Abstract

Balloon dilation catheters are often used to quantify the physiological state of peristaltic activity in tubular organs and comment on their ability to propel fluid which is important for healthy human function. To fully understand this system's behavior, we analyzed the effect of a solitary peristaltic wave on a fluid-filled elastic tube with closed ends. A reduced order model that predicts the resulting tube wall deformations, flow velocities, and pressure variations is presented. This simplified model is compared with detailed fluid–structure three-dimensional (3D) immersed boundary (IB) simulations of peristaltic pumping in tube walls made of hyperelastic material. The major dynamics observed in the 3D simulations were also displayed by our one-dimensional (1D) model under laminar flow conditions. Using the 1D model, several pumping regimes were investigated and presented in the form of a regime map that summarizes the system's response for a range of physiological conditions. Finally, the amount of work done during a peristaltic event in this configuration was defined and quantified. The variation of elastic energy and work done during pumping was found to have a unique signature for each regime. An extension of the 1D model is applied to enhance patient data collected by the device and find the work done for a typical esophageal peristaltic wave. This detailed characterization of the system's behavior aids in better interpreting the clinical data obtained from dilation catheters. Additionally, the pumping capacity of the esophagus can be quantified for comparative studies between disease groups.

References

References
1.
Jaffrin
,
M. Y.
, and
Shapiro
,
A. H.
,
1971
, “
Peristaltic Pumping
,”
Annu. Rev. Fluid Mech.
,
3
(
1
), pp.
13
37
.10.1146/annurev.fl.03.010171.000305
2.
Fung
,
Y. C.
, and
Yih
,
C. S.
,
1968
, “
Peristaltic Transport
,”
ASME J. Appl. Mech.
,
35
(
4
), pp.
669
675
.10.1115/1.3601290
3.
Burns
,
J. C.
, and
Parkes
,
T.
,
1967
, “
Peristaltic Motion
,”
J. Fluid Mech.
,
29
(
4
), pp.
731
743
.10.1017/S0022112067001156
4.
Latham
,
T. W.
,
1966
, “
Fluid Motions in a Peristaltic Pump
,”
Ph.D. thesis
,
Massachusetts Institute of Technology
, Cambridge, MA.http://hdl.handle.net/1721.1/17282
5.
Takabatake
,
S.
, and
Ayukawa
,
K.
,
1982
, “
Numerical Study of Two-Dimensional Peristaltic Flows
,”
J. Fluid Mech.
,
122
(
1
), p.
439
.10.1017/S0022112082002304
6.
Siddiqui
,
A.
, and
Schwarz
,
W.
,
1994
, “
Peristaltic Flow of a Second-Order Fluid in Tubes
,”
J. Non-Newtonian Fluid Mech.
,
53
, pp.
257
284
.10.1016/0377-0257(94)85052-6
7.
Bohme
,
G.
, and
Friedrich
,
R.
,
1983
, “
Peristaltic Flow of Viscoelastic Liquids
,”
J. Fluid Mech.
,
128
(
1
), pp.
109
122
.10.1017/S0022112083000403
8.
Mekheimer
,
K. S.
,
1998
,
Int. J. Theor. Phys.
,
37
(
11
), pp.
2895
2920
.10.1023/A:1026657629065
9.
Hung
,
T.-K.
, and
Brown
,
T. D.
,
1976
, “
Solid-Particle Motion in Two-Dimensional Peristaltic Flows
,”
J. Fluid Mech.
,
73
(
1
), pp.
77
96
.10.1017/S0022112076001262
10.
Chrispell
,
J.
, and
Fauci
,
L.
,
2011
, “
Peristaltic Pumping of Solid Particles Immersed in a Viscoelastic Fluid
,”
Math. Modell. Nat. Phenom.
,
6
(
5
), pp.
67
83
.10.1051/mmnp/20116504
11.
Takagi
,
D.
, and
Balmforth
,
N. J.
,
2011
, “
Peristaltic Pumping of Viscous Fluid in an Elastic Tube
,”
J. Fluid Mech.
,
672
, pp.
