On the fractality of the biological tree-like structures
The fractal tree-like structures can be divided into three classes, according to the value of the similarity dimension Ds:Ds<D,Ds=D and Ds>D, where D is the topological dimension of the embedding space. It is argued that most of the physiological tree-like structures have Ds≥D. The notion of t...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | Discrete Dynamics in Nature and Society |
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| Online Access: | http://dx.doi.org/10.1155/S102602269900031X |
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| _version_ | 1832567388055273472 |
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| author | Jaan Kalda |
| author_facet | Jaan Kalda |
| author_sort | Jaan Kalda |
| collection | DOAJ |
| description | The fractal tree-like structures can be divided into three classes, according to the value of the similarity dimension Ds:Ds<D,Ds=D and Ds>D, where D is the topological dimension of the embedding space. It is argued that most of the physiological tree-like structures have Ds≥D. The notion of the self-overlapping exponent is introduced to characterise the trees with Ds>D. A model of the human blood-vessel system is proposed. The model is consistent with the processes governing the growth of the blood-vessels and yields Ds=3.4. The model is used to analyse the transport of passive component by blood. |
| format | Article |
| id | doaj-art-903fe5691f4e461d9118f6cafb91a085 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-903fe5691f4e461d9118f6cafb91a0852025-02-03T01:01:39ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X1999-01-013429730610.1155/S102602269900031XOn the fractality of the biological tree-like structuresJaan Kalda0Institute of Cybernetics, Akadeemia tee 21, Tallinn EEO026, EstoniaThe fractal tree-like structures can be divided into three classes, according to the value of the similarity dimension Ds:Ds<D,Ds=D and Ds>D, where D is the topological dimension of the embedding space. It is argued that most of the physiological tree-like structures have Ds≥D. The notion of the self-overlapping exponent is introduced to characterise the trees with Ds>D. A model of the human blood-vessel system is proposed. The model is consistent with the processes governing the growth of the blood-vessels and yields Ds=3.4. The model is used to analyse the transport of passive component by blood.http://dx.doi.org/10.1155/S102602269900031XFractalsBlood-vesselsTree-like structuresSimilarity dimensionAdvective diffusion. |
| spellingShingle | Jaan Kalda On the fractality of the biological tree-like structures Discrete Dynamics in Nature and Society Fractals Blood-vessels Tree-like structures Similarity dimension Advective diffusion. |
| title | On the fractality of the biological tree-like structures |
| title_full | On the fractality of the biological tree-like structures |
| title_fullStr | On the fractality of the biological tree-like structures |
| title_full_unstemmed | On the fractality of the biological tree-like structures |
| title_short | On the fractality of the biological tree-like structures |
| title_sort | on the fractality of the biological tree like structures |
| topic | Fractals Blood-vessels Tree-like structures Similarity dimension Advective diffusion. |
| url | http://dx.doi.org/10.1155/S102602269900031X |
| work_keys_str_mv | AT jaankalda onthefractalityofthebiologicaltreelikestructures |