Publications by authors named "Christopher D Bertram"

9 Publications

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Modeling flow in embryonic lymphatic vasculature: what is its role in valve development?

Math Biosci Eng 2021 01;18(2):1406-1424

School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia.

A majority of lymphatic valves tend to form in proximity to vessel junctions, and it is often proposed that disturbed flow at junctions creates oscillating shear stress that leads to accumulation of transcription factors which bring about valvogenesis at these sites. In images of networks of dorsal skin lymphatics from embryonic mice (day E16), we compared simulated fluid flow patterns and observed distributions of the transcription factor Prox1, which is implicated in valve formation. Because of creeping-flow conditions, flow across vessel junctions was not 'disturbed', and within a given vessel, shear stress varied inversely with local conduit width. Prox1 concentration was indeed localised to vessel end-regions, but over three networks was not consistently correlated with the vessel normalised-distance distribution of either fluid shear stress or shear-stress axial gradient. These findings do not support the presently accepted mechanism for the role of flow in valve localisation.
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http://dx.doi.org/10.3934/mbe.2021073DOI Listing
January 2021

Lymphatic System Flows.

Annu Rev Fluid Mech 2018 Jan;50:459-482

School of Mathematics and Statistics, University of Sydney, Australia.

The supply of oxygen and nutrients to tissues is performed by the blood system, and involves a net leakage of fluid outward at the capillary level. One of the principal functions of the lymphatic system is to gather this fluid and return it to the blood system to maintain overall fluid balance. Fluid in the interstitial spaces is often at subatmospheric pressure, and the return points into the venous system are at pressures of approximately 20 cmHO. This adverse pressure difference is overcome by the active pumping of collecting lymphatic vessels, which feature closely spaced one-way valves and contractile muscle cells in their walls. Passive vessel squeezing causes further pumping. The dynamics of lymphatic pumping have been investigated experimentally and mathematically, revealing complex behaviours indicating that the system performance is robust against minor perturbations in pressure and flow. More serious disruptions can lead to incurable swelling of tissues called lymphœdema.
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http://dx.doi.org/10.1146/annurev-fluid-122316-045259DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5922450PMC
January 2018

Demonstration and Analysis of the Suction Effect for Pumping Lymph from Tissue Beds at Subatmospheric Pressure.

Sci Rep 2017 09 21;7(1):12080. Epub 2017 Sep 21.

Department of Bioengineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom.

Many tissues exhibit subatmospheric interstitial pressures under normal physiologic conditions. The mechanisms by which the lymphatic system extracts fluid from these tissues against the overall pressure gradient are unknown. We address this important physiologic issue by combining experimental measurements of contractile function and pressure generation with a previously validated mathematical model. We provide definitive evidence for the existence of 'suction pressure' in collecting lymphatic vessels, which manifests as a transient drop in pressure downstream of the inlet valve following contraction. This suction opens the inlet valve and is required for filling in the presence of low upstream pressure. Positive transmural pressure is required for this suction, providing the energy required to reopen the vessel. Alternatively, external vessel tethering can serve the same purpose when the transmural pressure is negative. Suction is transmitted upstream, allowing fluid to be drawn in through initial lymphatics. Because suction plays a major role in fluid entry to the lymphatics and is affected by interstitial pressure, our results introduce the phenomenon as another important factor to consider in the study of lymphoedema and its treatment.
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http://dx.doi.org/10.1038/s41598-017-11599-xDOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5608746PMC
September 2017

Consequences of intravascular lymphatic valve properties: a study of contraction timing in a multi-lymphangion model.

Am J Physiol Heart Circ Physiol 2016 Apr 8;310(7):H847-60. Epub 2016 Jan 8.

Department of Bioengineering, Imperial College, London, United Kingdom.

