Flow resistance along the rat renal tubule

Abstract

The Reynolds number in the renal tubule is extremely low, consistent with laminar flow. Consequently, luminal flow can be described by the Hagen-Poiseuille laminar flow equation. This equation calculates the volumetric flow rate from the axial pressure gradient and flow resistance, which is dependent on the length and diameter of each renal tubule segment. Our goal was to calculate the pressure drop along each segment of the renal tubule and to determine the points of highest resistance. When the Hagen-Poiseuille equation was used for rat superficial nephrons based on known tubule flow rates, lengths, and diameters, it was found that the maximum pressure drop occurred in two segments: the thin descending limbs of Henle and the inner medullary collecting ducts. The high resistance in the thin descending limbs is due to their small diameters. The steep pressure drop observed in the inner medullary collecting ducts is due to the convergent structure of the tubules, which channels flow into fewer and fewer tubules toward the papillary tip. For short-looped nephrons, the calculated glomerular capsular pressure matched measured values, even with the high collecting duct flow rates seen in water diuresis, provided that tubule compliance was taken into account. In long-looped nephrons, the greater length of thin limb segments is likely compensated for by a larger luminal diameter. Simulation of the effect of proximal diuretics, namely acetazolamide or type 2 sodium-glucose transporter inhibitors, predicts a substantial back pressure in Bowman’s capsule, which may contribute to observed decreases in glomerular filtration rate.

INTRODUCTION

Flow along the mammalian renal tubule depends on an axial pressure gradient, driven ultimately by the glomerular capsular pressure (i.e., the hydrostatic pressure in Bowman’s space). Flow resistance along the renal tubule is a function of the tubule diameter and length. Diameter and length vary among the different tubule segments and between superficial and deep nephrons (16, 18, 29). In this paper, we compiled values for diameter and length for each tubule segment in the rat kidney and calculated flow resistance and pressure drop using the Hagen-Poiseuille laminar flow equation. This allows calculation of the pressure drop along the totality of the renal tubule and of the back pressure in the glomerular capsule that would result from increases in flow. The calculations described here focus solely on physical flow resistance and do not attempt to take into account active biological elements such as tubuloglomerular feedback and glomerulotubular balance mechanisms. Understanding the main sites of flow resistance along the renal tubule is important for evaluation of the effects of diuretic conditions on glomerular capsular pressure, which is a determinant of glomerular filtration rate. We evaluated the theoretical effects of two types of diuresis, namely water diuresis and diuresis resulting from inhibition of salt and water absorption in the renal proximal tubule. The latter has seen increased clinical relevance because of the introduction of inhibitors of the type 2 sodium-glucose transporter (SGLT2) for treatment of diabetes mellitus (30).

METHODS

Calculations were done using Microsoft Excel spreadsheets. The supplementary materials include the spreadsheets produced in this study showing all calculations (Supplemental Material for this article is available online at the Journal website). Briefly, the laminar flow equation for a cylindrical tube (8) was used to estimate the pressure drop,

$$\Delta P=\frac{8\mu LQ}{\pi r^4}$$

where ΔP is the pressure drop, μ is the viscosity, L is the length, Q is the volumetric flow rate per tubule, and r is the radius. The units are summarized in Table 1. The hydrostatic pressure in the glomerular capsule (Bowman’s space) and at different points along the renal tubule was calculated by adding up all the pressure drop values for each renal tubule segment starting with the value at the end of the collecting duct system (ducts of Bellini). Therefore, all pressures reported in this paper are referenced to the pressure in the ducts of Bellini. The nephron was divided into the following segments: proximal tubule, thin descending limb, thin ascending limb, thick ascending limb, distal tubule, cortical collecting duct, outer medullary collecting duct, and inner medullary collecting duct. The distal tubule was defined as all tubules between the end of the thick ascending limb and the start of the cortical collecting duct. