Analysis of Brain Tissue Poroelastic Properties Using Multiscale Modelling
Mathematical models are developed to further understand ischaemic stroke formation and achieve treatment effectiveness. The existing poroelastic model of the brain assumed the brain as a homogenized structure with uniform capillary distribution. This paper describes the use of a multiscale modeling...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
IIUM Press, International Islamic University Malaysia
2025-01-01
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| Series: | International Islamic University Malaysia Engineering Journal |
| Subjects: | |
| Online Access: | https://journals.iium.edu.my/ejournal/index.php/iiumej/article/view/3259 |
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| Summary: | Mathematical models are developed to further understand ischaemic stroke formation and achieve treatment effectiveness. The existing poroelastic model of the brain assumed the brain as a homogenized structure with uniform capillary distribution. This paper describes the use of a multiscale modeling technique known as asymptotic expansion homogenization (AEH) to derive a new poroelastic model of brain tissue. The model consists of a homogenized governing macroscale model with the effective parameters determined from the microscale cell equations. The microscale cell equations are solved on a representative volume element (RVE) comprising brain tissue embedded with a capillary. Here, the effect of capillary tortuosity and radius on the effective parameters, which are the hydraulic conductivity of the capillary and interstitial space (K and G), homogenous Biot's coefficient of the blood and interstitial space (?c? and ?t?), Young's modulus and Poisson's ratio are investigated. From the results, it is found that the percentage difference of K is 97.98% with increasing tortuosity, which suggests that K is significantly influenced by the shape of the capillary. In contrast, the percentage difference of G is only 0.25%, showing that it is unaffected by the shape of the capillary. Meanwhile, ?c? and ?t decrease and increase with increasing tortuosity, respectively. Both E and ? are not significantly affected by tortuosity, as the percentage difference for each is just 0.14% and 0.03%, respectively. In terms of capillary radius, it is found that K increases and G decreases with the increase of radius. Meanwhile, ?c? increases with increasing radius, while ?t? shows the opposite trend. The percentage differences of 18.26% and 14.55% are observed for E? and ?, respectively, implying that both parameters are significantly affected by the capillary radius. In conclusion, including capillaries in the brain model significantly affects the effective parameters. Hence, important properties of the capillary, including shape and size, should be carefully emphasized so that accurate findings can be obtained when solving the poroelastic model of the brain.
ABSTRAK:
Model matematik dibangunkan untuk mendapatkan pemahaman lanjut tentang pembentukan strok iskemia supaya keberkesanan rawatan dapat dicapai. Model poroelastik otak yang sedia ada menganggap otak sebagai struktur homogen dengan taburan kapilari yang seragam. Makalah ini menerangkan penggunaan teknik pemodelan multiskala yang dikenali sebagai penghomogenan pengembangan asimtotik (PPA) untuk memperoleh model poroelastik baharu untuk tisu otak. Model ini terdiri daripada satu set model skala makro pentadbir homogen dengan parameter berkesan ditentukan daripada persamaan sel skala mikro. Persamaan sel skala mikro diselesaikan pada satu unsur isipadu perwakilan (RVE) yang terdiri daripada tisu otak dengan kapilari yang tertanam. Di sini, kesan kelikuan dan jejari kapilari pada parameter berkesan, iaitu kekonduksian hidraulik ruang kapilari dan celahan (K dan G), pekali Biot homogen bagi darah dan ruang celahan (?c? dan ?t?), modulus Young (E) dan nisbah Poisson (?), akan diselidiki. Daripada keputusan yang diperoleh, didapati perbezaan peratusan K ialah 97.98% dengan peningkatan kelikuan, yang menunjukkan bahawa K dipengaruhi oleh bentuk kapilari secara signifikan. Manakala peratusan perbezaan G hanyalah 0.25%, menunjukkan bahawa ia tidak dipengaruhi oleh kelikuan. Sementara itu, ?c? dan ?t? masing-masing menurun dan meningkat dengan peningkatan kelikuan. Kedua-dua E dan ? tidak terjejas dengan ketara oleh kelikuan kerana perbezaan peratusan bagi setiap satu ialah masing-masing hanya 0.14% dan 0.03%. Dari segi jejari kapilari pula, didapati K bertambah dan G berkurangan dengan pertambahan jejari. Sementara itu, ?c meningkat dengan peningkatan jejari, manakala ?t? menunjukkan sebaliknya. Peratusan perbezaan 18.26% dan 14.55% diperhatikan untuk E dan ?, menunjukkan bahawa kedua-dua parameter dipengaruhi dengan ketara oleh jejari kapilari. Kesimpulannya, kemasukan kapilari dalam model otak mempunyai kesan yang ketara terhadap parameter berkesan. Oleh itu, sifat penting kapilari termasuk bentuk dan saiz harus ditekankan dengan teliti supaya penemuan yang tepat boleh diperolehi apabila menyelesaikan model poroelastik otak.
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| ISSN: | 1511-788X 2289-7860 |