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Как моделируют мозг в томографии?

Привет, Хабр! На связи Smart Engines. Вы же помните, что кроме распознавания документов мы занимаемся и томографией.

Сегодня мы продолжаем нашу серию статей про фантомы для томографии. Мы уже рассмотрели медицинские тестово‑калибровочные фантомы, антропоморфные фантомы и ответили на вопрос: "Что такое пространственное разрешение в томографии и как его измерить?"

Дальнейшее продолжение предполагает рассказ о фантомах, полученных с помощью математических формул. Сегодня мы расскажем о самых первых математических фантомах, которые моделируют голову человека и его мозг, в частности. Такие фантомы нужны для различных расчетов, а для каких именно - рассказываем под катом.

Стилизованные антропоморфные фантомы

Первые математические фантомы появились для точных дозиметрических расчетов, обеспечивающих выработку безопасных протоколов рентгеноскопии, компьютерной рентгеновской томографии и ядерной медицины. В первых попытках математического моделирования использовали геометрические описания в виде сфер и эллипсоидов различного размера, но вскоре стало понятно, что эта информация имеет ограниченное применение при прогнозировании, поскольку фактическая геометрия тканей и органов не может быть хорошо смоделирована с помощью этого упрощенного предположения. Одним из первых (1969 г.) стилизованных (на основе уравнений) математических фантомов всего тела, в котором для моделирования внутренних органов использовался более широкий диапазон геометрических форм стал фантом, известный как MIRD-5 (Medical Internal Radiation Dosimetry (MIRD) Committee of the Society of Nuclear Medicine, Pamphlet No.5).

Рис. схема дозиметрического фантома MIRD-5, [DeWerd-2014]
Рис. схема дозиметрического фантома MIRD-5, [DeWerd-2014]

Этот фантом простыми уравнениями грубо моделировал скелет, пары легких и оставшиеся части мягких тканей для представления «среднего» здорового взрослого мужчины (эталонного человека), как это было определено Международной комиссией по радиологической защите (ICRP) на основе обширного обзора медицинской и другой научной литературы о популяциях Европы и Северной Америки. Новая серия стилизованных фантомов была разработана в 1980-1987 гг. и представляла собой целую «семью», которая состояла из взрослого мужчины и женщины, новорожденного и детей в возрасте 1, 5, 10 и 15 лет.

Рис. визуализация математических фантомов семейства MIRD, адаптировано из [Xu-2000], [DeWerd-2014]
Рис. визуализация математических фантомов семейства MIRD, адаптировано из [Xu-2000], [DeWerd-2014]

Каждый фантом состоит из трех типов тканей различной плотности: кости, мягкие ткани и легкие. Основные части тела определены как эллиптические цилиндры (руки, туловище и бедра), усеченный эллиптический конус (ноги и ступни) и эллиптический цилиндр (голову и шею).

Фантомы Шеппа и Логана (Shepp-Logan Phantom, 2d и 3d)

Первый компьютерный рентгеновский томограф был представлен в 1971 г., но ещё много лет вычислительных возможностей компьютеров не хватало для детального моделирования процесса томографического сканирования тела человека. Тем не менее, развитие методов реконструкции требовало референтных математических моделей. Первые КТ сканеры использовались для пространственного представления внутренней структуры головы, поэтому именно модель головы стала первым специализированным математическим КТ фантомом. Разумеется, речь идет о широко известном фантоме Шеппа и Логана, предложенном в 1974 г. в классической работе [Shepp-1974].

Рис. фантом Шеппа и Логана -  пример визуализации “уровней серого”, схема и таблица параметров [Shepp-1974]
Рис. фантом Шеппа и Логана - пример визуализации “уровней серого”, схема и таблица параметров [Shepp-1974]

Фантомы Шеппа и Логана формируются из эллипсоидов, они удобны для аналитического моделирования проекций (особенно для методов, опирающихся на фурье-преобразование). Оригинальный 2D фантом моделирует один поперечный срез головы и состоит из 10 эллипсов, которые за счет разных размеров, ориентации и “уровней серого” моделируют основные анатомические структуры на срезе. Возможность аналитического моделирования “исходного сигнала” оказалась крайне важной, и для исследования численного метода реконструкции МР-изображения на основе набора измерений в параллельных плоскостях. Уже в 1980 г. в работе [Shepp-1980] предложена обобщение фантома головы Шеппа-Логана на 3D.

Рис. схема 3d  фантома Шеппа и Логана для вида спереди, сбоку и сверху, [Shepp-1980]
Рис. схема 3d фантома Шеппа и Логана для вида спереди, сбоку и сверху, [Shepp-1980]

Этот фантом содержит уже 17 эллипсоидов, которые соответствуют геометрии и характеристикам различных геометрических структур (например, нос, глаза, сгустки крови, желудочки, опухоли и многие другие). Позже упрощенную версию из 10 эллипсоидов для трехмерного (или усложненную версию оригинального двумерного) фантома головы использовали, например [Kak-1988], при тестировании алгоритмов КТ реконструкции для конусной схемы получения проекций.