196
218
.10.1017/S0022112010005914
12.
Carew
,
E. O.
, and
Pedley
,
T. J.
,
1997
, “
An Active Membrane Model for Peristaltic Pumping—Part I: Periodic Activation Waves in an Infinite Tube
,”
ASME J. Biomech. Eng.
,
119
(
1
), pp.
66
76
.10.1115/1.2796066
13.
Griffiths
,
D. J.
,
1987
, “
Dynamics of the Upper Urinary Tract: I. Peristaltic Flow Through a Distensible Tube of Limited Length
,”
Phys. Med. Biol.
,
32
(
7
), pp.
813
822
.10.1088/0031-9155/32/7/002
14.
Li
,
M.
, and
Brasseur
,
J. G.
,
1993
, “
Non-Steady Peristaltic Transport in Finite-Length Tubes
,”
J. Fluid Mech.
,
248
, pp.
129
151
.10.1017/S0022112093000710
15.
Takabatake
,
S.
,
Ayukawa
,
K.
, and
Mori
,
A.
,
1988
, “
Peristaltic Pumping in Circular Cylindrical Tubes: A Numerical Study of Fluid Transport and Its Efficiency
,”
J. Fluid Mech.
,
193
(
1
), p.
267
.10.1017/S0022112088002149
16.
Carlson
,
D. A.
,
Lin
,
Z.
,
Kahrilas
,
P. J.
,
Sternbach
,
J.
,
Donnan
,
E. N.
,
Friesen
,
L.
,
Listernick
,
Z.
,
Mogni
,
B.
, and
Pandolfino
,
J. E.
,
2015
, “
The Functional Lumen Imaging Probe Detects Esophageal Contractility Not Observed With Manometry in Patients With Achalasia
,”
Gastroenterology
,
149
(
7
), pp.
1742
1751
.10.1053/j.gastro.2015.08.005
17.
Regan
,
J.
,
Walshe
,
M.
,
Rommel
,
N.
,
Tack
,
J.
, and
McMahon
,
B. P.
,
2013
, “
New Measures of Upper Esophageal Sphincter Distensibility and Opening Patterns During Swallowing in Healthy Subjects Using EndoFLIP
,”
Neurogastroenterol. Motil.
,
25
(
1
), pp.
e25
e34
.10.1111/nmo.12041
18.
Kwiatek
,
M. A.
,
Pandolfino
,
J. E.
,
Hirano
,
I.
, and
Kahrilas
,
P. J.
,
2010
, “
Esophagogastric Junction Distensibility Assessed With an Endoscopic Functional Luminal Imaging Probe (EndoFLIP)
,”
Gastrointest. Endoscopy
,
72
(
2
), pp.
272
278
.10.1016/j.gie.2010.01.069
19.
Jain
,
A. S.
,
Carlson
,
D. A.
,
Triggs
,
J.
,
Tye
,
M.
,
Kou
,
W.
,
Campagna
,
R.
,
Hungness
,
E.
,
Kim
,
D.
,
Kahrilas
,
P. J.
, and
Pandolfino
,
J. E.
,
2019
, “
Esophagogastric Junction Distensibility on Functional Lumen Imaging Probe Topography Predicts Treatment Response in Achalasia—Anatomy Matters!
,”
Am. J. Gastroenterol.
,
114
(
9
), pp.
1455
1463
.10.14309/ajg.0000000000000137
20.
Kou
,
W.
,
Pandolfino
,
J. E.
,
Kahrilas
,
P. J.
, and
Patankar
,
N. A.
,
2015
, “
Simulation Studies of Circular Muscle Contraction, Longitudinal Muscle Shortening, and Their Coordination in Esophageal Transport
,”
Am. J. Physiol.: Gastrointest. Liver Physiol.
,
309
(
4
), pp.
G238
G247
.10.1152/ajpgi.00058.2015
21.
