selected during operation (d); and 
(f) calculating the efficiency D=M/I.times.S in the means 18, thereby 
giving one of the points on one of the curves in FIG. 2. 
The efficiency D is calculated for each of the j values of the supply 
voltage V.sub.m without moving the phantom, i.e., by: 
(g) reiterating operations (e) and (f) for the same phantom but using (j-1) 
other values of the supply voltage V.sub.m. 
A set of points is thus obtained, such as that represented by the points 
21' in FIG. 2, for example. In order to obtain a complete array of points 
(22' to 25') as shown in FIG. 2, it is necessary to: 
(h) reiterate operations (e), (f), and (g) for the (n-1) other phantoms. 
In practice, the n values of A (thickness E.sub.p), the j values of the 
supply voltage V.sub.m, and the (n.times.j) values of D are delivered to a 
microprocessor 19 which, by means of suitable software, performs the 
following operation: 
(i) using a conventional estimation method to determine the analytic model 
D=f(V.sub.m, A) relating the values of the efficiency D to the values of 
the physical magnitude A (thickness E.sub.p) and of the voltage V.sub.m. 
Finally, the microprocessor 19 calculates the inverse function of 
f(V.sub.m,A) that enables A (thickness E.sub.p) to be determined as a 
function of V.sub.m and D. This function is written g(V.sub.m, D). 
In a variant of the calibration method, the operation (d) may be replaced 
by an operation (d') which consists in selecting an exposure time S for 
each phantom associated with each value of the voltage V.sub.m. In this 
case, the operation (e) is modified to measure M and the product I.times.S 
during the exposure time S selected during operation (d'). 
In the calibration method described above, it has been assumed that only 
the thickness of the phantom and the radiological parameters of the system 
are changed, with the other or "configuration" parameters such as a filter 
remaining identical. It will therefore be understood that the calibration 
method must be repeated after changing a single configuration parameter, 
e.g. the filter. This may give rise to a different analytic model 
providing a different formulation for thickness E.sub.p as a function of D 
and V.sub.m. 
Since there are numerous configuration parameters that may have an effect, 
such a procedure gives rise to numerous manipulations. The number of such 
calibration manipulations can be reduced by observing that some of these 
parameters are interdependent. These configurations constitute classes C 
having the following property: the efficiencies D which are measured for 
each of the configurations defined by a class C can be deduced from one 
another by a weighting coefficient for analogous radiological conditions. 
This weighting factor is due to the fact that the incident energy spectra 
on the detector are similar or very close in each of the classes. 
In order to reduce the number of calibration operations, the invention 
proposes selecting, for each class (C), a reference configuration and 
performing a full calibration operation thereon as described above. 
Thereafter, a weighting factor needs to be determined for each element in 
the class (C) compared with the reference configuration by measuring the 
efficiency D at a supply voltage V.sub.m for a given value of the physical 
magnitude A, and by defining the weighting factor of the configuration as 
being equal to the ratio between this measurement of the efficiency D and 
the efficiency measured under analogous conditions using the reference 
configuration. In order to improve the accuracy of this coefficient, the 
value used may be the result of taking the mean of efficiency ratios as 
defined above and as measured under various radiological conditions. This 
mean may be calculated using efficiency ratios measured on several times 
over for the same element in the class (C) under the same radiological 
conditions. It may alternatively be calculated using efficiency ratios 
measured on one or more occasions with various different phantoms and for 
various values of the supply voltage V.sub.m. 
Further, if the function f(V.sub.m, A) is assumed to be separable into two 
functions, it is possible to reduce the number of calibration measurements 
by measuring the efficiency D for various values V.sub.m of the supply 
voltage, while E.sub.p is fixed, and then by measuring efficiency D for 
different values of thickness E.sub.p while V.sub.m is fixed. In the first 
case, the following function is obtained: 
EQU G.sub.E.sbsb.p (V.sub.m)=f(V.sub.m, E.sub.p) for fixed E.sub.p 
and in the second case the following function is obtained: 
EQU H.sub.V.sbsb.m (E.sub.p)=f(V.sub.m, E.sub.p) for fixed V.sub.m. 
Thus, when the function f(V.sub.m, E.sub.p) is separable into two 
functions, then: 
EQU f(V.sub.m, E.sub.p)=G.sub.E.sbsb.p (V.sub.m).times.H.sub.V.sub.m (E.sub.p) 
The functions G.sub.E.sbsb.p (V.sub.m) and H.sub.V.sbsb.m (E.sub.p) may be 
defined analytically as follows. Firstly, for each of these functions, the 
degree of the polynomial suitable for describing its curve is determined, 
after which the coefficients of the polynomial are determined using an 
estimation method. In order to implement this method, it is necessary to 
make (n+j) measurements whereas (n.times.j) measurements are required 
using the method of FIG. 2. The invention is described above using 
phantoms of determined thickness E.sub.p, however it is clear that the 
phantoms could be arbitrary and, in particular, they need not be 
rectangular in shape, for example they could be cylindrical. 
Once a radiological system has been calibrated in the manner described 
above, it is operational for measuring the equivalent thickness of an 
object. This measurement takes place using the following steps: 
(1) placing the object on the path of the radiation; 
(2) adjusting the tube supply voltage V.sub.m by means of the power supply 
15; 
(3) measuring the efficiency D using the means 18 which receive information 
concerning the values V.sub.m, I, and S, from the power supply 15, and 
information concerning the measured radiation M from the circuit 16; 
(4) using the microprocessor 19 to calculate the equivalent thickness 
E.sub.p using the formula E.sub.p =g (V.sub.m, D); and 
(5) displaying the result of the calculation on a display device 20. 
The display device 20 may be replaced by any other means for making use of 
the thickness E.sub.p, e.g. a computer file, a printer, or a calculator.