Quantification of particle deposition patterns, transit times, and shear exposure is important for computational fluid dynamic (CFD) studies involving respiratory and arterial models. To numerically compute such path-dependent quantities, it is necessary to employ a Lagrangian approach where particles are tracked through a pre-computed velocity field. However, it is difficult to determine in advance whether a particular velocity field is sufficiently resolved for the purposes of tracking particles accurately. Towards this end, we propose the use of volumetric residence time (VRT)—previously defined for 2-D studies of platelet activation and here extended to more physiologically relevant 3-D models—as a means of quantifying whether a volume of Lagrangian fluid elements (LFE’s) seeded uniformly and contiguously at the model inlet remains uniform throughout the flow domain. Such “Lagrangian mass conservation” is shown to be satisfied when VRT=1 throughout the model domain. To demonstrate this novel concept, we computed maps of VRT and particle deposition in 3-D steady flow models of a stenosed carotid bifurcation constructed with one adaptively refined and three nominally uniform finite element meshes of increasing element density. A key finding was that uniform VRT could not be achieved for even the most resolved meshes and densest LFE seeding, suggesting that care should be taken when extracting quantitative information about path-dependent quantities. The VRT maps were found to be useful for identifying regions of a mesh that were under-resolved for such Lagrangian studies, and for guiding the construction of more adequately resolved meshes.

1.
Oldham
,
M. J.
,
Phalen
,
R. F.
, and
Heistracher
,
T.
,
2000
, “
Computational Fluid Dynamic Predictions and Experimental Results for Particle Deposition in an Airway Model
,”
Aerosol. Sci. Technol.
,
32
, pp.
61
71
.
2.
Bala´sha´zy
,
I.
,
Hofmann
,
W.
, and
Heistracher
,
T.
,
1999
, “
Computation of Local Enhancement Factors for the Quantification of Particle Deposition Patterns in Airway Bifurcations
,”
J. Aerosol Sci.
,
30
, No.
2
, pp.
185
203
.
3.
Comer
,
J. K.
,
Kleinstreuer
,
C.
,
Hyun
,
S.
, and
Kim
,
C. S.
,
2000
, “
Aerosol Transport and Deposition in Sequentially Bifurcating Airways
,”
ASME J. Biomech. Eng.
,
122
, pp.
152
158
.
4.
Sarangapani
,
R.
, and
Wexler
,
A. S.
,
2000
, “
Modeling Particle Deposition in Extrathoracic Airways
,”
Aerosol Sci. Technol.
,
32
, pp.
72
89
.
5.
Heistracher
,
T.
,
Hofmann
,
W.
, and
Bala´sha´zy
,
I.
,
1996
, “
Transit Time Distribution of Aerosols in 3-D Lung Bifurcations
,”
J. Aerosol Sci.
,
27
, Suppl 1, pp.
5603
5604
.
6.
Buchanan
, Jr.,
J. R.
, and
Kleinstreuer
,
C.
,
1998
, “
Simulation of Particle Hemodynamics in a Partially Occluded Artery Segment With Implications to the Initiation of Microemboli and Secondary Stenoses
,”
J. Biomech. Eng.
,
120
, pp.
446
454
.
7.
Buchanan
, Jr.,
J. R.
,
Kleinstreuer
,
C.
, and
Comer
,
J. K.
,
2000
, “
Rheological Effects on Pulsatile Hemodynamics in a Stenosed Tube
,”
Comput. Fluids
,
29
, pp.
695
724
.
8.
Schoephoerster
,
R. T.
,
Oynes
,
F.
, and
Nunez
,
G.
,
Kapadvanjwala
,
M.
, and
Dewanjee
,
M. K.
,
1993
, “
Effects of Local Geometry and Fluid Dynamics on Regional Platelet Deposition on Artificial Surfaces
,”
Arterioscler. Thromb.
,
13
, No.
12
, pp.
1806
1813
.
9.
Bala´sha´zy
,
I.
,
1994
, “
Simulation of Particle Trajectories in Bifurcating Tubes
,”
J. Comput. Phys.
,
110
, pp.
11
22
.
10.
