RU2558001C2 - Method of two-energy estimation of average density and effective atomic number of multicomponent materials - Google Patents

Abstract

FIELD: instrumentation.

SUBSTANCE: invention relates to problem of radiation analysis of the materials, namely to methods of numeric evaluation of density and effective atomic number of solid and liquid multicomponent materials. Method of two-energy estimation of the average density and effective atomic number of the multicomponent materials ensures these parameters determination in the materials comprising any number of the components without the a priori information about their characteristics.

EFFECT: suggested by the invention calibration-less method provides unbiased estimates of density and effective atomic number of the multicomponent structure (without limitation of the components number) and upon absence of the a priori information relating density and effective number of the components.

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Description

The technical field to which the invention relates.

The invention relates to the problem of radiation analysis of materials, specifically to methods for numerically estimating the density and effective atomic number of solid and liquid multicomponent materials.

The level of technology.

The physical basis of most existing methods for estimating the average density and effective atomic number of two-component materials by means of two-energy radioscopy is the dependence of the ratio F of the mass absorption coefficients for low μ ^L and high μ ^H radiation energies on the atomic number Ζ of the elements of the periodic system of D. Mendeleev (Fig. 1).

For objects with a constant chemical composition, the unknown two variables (average density and effective atomic number) are determined using two equations that relate the fraction of photons that have passed without interaction with the products of the mass absorption coefficient, density and thickness of the object at two different energies of the initial radiation.

The fraction of photons transmitted through an object without interaction is determined for a monoenergetic source as

where µ (Ζ (x), E) is the distribution of the mass coefficient of total absorption over the input vector x of radiation, determined by the distribution of the atomic number Z (x) and energy E,

ρ (x) is the density distribution,

N _O is the initial number of photons,

N is the number of recorded photons that passed the object without interaction,

d is the thickness of the object.

For an object with a constant atomic number, this ratio is determined by the product of the mass absorption coefficient by the average density and thickness

where ρ _a is the average density.

The ratio of the logarithms of the reciprocal of the recorded photons for an object with a constant atomic number depends only on the atomic number

where the indices L and H correspond to low and high energies, respectively.

Atomic number is defined as the inverse function of the ratio of the logarithms in question

, по любому из которых вычисляется средняя плотностьThe atomic number value determines the mass absorption coefficients (µ ^L (Z), µ ^H (Z)) $$$$

according to any of which the average density is calculated

Known methods for measuring the ratio of the fractions of photons transmitted without interaction with an object at low and high energies of the initial x-ray radiation to obtain an estimate of the effective atomic number of a two-component structure.

These methods include the following patents.

1. US 6683934 B1, 2004. Dual energy x-ray imaging system and method for radiography and mammography. J. Zhao, B. Hibbs Opsahl-Ong, M.K. Hopple.

2. US 7158611 B2. 2007. B. Heismann, K. Stierstorfer. Method for determining density distributions and atomic number distributions during radiographic examination methods.

3. DE 10 305 105 A1. 2004. B. Heismann. Eichung der Transformation spektraler Röntgenschwȁchungswerte in Dichte - und Ordnungs - zahlinformation.

A common drawback of the solutions presented in these patents is that in them when evaluating the density there is a systematic error.

The presence of a systematic error in the estimation of the linear absorption coefficient in the direction of its decrease (and, consequently, of systematic shifts in the estimates of the effective atomic number and average density) was noted in the work:

Torikoshi, M. Ohno, Y. Endo, et al. M. Measurement of electron density and effective atomic number using dual-energy X-ray CT. Nuclear Science Symposium Conference Record, 2004 IEEE, Vol.6, Page (s): 3764-3768.

The presence of a systematic error in estimating the effective atomic number was noted in the works:

1. A. Pietrobelli, C. Formica, Z. Wang, S. B. Hemsfield. Dual-energy X-ray absorptiometry body composition model: review of physical concepts. Am J Physiol Endocrinol Metab 271: E941-E951, 1996.