Рис. иллюстрация вертикального среза реконструированного объема фантома и схемы горизонтальных срезов в плоскостях, [Kak-1988]
Рис. иллюстрация вертикального среза реконструированного объема фантома и схемы горизонтальных срезов в плоскостях, [Kak-1988]

Наиболее полно аналитические свойства 3D фантома Шеппа и Логана раскрыты в работе [Koay-2007], которая придерживается классической геометрии и вносит небольшие вариации в уровни серого.

Рис. визуализации срезов и рендеринг 3d фантома Шеппа и Логана по версии [Koay-2007]
Рис. визуализации срезов и рендеринг 3d фантома Шеппа и Логана по версии [Koay-2007]

Фантом мозга (Hoffman’s 3D brain phantom)

Голова человека много лет остается предметом интереса исследователей. Для изучения процессов диффузии растворов в головном мозге для развития методов позитронно-эмиссионной томографии (ПЭТ) в 1990 г. [Hoffman-1990] был предложен физический 3D фантом, который стал “золотым стандартом” в этой области.

Рис. схема пластин для моделирования поперечных срезов мозга [Hoffman-1990]
Рис. схема пластин для моделирования поперечных срезов мозга [Hoffman-1990]

Фантом состоит из пластин с вырезами сложной формы, которые чередуются в определенном порядке и физически моделируют систему кровотока головного мозга человека образуя систему полостей и каналов.

Рис. визуализация эталонных срезов и результатов регистрации фантомы, [Hoffman-1990]
Рис. визуализация эталонных срезов и результатов регистрации фантомы, [Hoffman-1990]

Дополнительные вставки позволяют имитировать “горячие” и “холодные” сферические поражения, делать количественную оценку пространственного разрешения и размеров исследуемого объекта, оценивать эффекты ослабления и рассеяния.

В 2020 г. для физического фантома был создан цифровой двойник [Harrison-2020], при этом авторы провели серьезную работу по уточнению параметров цифрового фантома и согласования математической и физических моделей.

Рис. сопоставление схем физического и математического фантомов Hoffman’s 3D brain, [Harrison-2020]
Рис. сопоставление схем физического и математического фантомов Hoffman’s 3D brain, [Harrison-2020]

Фантом является воксельным, доступен в DICOM и RAW форматах, может применяться для тестирования или проверки программного обеспечения анализа изображений в качестве достоверного эталона, для которого в настоящее время не существует общепринятых стандартов.

Многослойный (дисковый) фантом (Defrise phantom)

Для развития спиральной схемы сканирования с широким конусным пучком, которую и сейчас активно используют в КТ, необходимы свои тестовые объекты. Дисковый фантом является стандартным “простым объектом” для выявления проблем и анализа качества реконструкции при использовании широкого конусного пучка. Он упоминается под разными названиями и приводится в качестве иллюстрации в большом количестве работ, но мы затрудняемся указать оригинальную публикацию, поскольку ссылки на первоисточник отсутствуют. Отметим, что в некоторых публикациях диски имеют вид сильно сплюснутых эллипсоидов для упрощения численного моделирования.

Рис. моделирование результатов реконструкции фантома для разных вариантов ширины конуса [Zeng-2010]
Рис. моделирование результатов реконструкции фантома для разных вариантов ширины конуса [Zeng-2010]

Рис. моделирование результатов реконструкции фантома для разных вариантов ширины конуса [Zeng-2010]В других работах многослойность достигается при помощи обычных плоских цилиндрических дисков, которые легко могут быть воспроизведены в физическом воплощении фантома, или даже при помощи цилиндрических слоев для других направлений.

Рис. схема усиройства дискового фантома [Zeng-2010]
Рис. схема усиройства дискового фантома [Zeng-2010]

Фантомы для радиомики (Stanford DRO Toolkit)

Радиомика возникла на стыке онкологии, радиологии, обработки и анализа изображений, однако этот метод можно применить к любому медицинскому исследованию, при котором можно визуализировать патологический процесс. В основе подхода подтвержденная исследованиями гипотеза, что количественный анализ характеристик изображений позволяет улучшить компьютерную диагностику, улучшить выбор стратегий лечения и сделать более точным прогнозирование ответа на терапию. В радиомике основные характеристики изображений относятся к 5 классам дескрипторов: размер, форма, интенсивность, текстура и резкость границ, при этом часть значимых признаков может быть не видна человеческому глазу. Применение метода сильно усложняется тем, что при разных протоколах сканирования, реконструкции и постобработки для одних и тех же объектов изображения могут сильно отличаться, то есть под большим вопросом оказывается воспроизводимость и повторяемость вычисления признаков, а также возможность построения достоверных моделей. Для возможности анализа влияния всех многочисленных факторов на извлекаемые признаки и стандартизации между различными производителями оборудования и программного обеспечения были разработаны [McNitt-Gray-2020] цифровые референсные объекты (Digital Reference Objects, DRO).

