A Mathematical Investigation of Sex Differences in Alzheimer’s Disease
Alzheimer’s disease (AD) is an age-related degenerative disorder of the cerebral neuro-glial-vascular units. Not only are post-menopausal females, especially those who carry the APOE4 gene, at a higher risk of AD than males, but also AD in females appears to progress faster than in aged-matched male...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/8/457 |
| _version_ | 1797432173654966272 |
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| author | Corina S. Drapaca |
| author_facet | Corina S. Drapaca |
| author_sort | Corina S. Drapaca |
| collection | DOAJ |
| description | Alzheimer’s disease (AD) is an age-related degenerative disorder of the cerebral neuro-glial-vascular units. Not only are post-menopausal females, especially those who carry the APOE4 gene, at a higher risk of AD than males, but also AD in females appears to progress faster than in aged-matched male patients. Currently, there is no cure for AD. Mathematical models can help us to understand mechanisms of AD onset, progression, and therapies. However, existing models of AD do not account for sex differences. In this paper a mathematical model of AD is proposed that uses variable-order fractional temporal derivatives to describe the temporal evolutions of some relevant cells’ populations and aggregation-prone amyloid-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> fibrils. The approach generalizes the model of Puri and Li. The variable fractional order describes variable fading memory due to neuroprotection loss caused by AD progression with age which, in the case of post-menopausal females, is more aggressive because of fast estrogen decrease. Different expressions of the variable fractional order are used for the two sexes and a sharper decreasing function corresponds to the female’s neuroprotection decay. Numerical simulations show that the population of surviving neurons has decreased more in post-menopausal female patients than in males at the same stage of the disease. The results suggest that if a treatment that may include estrogen replacement therapy is applied to female patients, then the loss of neurons slows down at later times. Additionally, the sooner a treatment starts, the better the outcome is. |
| first_indexed | 2024-03-09T09:56:28Z |
| format | Article |
| id | doaj.art-8b607df9cfe040c39f4e9d01d82a6dd1 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T09:56:28Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-8b607df9cfe040c39f4e9d01d82a6dd12023-12-01T23:43:15ZengMDPI AGFractal and Fractional2504-31102022-08-016845710.3390/fractalfract6080457A Mathematical Investigation of Sex Differences in Alzheimer’s DiseaseCorina S. Drapaca0Department of Engineering Science and Mechanics, Pennsylvania State University, University Park, PA 16802, USAAlzheimer’s disease (AD) is an age-related degenerative disorder of the cerebral neuro-glial-vascular units. Not only are post-menopausal females, especially those who carry the APOE4 gene, at a higher risk of AD than males, but also AD in females appears to progress faster than in aged-matched male patients. Currently, there is no cure for AD. Mathematical models can help us to understand mechanisms of AD onset, progression, and therapies. However, existing models of AD do not account for sex differences. In this paper a mathematical model of AD is proposed that uses variable-order fractional temporal derivatives to describe the temporal evolutions of some relevant cells’ populations and aggregation-prone amyloid-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> fibrils. The approach generalizes the model of Puri and Li. The variable fractional order describes variable fading memory due to neuroprotection loss caused by AD progression with age which, in the case of post-menopausal females, is more aggressive because of fast estrogen decrease. Different expressions of the variable fractional order are used for the two sexes and a sharper decreasing function corresponds to the female’s neuroprotection decay. Numerical simulations show that the population of surviving neurons has decreased more in post-menopausal female patients than in males at the same stage of the disease. The results suggest that if a treatment that may include estrogen replacement therapy is applied to female patients, then the loss of neurons slows down at later times. Additionally, the sooner a treatment starts, the better the outcome is.https://www.mdpi.com/2504-3110/6/8/457Alzheimer’s diseasemathematical modelvariable-order fractional derivativesex differences |
| spellingShingle | Corina S. Drapaca A Mathematical Investigation of Sex Differences in Alzheimer’s Disease Fractal and Fractional Alzheimer’s disease mathematical model variable-order fractional derivative sex differences |
| title | A Mathematical Investigation of Sex Differences in Alzheimer’s Disease |
| title_full | A Mathematical Investigation of Sex Differences in Alzheimer’s Disease |
| title_fullStr | A Mathematical Investigation of Sex Differences in Alzheimer’s Disease |
| title_full_unstemmed | A Mathematical Investigation of Sex Differences in Alzheimer’s Disease |
| title_short | A Mathematical Investigation of Sex Differences in Alzheimer’s Disease |
| title_sort | mathematical investigation of sex differences in alzheimer s disease |
| topic | Alzheimer’s disease mathematical model variable-order fractional derivative sex differences |
| url | https://www.mdpi.com/2504-3110/6/8/457 |
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