How is the brain modeled in tomography?

Smart Engines. Do you remember that in addition to document recognition We also do tomography.

Today we continue our series of articles about phantoms for tomography. We have already looked at medical test and calibration phantoms, anthropomorphic phantoms and answered the question: “What is spatial resolution in tomography and how to measure it?”

Further continuation involves a story about phantoms obtained using mathematical formulas. Today we will talk about the very first mathematical phantoms that model the human head and his brain, in particular. Such phantoms are needed for various calculations, and for which ones we’ll tell you below the cut.

Stylized anthropomorphic phantoms

The first mathematical phantoms appeared for precise dosimetric calculations, ensuring the development of safe protocols for fluoroscopy, computed x-ray tomography and nuclear medicine. Early attempts at mathematical modeling used geometric descriptions in the form of spheres and ellipsoids of various sizes, but it soon became clear that this information was of limited use in prediction because the actual geometry of tissues and organs could not be well modeled using this simplified assumption. One of the first (1969) stylized (equation-based) full-body mathematical phantoms that used a wider range of geometric shapes to simulate internal organs was the phantom known as MIRD-5 (Medical Internal Radiation Dosimetry (MIRD) Committee of the Society of Nuclear Medicine, Pamphlet No.5).

This phantom, using simple equations, roughly modeled the skeleton, lung pairs, and remaining soft tissue portions to represent the “average” healthy adult male (reference human) as defined by the International Commission on Radiological Protection (ICRP) based on an extensive review of medical and other scientific literature about populations of Europe and North America. A new series of stylized phantoms was developed in 1980-1987. and was a whole “family”, which consisted of an adult man and woman, a newborn and children aged 1, 5, 10 and 15 years.

Each phantom is composed of three types of tissue of varying densities: bone, soft tissue and lung. The main body parts are defined as elliptical cylinders (arms, torso and thighs), truncated elliptical cone (legs and feet) and elliptical cylinder (head and neck).

Phantoms of Shepp and Logan (Shepp-Logan Phantom, 2d and 3d)

The first computed x-ray tomograph was introduced in 1971, but for many years the computing capabilities of computers were not enough to simulate in detail the process of tomographic scanning of the human body. However, the development of reconstruction methods required reference mathematical models. The first CT scanners were used to spatially represent the internal structure of the head, so the head model became the first specialized mathematical CT phantom. Of course, we are talking about the well-known Shepp and Logan phantom, proposed in 1974 in a classic paper [Shepp-1974].

Shepp and Logan phantoms are formed from ellipsoids; they are convenient for analytical modeling of projections (especially for methods based on the Fourier transform). The original 2D phantom models one cross section of the head and consists of 10 ellipses, which, due to different sizes, orientations and “gray levels”, model the main anatomical structures on the section. The ability to analytically model the “original signal” turned out to be extremely important for the study of a numerical method for reconstructing an MR image based on a set of measurements in parallel planes. Already in 1980 in work [Shepp-1980] A generalization of the Shepp-Logan head phantom to 3D is proposed.

This phantom already contains 17 ellipsoids that correspond to the geometry and characteristics of various geometric structures (for example, nose, eyes, blood clots, ventricles, tumors and many others). Later, a simplified version of 10 ellipsoids for the 3D (or a more complex version of the original 2D) head phantom was used, e.g. [Kak-1988]when testing CT reconstruction algorithms for a conical scheme for obtaining projections.

The most complete analytical properties of the Shepp and Logan 3D phantom are revealed in the work [Koay-2007]which adheres to classical geometry and introduces slight variations in gray levels.

Hoffman's 3D brain phantom

The human head has remained a subject of interest to researchers for many years. To study the processes of diffusion of solutions in the brain for the development of positron emission tomography (PET) methods in 1990. [Hoffman-1990] a physical 3D phantom was proposed, which became the “gold standard” in this field.