Ott
,
D. J.
,
Chen
,
Y. M.
,
Hewson
,
E. G.
,
Richter
,
J. E.
,
Dalton
,
C. B.
,
Gelfand
,
D. W.
, and
Wu
,
W. C.
,
1989
, “
Esophageal Motility: Assessment With Synchronous Video Tape Fluoroscopy and Manometry
,”
Radiology
,
173
(
2
), pp.
419
422
.10.1148/radiology.173.2.2798872
22.
Wang
,
X.
,
Fullana
,
J.-M.
, and
Lagrée
,
P.-Y.
,
2015
, “
Verification and Comparison of Four Numerical Schemes for a 1D Viscoelastic Blood Flow Model
,”
Comput. Methods Biomech. Biomed. Eng.
,
18
(
15
), pp.
1704
1725
.10.1080/10255842.2014.948428
23.
Manopoulos
,
C. G.
,
Mathioulakis
,
D. S.
, and
Tsangaris
,
S. G.
,
2006
, “
One-Dimensional Model of Valveless Pumping in a Closed Loop and a Numerical Solution
,”
Phys. Fluids
,
18
(
1
), p.
017106
.10.1063/1.2165780
24.
Bringley
,
T. T.
,
Childress
,
S.
,
Vandenberghe
,
N.
, and
Zhang
,
J.
,
2008
, “
An Experimental Investigation and a Simple Model of a Valveless Pump
,”
Phys. Fluids
,
20
(
3
), p.
033602
.10.1063/1.2890790
25.
Ottesen
,
J.
,
2003
, “
Valveless Pumping in a Fluid-Filled Closed Elastic Tube-System: One-Dimensional Theory With Experimental Validation
,”
J. Math. Biol.
,
46
(
4
), pp.
309
332
.10.1007/s00285-002-0179-1
26.
Kwiatek
,
M. A.
,
Hirano
,
I.
,
Kahrilas
,
P. J.
,
Rothe
,
J.
,
Luger
,
D.
, and
Pandolfino
,
J. E.
,
2011
, “
Mechanical Properties of the Esophagus in Eosinophilic Esophagitis
,”
Gastroenterology
,
140
(
1
), pp.
82
90
.10.1053/j.gastro.2010.09.037
27.
Whittaker
,
R. J.
,
Heil
,
M.
,
Jensen
,
O. E.
, and
Waters
,
S. L.
,
2010
, “
A Rational Derivation of a Tube Law From Shell Theory
,”
Q. J. Mech. Appl. Math.
,
63
(
4
), pp.
465
496
.10.1093/qjmam/hbq020
28.
LeVeque
,
R. J.
,
1990
,
Numerical Methods for Conservation Laws
,
Birkhäuser
,
Basel, Switzerland
.10.1007/978-3-0348-5116-9
29.
Grotberg
,
J. B.
, and
Jensen
,
O. E.
,
2004
, “
Biofluid Mechanics in Flexible Tubes
,”
Annu. Rev. Fluid Mech.
,
36
(
1
), pp.
121
147
.10.1146/annurev.fluid.36.050802.121918
30.
Mcclurken
,
M. E.
,
Kececioglu
,
I.
,
Kamm
,
R. D.
, and
Shapiro
,
A. H.
,
1981
, “
Steady, Supercritical Flow in Collapsible Tubes—Part 2: Theoretical Studies
,”
J. Fluid Mech.
,
109
, pp.
391
415
.10.1017/S0022112081001134
31.
Pouderoux
,
P.
,
Lin
,
S.
, and
Kahrilas
,
P. J.
,
1997
, “
Timing, Propagation, Coordination, and Effect of Esophageal Shortening During Peristalsis
,”
Gastroenterology
,
112
(
4
), pp.
1147
1154
.10.1016/S0016-5085(97)70125-2
32.
Kou
,
W.
