Abstract
Assuming that along the pulmonary arteries, mathematical expectations of branching are equal to matrix (E i,j; i: parent branch class, j: daughter branch class number), we made computer drafts of patterns of pulmonary arterial branching trees from the published data of canine pulmonary arterial casts with the “Monte Carlo methods” by FORTRAN, calculating from these data, the numbers of branches, size and resistance of the trees. We also analyzed blood flow distribution in a pulmonary branch according to the pathlength from the entrance of the tree. The graphics of the trees were similar to the original arterial casts, and numbers of the branches were nearly the same as the previous reported values. Calculated resistance was reasonable. The rate of blood flow per unit vessel in the short pathlength group was calculated as 1.5 times that of the long pathlength group of the same diameter. We believe that our method of describing the branching pattern matrix (E i,j) provides a reasonable simulation of complex branching patterns such as pulmonary arteries and a useful means to analyze local hemodynamics.
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Abbreviations
- i:
-
class number of parent element
- j:
-
class number of daughter element
- k :
-
branching number
- m :
-
daughter element number at one branching
- n :
-
number of pathlength group
- z :
-
generation number
- d z,i :
-
diameter ofzth-generation and i-class element
- len(i):
-
length of i-class element
- N i,j :
-
observed number of j-class from i-class
- Nt:
-
total number of branching
- N el(i):
-
element number of i-class element
- N tr(i):
-
tree number of i-class element
- TNEEt :
-
total number of the exits of the model of tree
- TNEE(n):
-
total number of the exit elements of group-n
- R:
-
resistance
- Rp:
-
peripheral resistance from one exit to left atrium
- Rt:
-
peripheral resistance from one exit to left atrium
- Rt(n):
-
Rt when the Rp ofn-group is infinite
- Rc:
-
the imaginary resistance of the model of tree
- C 1(n):
-
the imaginary conductance of one exit vessel of n-group
- r :
-
random disit
- E i,j :
-
the matrix of mathematical expectation of branching
- a :
-
coefficient of becoming narrow
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Onuki, T., Nitta, S. Computer simulation of geometry and hemodynamics of canine pulmonary arteries. Ann Biomed Eng 21, 107–115 (1993). https://doi.org/10.1007/BF02367606
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DOI: https://doi.org/10.1007/BF02367606