The phantom consists of plates with cutouts of complex shapes, which alternate in a certain order and physically simulate the blood flow system of the human brain, forming a system of cavities and channels.

Additional inserts allow you to simulate “hot” and “cold” spherical lesions, quantify the spatial resolution and size of the object under study, and evaluate the effects of attenuation and scattering.

In 2020, a digital twin was created for the physical phantom [Harrison-2020]while the authors carried out serious work to clarify the parameters of the digital phantom and harmonize the mathematical and physical models.

The phantom is voxel-based, available in DICOM and RAW formats, and can be used to test or validate image analysis software as a valid reference for which no generally accepted standards currently exist.

Multilayer (disk) phantom (Defrise phantom)

To develop a spiral scanning scheme with a wide cone beam, which is still actively used in CT, our own test objects are needed. The disk phantom is a standard “simple object” for identifying problems and analyzing the quality of reconstruction when using a wide cone beam. It is mentioned under different names and given as illustrations in a large number of works, but we find it difficult to indicate the original publication, since there are no references to the original source. Note that in some publications the disks have the form of highly oblate ellipsoids to simplify numerical modeling.

Rice. modeling the results of phantom reconstruction for different cone widths [Zeng-2010]In other works, multi-layering is achieved using ordinary flat cylindrical disks, which can easily be reproduced in the physical embodiment of the phantom, or even using cylindrical layers for other directions.

Phantoms for radiomics (Stanford DRO Toolkit)

Radiomics arose at the intersection of oncology, radiology, image processing and analysis, but this method can be applied to any medical research in which a pathological process can be visualized. The approach is based on a research-proven hypothesis that quantitative analysis of image characteristics can improve computer diagnostics, improve the choice of treatment strategies and make the prediction of response to therapy more accurate. In radiomics, the main characteristics of images belong to 5 classes of descriptors: size, shape, intensity, texture and sharpness of edges, while some significant features may not be visible to the human eye. The application of the method is greatly complicated by the fact that with different scanning, reconstruction and post-processing protocols for the same objects, images can differ greatly, that is, the reproducibility and repeatability of feature calculations, as well as the possibility of constructing reliable models, are a big question. To be able to analyze the influence of all numerous factors on the extracted features and standardization between different hardware and software manufacturers, [McNitt-Gray-2020] digital reference objects (DRO).

Rigorous mathematical descriptions allow control of the main features, and accompanying software allows the generation of voxel representations for given quantization parameters, as well as reference segmentation.

Conclusion

The phantoms we described in this article serve us to quantify the reconstruction algorithms we develop, artifact suppression algorithms, or algorithms for refining experimental parameters. After a thorough check of the performance of the methods, they are processed into our product for tomographic reconstruction Smart Tomo Engine. You can watch a video with the results of tomographic reconstruction on our YouTube channel. You can read about one of the applied applications of tomography in our article.

Bibliography

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[Harrison-2020] Harrison RL et al. Technical Note: A digital reference object representing Hoffman's 3D brain phantom for PET scanner simulations // Medical physics. – 2020. – V. 47. – No. 3. – P. 1174-1180.

[Hoffman-1990] Hoffman EJ et al. 3-D phantom to simulate cerebral blood flow and metabolic images for PET //IEEE Transactions on Nuclear Science. – 1990. – V. 37. – No. 2. – P. 616-620.

[Kak-1988] Kak AC, Slaney M. Principles of computerized tomographic imaging. IEEE Press, New York, 1988.

[Koay-2007] Koay CG, Sarlls JE, Ozarslan E. Three-dimensional analytical magnetic resonance imaging phantom in the Fourier domain. Magn Reson Med 2007;58:430–436

[McNitt-Gray-2020] McNitt-Gray M. et al. Standardization in quantitative imaging: a multicenter comparison of radiomic features from different software packages on digital reference objects and patient data sets //Tomography. – 2020. – V. 6. – No. 2. – P. 118-128.

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