2. A. Pietrobelli, Z. Wang, C. Formica, S.B. Hemsfield. Dual-energy X-ray absorptiometry: fat estimation errors due to variation in soft tissue hydration. AJP - Endocrinology and Metabolism, Volume 274 (5): E808 The American Physiological Society - 1998.

A significant proportion of patents is based on visualization of the linear difference of the logarithms of the ratio of the number of source photons to the number of transmitted objects without interaction for different radiation energies, which for monochromatic sources is proportional to the difference in mass absorption coefficients, which in turn depends on the effective atomic number (Fig. 1)

This method is most widely used in dual-energy difference mammography and is represented by patents:

1. US 6683934 B1. 2004. J. Zhao et al. Dual energy x-ray imaging system and method for radiography and mammography.

2. EP 0092767 B1. 1986. Gary Sylvester Keyes et al. Method and apparatus for x-ray image subtraction.

The disadvantages of these methods include the fact that the difference between the logarithms under consideration is proportional to the product of the mass absorption coefficient and density, which makes it difficult to separate the identification of density and effective atomic number.

A more generalized way is to visualize a linear composition of the logarithms of the ratio of the number of source photons to the number of transmitted objects without interaction χ for various radiation energies

where k ₁ , k ₂ , k _O are constants.

This method should include patents.

1. US 8306180 B2. 2012. Zhiqiang Chen et al. Image reconstruction method for high-energy, dual-energy CT system.

2. US 20130028371, 2012. N. Derzhi. Method For Estimating Effective Atomic Number And Bulk Density Of Rock Samples Using Dual Energy X-Ray Computed Tomographic Imaging.

In patent RU 2012108684. 2013. V.A. Gorshkov, R.R. Nazirov, V.G. Rodin et al. “A method of dual-energy fission-difference mammography” proposed a method for visualizing a linear composition of the difference and the ratio of the logarithms of the ratio of the number of source photons to the number of transmitted objects without interaction for different radiation energies

where k ₁ , k ₂ , k _O are constants.

However, this method leads to a systematic shift in the resulting effective atomic number, which allows better identification of the smallest microcalcinates in the mammary gland.

US 6857640 B2, 2002 “Dual-energy radiography process differentiating bone tissues, lean tissues and fatty tissues” (Jean-Marc Dinten, Lionel Herve, Christine Robert-Coutant) proposes a method for estimating the mass concentration of components in bones and tissues (in a three-component structure), consisting in solving the system of equations

where M _m , M _g , M _os is the mass of material per unit area, g / cm ² ,

ρ is the density of the material,

m, g, os - indices corresponding to muscle, adipose and bone tissues,

1, 2 - indices corresponding to low and high radiation energies,

X ₁ , X ₂ - logarithms of the ratio of the original number of photons to the number of transmitted without interaction,

L is the thickness of the study area, calculated using the polynomial

where α, β, γ, δ, ε are constants.

In modern osteodensitometers, the thickness of the test site is not calculated, but measured by a laser device, as is implemented in the Swedish Lund DEXA & Laser densitometer (http://www.lundltd.ru/index.php?razd=106&catalog=111).

It is not a problem for measured mass concentrations of components to obtain unbiased estimates of average density and effective atomic number.

In this case, a priori information is required on the density and mass absorption coefficients (i.e., on the effective atomic number) of each of the 3 components.

However, this approach is not applicable for estimating the average density and effective atomic number of a multicomponent medium (without limiting the number of components) in the absence of a priori information on the density and effective number of its constituent components.

A method for eliminating a systematic error in estimating the density of a multicomponent object is presented in the aforementioned patent US 20130028371, 2012. N. Derzhi. Method For Estimating Effective Atomic Number And Bulk Density Of Rock Samples Using Dual Energy X-Ray Computed Tomographic Imaging. In this patent, it is proposed to obtain a system of equations for the relationship between the density and the effective atomic number with the logarithms of the ratio of the initial number of photons to transmitted ones without interaction with the object on calibration homogeneous samples with different known densities and effective atomic numbers. Based on the obtained equations, the relationship of the absolute systematic error in determining the density with the atomic number is determined.

where ε is the systematic error,

a, b are constants.