The observed properties of valves in collecting lymphatic vessels include transmural pressure-dependent bias to the open state and hysteresis. The bias may reduce resistance to flow when the vessel is functioning as a conduit. However, lymphatic pumping implies a streamwise increase in mean pressure across each valve, suggesting that the bias is then potentially unhelpful. Lymph pumping by a model of several collecting lymphatic vessel segments (lymphangions) in series, which incorporated these properties, was investigated under conditions of adverse pressure difference while varying the refractory period between active muscular contractions and the inter-lymphangion contraction delay. It was found that many combinations of the timing parameters and the adverse pressure difference led to one or more intermediate valves remaining open instead of switching between open and closed states during repetitive contraction cycles. Cyclic valve switching was reliably indicated if the mean pressure in a lymphangion over a cycle was higher than that in the lymphangion upstream, but either lack of or very brief valve closure could cause mean pressure to be lower downstream. Widely separated combinations of refractory period and delay time were found to produce the greatest flow-rate for a given pressure difference. The efficiency of pumping was always maximized by a long refractory period and lymphangion contraction starting when the contraction of the lymphangion immediately upstream was peaking. By means of an ex vivo experiment, it was verified that intermediate valves in a chain of pumping lymphangions can remain open, while the lymphangions on either side of the open valve continue to execute contractions.
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http://dx.doi.org/10.1152/ajpheart.00669.2015DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4867355PMC
April 2016

Parameter sensitivity analysis of a lumped-parameter model of a chain of lymphangions in series.

Am J Physiol Heart Circ Physiol 2013 Dec 11;305(12):H1709-17. Epub 2013 Oct 11.

Department of Bioengineering, South Kensington Campus, Imperial College London, London, United Kingdom;

Any disruption of the lymphatic system due to trauma or injury can lead to edema. There is no effective cure for lymphedema, partly because predictive knowledge of lymphatic system reactions to interventions is lacking. A well-developed model of the system could greatly improve our understanding of its function. Lymphangions, defined as the vessel segment between two valves, are the individual pumping units. Based on our previous lumped-parameter model of a chain of lymphangions, this study aimed to identify the parameters that affect the system output the most using a sensitivity analysis. The system was highly sensitive to minimum valve resistance, such that variations in this parameter caused an order-of-magnitude change in time-average flow rate for certain values of imposed pressure difference. Average flow rate doubled when contraction frequency was increased within its physiological range. Optimum lymphangion length was found to be some 13-14.5 diameters. A peak of time-average flow rate occurred when transmural pressure was such that the pressure-diameter loop for active contractions was centered near maximum passive vessel compliance. Increasing the number of lymphangions in the chain improved the pumping in the presence of larger adverse pressure differences. For a given pressure difference, the optimal number of lymphangions increased with the total vessel length. These results indicate that further experiments to estimate valve resistance more accurately are necessary. The existence of an optimal value of transmural pressure may provide additional guidelines for increasing pumping in areas affected by edema.
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http://dx.doi.org/10.1152/ajpheart.00403.2013DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3882543PMC
December 2013

Passive pressure-diameter relationship and structural composition of rat mesenteric lymphangions.

Lymphat Res Biol 2012 Dec 12;10(4):152-63. Epub 2012 Nov 12.

Department of Biomedical Engineering, Texas A&M University, College Station, Texas 77843-3120, USA.

Background: Lymph flow depends on both the rate of lymph production by tissues and the extent of passive and active pumping. Here we aim to characterize the passive mechanical properties of a lymphangion in both mid-lymphangion and valve segments to assess regional differences along a lymphangion, as well as evaluating its structural composition.

Methods And Results: Mesenteric lymphatic vessels were isolated and cannulated in a microchamber for pressure-diameter (P-D) testing. Vessels were inflated from 0 to 20 cmH(2)O at a rate of 4 cmH(2)O/min, and vessel diameter was continuously tracked, using an inverted microscope, video camera, and custom LabVIEW program, at both mid-lymphangion and valve segments. Isolated lymphatic vessels were also pressure-fixed at 2 and 7 cmH(2)O and imaged using a nonlinear optical microscope (NLOM) to obtain collagen and elastin structural information. We observed a highly nonlinear P-D response at low pressures (3-5 cmH(2)O), which was modeled using a three-parameter constitutive equation. No significant difference in the passive P-D response was observed between mid-lymphangion and valve regions. NLOM imaging revealed an inner elastin layer and outer collagen layer at all locations. Lymphatic valve leaflets were predominantly elastin with thick axially oriented collagen bands at the insertion points.