,
Griffith
,
B. E.
,
Pandolfino
,
J. E.
,
Kahrilas
,
P. J.
, and
Patankar
,
N. A.
,
2017
, “
A Continuum Mechanics-Based Musculo-Mechanical Model for Esophageal Transport
,”
J. Comput. Phys.
,
348
, pp.
433
459
.10.1016/j.jcp.2017.07.025
33.
IBAMR
,
2020
, “
IBAMR: An Adaptive and Distributed-Memory Parallel Implementation of the Immersed Boundary (IB) Method
,” IBAMR, accessed Aug. 25, 2020, https://ibamr.github.io/
34.
Griffith
,
B. E.
, and
Luo
,
X.
,
2017
, “
Hybrid Finite Difference/Finite Element Immersed Boundary Method
,”
Int. J. Numer. Methods Biomed. Eng.
,
33
(
12
), p.
e2888
.10.1002/cnm.2888
35.
Kou
,
W.
,
Bhalla
,
A. P. S.
,
Griffith
,
B. E.
,
Pandolfino
,
J. E.
,
Kahrilas
,
P. J.
, and
Patankar
,
N. A.
,
2015
, “
A Fully Resolved Active Musculo-Mechanical Model for Esophageal Transport
,”
J. Comput. Phys.
,
298
, pp.
446
465
.10.1016/j.jcp.2015.05.049
36.
Stankovic
,
Z.
,
Allen
,
B. D.
,
Garcia
,
J.
,
Jarvis
,
K. B.
, and
Markl
,
M.
,
2014
, “
4D Flow Imaging With MRI
,”
Cardiovasc. Diagn. Ther.
,
4
(
2
), pp. 173–192https://cdt.amegroups.com/article/view/3630.
37.
Mittal
,
R. K.
,
2016
, “
Regulation and Dysregulation of Esophageal Peristalsis by the Integrated Function of Circular and Longitudinal Muscle Layers in Health and Disease
,”
Am. J. Physiol.: Gastrointest. Liver Physiol.
,
311
(
3
), pp.
G431
G443
.10.1152/ajpgi.00182.2016
38.
Abrahao
, Jr.
,
L.
,
Bhargava
,
V.
,
Babaei
,
A.
,
Ho
,
A.
, and
Mittal
,
R. K.
,
2011
, “
Swallow Induces a Peristaltic Wave of Distension That Marches in Front of the Peristaltic Wave of Contraction
,”
Neurogastroenterol. Motil.
,
23
(
3
), pp.
201
e110
.10.1111/j.1365-2982.2010.01624.x
39.
Halder
,
S.
,
Acharya
,
S.
,
Kou
,
W.
,
Kahrilas
,
P. J.
,
Pandolfino
,
J. E.
, and
Patankar
,
N. A.
,
2021
, “
Mechanics Informed Fluoroscopy of Esophageal Transport
,”
Biomech. Model. Mechanobiol.
, epub.10.1007/s10237-021-01420-0
40.
Acharya
,
S.
,
Halder
,
S.
,
Carlson
,
D. A.
,
Kou
,
W.
,
Kahrilas
,
P. J.
,
Pandolfino
,
J. E.
, and
Patankar
,
N. A.
,
2021
, “
Assessment of Esophageal Body Peristaltic Work Using Functional Lumen Imaging Probe Panometry
,”
Am. J. Physiol.: Gastrointest. Liver Physiol.
,
320
(
2
), pp.
G217
G226
.10.1152/ajpgi.00324.2020
41.
Towns
,
J.
,
Cockerill
,
T.
,
Dahan
,
M.
,
Foster
,
I.
,
Gaither
,
K.
,
Grimshaw
,
A.
,
Hazlewood
,
V.
,
Lathrop
,
S.
,
Lifka
,
D.
,
Peterson
,
G. D.
,
Roskies
,
R.
,
Scott
,
J. R.
, and
Wilkins-Diehr
,
N.
,
2014
, “
XSEDE: Accelerating Scientific Discovery
,”
Comput. Sci. Eng.
,
16
(
5
), pp.
62
74
.10.1109/MCSE.2014.80
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