This equation is the basis for the correction of the calculated density for all vectors of the scanning system.

Initial estimates of density and effective atomic number are calculated based on a system of equations obtained from calibration samples.

To estimate the density and effective atomic number of a multicomponent structure (without limiting the number of components) in the absence of a priori information about the density and effective number of its constituent components, a non-calibration iterative method for their estimation is proposed, which is the subject of the proposed invention

Disclosure of invention

The problem of calculating the average density of a multicomponent medium is the difficulty in determining the effective mass absorption of the entire medium in the absence of a priori information about the effective number of its constituent components.

If there is an estimate of the effective atomic number, then an estimate of the density can be defined as

- оценка эффективного атомного номера среды.Where

- assessment of the effective atomic number of the medium.

Only with an accurate estimate of the effective atomic number is it possible to accurately calculate the average density

The denominator of expression (15) is the measured value (Measured_ Value), and the numerator is the calculated value (Calculated_value)

Thus, when measuring at two different energies, two estimates of the average density take place

Hence the ratio of the logarithms under consideration will be

Equations (17) and (18) are the basis of an iterative method for estimating the average density and effective atomic number of multicomponent materials.

Assuming for the initial estimate of the effective atomic number the equality of densities

taken as the initial estimate of the ratio of mass absorption coefficients

whence we get the initial estimate (0th iteration) of the effective atomic number

по известным табличным значениям массовых коэффициентов поглощения для различных элементов и энергий (с применением интерполяции) оцениваются массовые коэффициенты

According to the obtained estimate of the effective atomic number $${\widetilde{{\rm Z}}}_0$$

using known tabular values of mass absorption coefficients for various elements and energies (using interpolation), mass coefficients are estimated

Based on the obtained mass coefficients, the conditional densities are specified (1st iteration)

Based on the obtained densities, the ratio of the mass absorption coefficients is refined.

on the basis of which the value of the effective atomic number is specified

Further, the procedures are repeated, i.e. mass absorption coefficients, conditional densities, ratios of mass absorption coefficients, effective atomic numbers are iteratively refined.

So, at the i-th iteration, the following are calculated:

- mass absorption coefficients

- conditional densities

- ratios of mass absorption coefficients

- effective atomic numbers

where i is the iteration number.

Iterations are repeated until the densities and effective atomic number are stabilized, or until their changes satisfy the specified criterion that determines the given accuracy in their estimation.

It is the sequence of these actions that is an essential distinguishing feature of this method.

Brief Description of the Drawings

Figure 1 represents the dependence of the ratio of mass absorption coefficients on the atomic number.

Figure 2 represents the dependence of the difference of the mass absorption coefficients on the atomic number.

Figure 3 is a structural diagram of a method implementation

Figure 4 represents the distribution of components in an object.

Figure 5 represents the distribution of the actual effective atomic number and calculated by the initial estimate (0th iteration).

6 represents the distribution of the actual and calculated conditional densities according to the intensity of registration of radiation at low and high energies after the initial iteration.

7 represents the distribution of the effective atomic number and its estimates after the 0th and 2nd iterations.

Fig.8 represents the distribution of the actual and calculated conditional densities according to the intensity of registration of radiation at low and high energies after the 2nd iteration.

Fig.9 represents the distribution of the effective atomic number and its estimates after the 0th and 3rd iterations.

Figure 10 represents the distribution of density (a) and effective atomic number (b) in the phantom of the bone.

11 represents the results of identifying a density distribution and an effective atomic number in an iterative manner.

12 represents the results of identifying a density distribution and an effective atomic number by a method protected by US Pat. No. 6,857,640.

The implementation of the invention

The invention is carried out in accordance with the following sequence and is illustrated by the structural diagram presented in figure 3.