90d556c94a10a05915e6f6e6e5a049bd.png

Строгие математические описания позволяют управлять основными признаками, а сопровождающее программное обеспечение позволяет сгенерировать воксельные представления для заданных параметров квантования, а также эталонную сегментацию.

Заключение

Фантомы, о которых мы рассказали в этой статье, служат нам для количественной оценки разрабатываемых нами алгоритмов реконструкции, алгоритмов подавления артефактов или алгоритмов уточнения экспериментальных параметров. После тщательной проверки работоспособности методов они попадают в продуктизацию в наш продукт для томографической реконструкции Smart Tomo Engine. Видео с результатами томографической реконструкцией можно посмотреть в нашем ютуб-канале. Почитать об одном из прикладных применений томографии можно в нашей статье.

Список литературы

[DeWerd-2014] DeWerd L. A. The phantoms of medical and health physics. – Berlin : Springer, 2014.

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

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

[Kak-1988] Kak A.C., 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 ResonMed 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. – №. 2. – P. 118-128.

[Shepp-1974] Shepp LA, Logan BF. The Fourier reconstruction of a head section.IEEE Trans Nucl Sci 1974;21:21–43.

[Shepp-1980] Shepp L. A. et al. Computerized tomography and nuclear magnetic resonance //J. Comput. Assist. Tomogr. – 1980. – V. 4. – №. 1. – P. 94-107.

[Xu-2000] Xu X. G., Chao T. C., Bozkurt A. VIP-Man: an image-based whole-body adult male model constructed from color photographs of the Visible Human Project for multi-particle Monte Carlo calculations //Health physics. – 2000. – V. 78. – №. 5. – P. 476-486.

[Zeng-2010] Zeng G. L. Medical image reconstruction. – Heidelberg : Springer, 2010. – V. 530.

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  • 26.06.24 18:46 Jacobethannn098

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  • 04.07.24 04:49 ZionNaomi

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  • 17.07.24 02:26 thompsonrickey

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  • 27.08.24 12:50 James889900

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  • 02.09.24 20:24 [email protected]

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  • 06.09.24 01:35 Celinagarcia

    HOW TO RECOVER MONEY LOST IN BITCOIN/USDT TRADING OR TO CRYPTO INVESTMENT !! Hi all, friends and families. I am writing From Alberton Canada. Last year I tried to invest in cryptocurrency trading in 2023, but lost a significant amount of money to scammers. I was cheated of my money, but thank God, I was referred to Hack Recovery Wizard they are among the best bitcoin recovery specialists on the planet. they helped me get every penny I lost to the scammers back to me with their forensic techniques. and I would like to take this opportunity to advise everyone to avoid making cryptocurrency investments online. If you ​​​​​​have already lost money on forex, cryptocurrency or Ponzi schemes, please contact [email protected] or WhatsApp: +1 (757) 237–1724 at once they can help you get back the crypto you lost to scammers. BEST WISHES. Celina Garcia.

  • 06.09.24 01:44 Celinagarcia

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  • 23.09.24 18:56 matthewshimself

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  • 01.10.24 14:54 Sinewclaudia

    I lost about $876k few months ago trading on a fake binary option investment websites. I didn't knew they were fake until I tried to withdraw. Immediately, I realized these guys were fake. I contacted Sinew Claudia world recovery, my friend who has such experience before and was able to recover them, recommended me to contact them. I'm a living testimony of a successful recovery now. You can contact the legitimate recovery company below for help and assistance. [email protected] [email protected] WhatsApp: 6262645164

  • 02.10.24 22:27 Emily Hunter

    Can those who have fallen victim to fraud get their money back? Yes, you might be able to get back what was taken from you if you fell prey to a fraud from an unregulated investing platform or any other scam, but only if you report it to the relevant authorities. With the right plan and supporting documentation, you can get back what you've lost. Most likely, the individuals in control of these unregulated platforms would attempt to convince you that what happened to your money was a sad accident when, in fact, it was a highly skilled heist. You should be aware that there are resources out there to help you if you or someone you know has experienced one of these circumstances. Do a search using (deftrecoup (.) c o m). Do not let the perpetrators of this hoaxes get away with ruining you mentally and financially.

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  • 31.10.24 00:13 ytre89

    Can those who have fallen victim to fraud get their money back? Yes, you might be able to get back what was taken from you if you fell prey to a fraud from an unregulated investing platform or any other scam, but only if you report it to the relevant authorities. With the right plan and supporting documentation, you can get back what you've lost. Most likely, the individuals in control of these unregulated platforms would attempt to convince you that what happened to your money was a sad accident when, in fact, it was a highly skilled heist. You should be aware that there are resources out there to help you if you or someone you know has experienced one of these circumstances. Do a search using (deftrecoup (.) c o m). Do not let the perpetrators of this hoaxes get away with ruining you mentally and financially.

  • 02.11.24 14:44 diannamendoza732

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