The relationship between lymphangion chain length and maximum pressure generation established through in vivo imaging and computational modeling

Abstract

The intrinsic contraction of collecting lymphatic vessels serves as a pumping system to propel lymph against hydrostatic pressure gradients as it returns interstitial fluid to the venous circulation. In the present study, we proposed and validated that the maximum opposing outflow pressure along a chain of lymphangions at which flow can be achieved increases with the length of chain. Using minimally invasive near-infrared imaging to measure the effective pumping pressure at various locations in the rat tail, we demonstrated increases in pumping pressure along the length of the tail. Computational simulations based on a microstructurally motivated model of a chain of lymphangions informed from biaxial testing of isolated vessels was used to provide insights into the pumping mechanisms responsible for the pressure increases observed in vivo. These models suggest that the number of lymphangions in the chain and smooth muscle cell force generation play a significant role in determining the maximum outflow pressure, whereas the frequency of contraction has no effect. In vivo administration of nitric oxide attenuated lymphatic contraction, subsequently lowering the effective pumping pressure. Computational simulations suggest that the reduction in contractile strength of smooth muscle cells in the presence of nitric oxide can account for the reductions in outflow pressure observed along the lymphangion chain in vivo. Thus, combining modeling with multiple measurements of lymphatic pumping pressure provides a method for approximating intrinsic lymphatic muscle activity noninvasively in vivo while also providing insights into factors that determine the extent that a lymphangion chain can transport fluid against an adverse pressure gradient. NEW & NOTEWORTHY Here, we report the first minimally invasive in vivo measurements of the relationship between lymphangion chain length and lymphatic pumping pressure. We also provide the first in vivo validation of lumped parameter models of lymphangion chains previously developed through data obtained from isolated vessel testing.

Keywords: contractility; lymph transport; lymphedema; microstructure-constitutive models.

Fig. 1.

Experimental setup for measuring lymphatic pumping pressure. The pressure cuff is positioned at various locations measured from the tip of the tail. Flow restoration is imaged by capturing the return of fluorescence into the collecting lymphatic vessel (LV) in a region proximal to cuff. The pressure at which flow restoration is observed is reported as the effective lymphatic pumping pressure and compared with barometric pressure in the computational model. ROI, region of interest.

Fig. 2.

Geometric and microstructural properties of rat tail lymphatics along various regions of the tail. A–C: cannulated lymphatic vessels isolated from regions 12 cm (A), 8 cm (B), and 4 cm (C) from the tip of the tail, as shown in D. E–G: second harmonic generation images of collagen microstructure of vessels isolated from regions 12 cm (E), 8 cm (F), and 4 cm (G) from the tip of the tail. H: chain of lymphangions showing typical valve spacing along the length of the chain.

Fig. 3.

Schematic of the solving routine for computational framework used to model a chain of lymphangions in a series arrangement. T_act, activation parameter; t, time.

Fig. 4.

The maximum outflow pressure at which flow can be achieved as a function of chain length using in vivo near-infrared imaging measurements and computational modeling. The activation parameter (T_act) that is associated with the degree of smooth muscle cell activation is the sum of phasic and tonic activation parameters (see Eq. 7) and was iteratively solved for to provide the best fit for the experimental data. SEs along with the mean at 4 cm (n = 3), 8 cm (n = 4), and 12 cm (n = 5) distance from the tip of tail were plotted. Statistical significance was determined through a Kruskal-Wallis test with a post hoc Dunn’s test for multiple comparisons (**P < 0.05).

Fig. 5.

Flow rate as function of outflow pressure in the lymphangion chains. A: flow rates for different numbers of lymphangions in a chain with an activation parameter (T_act) = 10.9 kPa. B: flow rates for different values of T_act of smooth muscle cells in a chain with 36 lymphangions.

Fig. 6.

Muscle activation (T_act) and the number of lymphangions in a chain both serve to increase the maximum pressure generation capacity of a lymphatic chain. T_act and lymphangion number were both varied over ranges that have been measured in vivo. T_act = 10.9 kPa (y = 1.3733x, R² = 0.947); T_act = 8.7 kPa (y = 1.0526x, R² = 0.9609); T_act = 6.6 kPa (y = 0.7026x, R² = 0.9517); T_act = 4.4 kPa (y = 0.3619x; R² = 0.908), where x and y denote outflow pressure – inflow pressure and lymphangion number, respectively.

Fig. 7.

Maximum flow rate that can be achieved when there is no adverse pressure gradient present due to the intrinsic contraction of lymphangions with a different number of lymphangions in the chain as a function of lymphatic smooth muscle activation. T_act, activation parameter.

Fig. 8.

Effect of refractory time on flow rate and maximum pressure in a chain of 8 lymphangions (A) and flow rate generated by intrinsic contraction of lymphangions for chains exposed to different opposing outflow pressures (B).

Fig. 9.

Effect of frequency on maximum pressure that can be overcome by a lymphangion chain to maintain flow rate. A: computational results for a chain of 8 lymphangions (activation parameter = 10.9 kPa). B: experimental results from the rat tail model demonstrate that there was no correlation between the baseline packet frequency and effective pumping pressure.

Fig. 10.

Effect of dermal nitric oxide (NO) delivery on the relationship between maximum outflow pressure and length from the tip of the tail using in vivo near-infrared imaging pumping pressure measurements and the computational model. The activation parameter associated with the degree of smooth muscle cell activation that best fits the in vivo NO experiments was found to be T_act = 4.4 kPa. SEs along with the mean at 4 cm (n = 4), 8 cm (n = 3), and 12 cm (n = 12) distance from the tip of the tail were plotted. Significant difference between the control and glyceryl trinitrate ointment data sets was determined using an extra sum of squares F-test on the quadratic best-fit regressions of the data (P < 0.05).