Buchanan, J. R., Jr., 1996, “Hemodynamic Analysis of Blood in a Stenosed Artery Segment,” M.S. Thesis, North Carolina State University, Raleigh, NC.
11.
Kunov
,
M. J.
,
Steinman
,
D. A.
, and
Ethier
,
C. R.
,
1996
, “
Particle Volumetric Residence Time Calculations in Arterial Geometries
,”
ASME J. Biomech. Eng.
,
118
, No.
2
, pp.
158
164
.
12.
Caro, C. G., Pedley, T. J., Schroter, R. C., and Seed, W. A., 1978, The Mechanics of the Circulation, Oxford University Press, New York, p. 40.
13.
Smith
,
R. F.
,
Rutt
,
B. K.
,
Fox
,
A. J.
,
Rankin
,
R. N.
, and
Holdsworth
,
D. W.
,
1996
, “
Geometric Characterization of Stenosed Human Carotid Arteries
,”
Acad. Radiol.
,
3
, No.
11
, pp.
898
911
.
14.
Ethier
,
C. R.
,
Prakash
,
S.
,
Steinman
,
D. A.
,
Leask
,
R.
,
Couch
,
G.
, and
Ojha
,
M.
,
2000
, “
Steady Flow Separation Patterns in a 45 Degree Junction
,”
J. Fluid Mech.
,
411
, pp.
1
38
.
15.
Minev
,
P. D.
, and
Ethier
,
C. R.
,
1999
, “
A Characteristic/Finite Element Algorithm for the 3-D Navier-Stokes Equations Using Unstructured Grids
,”
Comput. Methods Appl. Mech. Eng.
,
178
, pp.
39
50
.
16.
Bharadvaj
,
B. K.
,
Mabon
,
R. F.
, and
Giddens
,
D. P.
,
1982
, “
Steady Flow in a Model of the Human Carotid Bifurcation. Part II—Laser-Doppler Anemometer Measurements
,”
J. Biomech.
,
15
, No.
5
, pp.
363
378
.
17.
Prakash
,
S.
, and
Ethier
,
C. R.
,
2001
, “
Requirements for Mesh Resolution in 3-D Computational Hemodynamics
,”
ASME J. Biomech. Eng.
,
123
, No.
2
, pp.
134
144
.
18.
Jandl, J. H., 1996, Blood: Textbook of Hematology, 2nd ed., Little, Brown and Company, Toronto, p. 652 & 1301.
19.
Kenwright
,
D. N.
, and
Lane
,
D. A.
,
1996
, “
Interactive Time-Dependent Particle Tracing Using Tetrahedral Decomposition
,”
IEEE Trans. Vis. Comput. Graph.
,
2
, No.
2
, pp.
120
129
.
20.
Affeld
,
K.
,
Reininger
,
A. J.
,
Gadischke
,
J.
,
Grunert
,
K.
,
Schmidt
,
S.
, and
Thiele
,
F.
,
1995
, “
Fluid Mechanics of the Stagnation Point Flow Chamber and Its Platelet Deposition
,”
Artif. Organs
,
19
, No.
7
, pp.
597
602
.
21.
Tambasco
,
M.
, and
Steinman
,
D. A.
,
2001
, “
Calculating Particle-to-Wall Distances in Unstructured Computational Fluid Dynamic Models
,”
Appl. Math. Model.
,
25
, pp.
803
814
.
22.
Goldsmith
,
H. L.
, and
Turitto
,
V. T.
,
1986
, “
Rheological Aspects of Thrombosis and Haemostasis: Basic Principles and Applications
,”
Thromb. Haemostasis
,
55
, No.
3
, pp.
415
435
.
23.
Berger
,
S. A.
, and
Jou
,
L.-D.
,
2000
, “
Flows in Stenotic Vessels
,”
Annu. Rev.
,
32
, pp.
347
382
.
24.
Heistracher
,
T.
, and
Hofmann
,
W.
,
1995
, “
Physiologically Realistic Models of Bronchial Airway Bifurcations
,”
J. Aerosol Sci.
,
26
, No.
3
, pp.
497
509
.
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