.1. Measure the fraction of the recorded photons that passed the object without interaction $$N_0^L/N^L,N_0^H/N^H$$

.

2. The initial iteration (i = 0). The initial estimate (i = 0) of the ratio of the mass absorption coefficients is calculated

3. Calculate the initial estimate (i = 0) of the effective atomic number (Fig. 4)

по известным табличным значениям массовых коэффициентов поглощения для различных элементов и энергий оцениваются массовые коэффициенты4. Next iteration (i = i + 1). According to the obtained estimate of the effective atomic number $${\widetilde{{\rm Z}}}_{i-\mathrm{one}}$$

the known tabular values of the mass absorption coefficients for various elements and energies are estimated mass coefficients

5. Based on the obtained mass coefficients, conditional densities are specified (Fig. 5)

6. Based on the obtained densities, the estimate of the ratio of mass absorption coefficients is adjusted

7. Based on the adjusted estimate of the ratio of mass absorption coefficients, a new estimate of the effective atomic number is calculated

Further, the actions in paragraph 4, 5, 6, 7 are repeated, i.e. iteratively specified:

- mass absorption coefficients,

- conditional densities,

- the ratio of mass absorption coefficients,

- effective atomic numbers.

Actions are repeated until the densities and effective atomic number are stabilized, or until their changes satisfy the specified criterion that determines the given accuracy in their estimation.

The results of a two-energy estimate of the average density and effective atomic number of multicomponent materials are illustrated on a 4-component object (Fig. 4), 4 cm thick with a density and atomic number, shown in Table 1.

Table 1. Atomic numbers and densities of the components of an object d6 d10 d12 d14 Ζ _i 6 10 12 fourteen ρ _i one 1,5 2 2,5

, стремятся к фактическим значениям

, а условные плотности, рассчитанные на низкой и высокой энергиях (ρL,iter(i),ρН,iter(i)) к фактическим средним значениям ρ_а . Fig. 5, Fig. 6, Fig. 7, Fig. 8, Fig. 9 illustrate the increase in the accuracy of identification of the effective atomic number and average density with an increase in the number of iterations. As can be seen, with an increase in the iteration number i, the estimates of the effective atomic number

seek actual values

, and conditional densities calculated at low and high energies (ρL, iter (i), ρН, iter (i)) to the actual average values of ρ _a .

The repetition of these operations is carried out until the refinement of the values of density and effective atomic number either leads to noticeable changes, or until it meets the selected criterion.

This method was compared with the method presented in the above patent US 6857640, allowing to identify the density and effective atomic number for 2 and 3-component structures.

Figure 10 represents the distribution of density and effective atomic number in a two-component phantom of the bone, consisting of periosteum, dense and cancellous bone, bone marrow.

11 represents the results of density and effective atomic number estimation by the presented method.

Fig. 12. It presents the results of identifying the density distribution and effective atomic number based on the method presented in US Pat. No. 6,857,640. As you can see, for a two-component medium, there is complete equivalence of the distributions obtained by the proposed method and the calculation method presented in US 6857640.

Claims (1)

The method of two-energy estimation of the average density and effective atomic number of multicomponent materials, which consists in the fact that the analyzed object is irradiated with monoenergetic radiation at two energies, the radiation transmitted through the object is recorded, the ratio of the logarithms of the fractions of the number of photons transmitted through the object is calculated,

,
according to which, by the inverse communication function, the ratios of the mass absorption coefficients with the atomic number F (Z) calculate the initial estimate of the effective atomic number

,
characterized in that according to the obtained (i-1) th estimate of the atomic number, the estimates of the mass absorption coefficients are successively calculated from the tables

and from them, and by the fraction of the recorded radiation for low and high energy, i-th estimates of conditional densities are calculated

,

,
the values of which adjust the ratio of mass absorption coefficients

,
calculate a new estimate of the effective atomic number

,
and operations to refine the effective atomic number and densities are repeated until the iterative procedure meets the selected criterion.

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