Conclusions: We observed a highly nonlinear P-D response at low pressures (3-5 cmH(2)O) and developed the first constitutive equation to describe the passive P-D response for a lymphangion. The passive P-D response did not vary among regions, in agreement with the composition of elastin and collagen in the lymphatic wall.
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http://dx.doi.org/10.1089/lrb.2011.0015DOI Listing
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3525898PMC
December 2012

Three-dimensional ray tracing through curvilinear interfaces with application to laser Doppler anemometry in a blood analogue fluid.

Med Biol Eng Comput 2010 Feb 11;48(2):147-56. Epub 2009 Aug 11.

Graduate School of Biomedical Engineering, University of New South Wales, Sydney, NSW, Australia.

Prediction of the effects of refractive index (RI) mismatch on laser Doppler anemometer (LDA) measurements within a curvilinear cavity (an artificial ventricle) was achieved by developing a general technique for modelling the paths of the convergent beams of the LDA system using 3D vector geometry. Validated by ray tracing through CAD drawings, the predicted maximum tolerance in RI between the solid model and the working fluid was +/- 0.0005, equivalent to focusing errors commensurate with the geometric and alignment uncertainties associated with the flow model and the LDA arrangement. This technique supports predictions of the effects of refraction within a complex geometry. Where the RI mismatch is unavoidable but known, it is possible not only to calculate the true position of the measuring volume (using the probe location and model geometry), but also to estimate degradation in signal quality arising from differential displacement and refraction of the laser beams.
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http://dx.doi.org/10.1007/s11517-009-0511-7DOI Listing
February 2010

Flow-induced oscillation of collapsed tubes and airway structures.

Respir Physiol Neurobiol 2008 Nov 26;163(1-3):256-65. Epub 2008 Apr 26.

Biofluid Mechanics Laboratory, Faculty of Engineering, University of New South Wales, Sydney 2052, Australia.

The self-excited oscillation of airway structures and flexible tubes in response to flow is reviewed. The structures range from tiny airways deep in the lung causing wheezing at the end of a forced expiration, to the pursed lips of a brass musical instrument player. Other airway structures that vibrate include the vocal cords (and their avian equivalent, the syrinx) and the soft palate of a snorer. These biological cases are compared with experiments on and theories for the self-excited oscillation of flexible tubes conveying a flow on the laboratory bench, with particular reference to those observations dealing with the situation where the inertia of the tube wall is dominant. In each case an attempt is made to summarise the current state of understanding. Finally, some outstanding challenges are identified.
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http://dx.doi.org/10.1016/j.resp.2008.04.011DOI Listing
November 2008

Transitional flow at the venous anastomosis of an arteriovenous graft: potential activation of the ERK1/2 mechanotransduction pathway.

J Biomech Eng 2003 Feb;125(1):49-61

Department of Mechanical Engineering and Industrial Engineering, University of Illinois at Chicago, Chicago, Illinois 60607, USA.

We present experimental and computational results that describe the level, distribution, and importance of velocity fluctuations within the venous anastomosis of an arteriovenous graft. The motivation of this work is to understand better the importance of biomechanical forces in the development of intimal hyperplasia within these grafts. Steady-flow in vitro studies (Re = 1060 and 1820) were conducted within a graft model that represents the venous anastomosis to measure velocity by means of laser Doppler anemometry. Numerical simulations with the same geometry and flow conditions were conducted by employing the spectral element technique. As flow enters the vein from the graft, the velocity field exhibits flow separation and coherent structures (weak turbulence) that originate from the separation shear layer. We also report results of a porcine animal study in which the distribution and magnitude of vein-wall vibration on the venous anastomosis were measured at the time of graft construction. Preliminary molecular biology studies indicate elevated activity levels of the extracellular regulatory kinase ERK1/2, a mitogen-activated protein kinase involved in mechanotransduction, at regions of increased vein-wall vibration. These findings suggest a potential relationship between the associated turbulence-induced vein-wall vibration and the development of intimal hyperplasia in arteriovenous grafts. Further research is necessary, however, in order to determine if a correlation exists and to differentiate the vibration effect from that of flow related effects.
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http://dx.doi.org/10.1115/1.1537737DOI Listing
February 2003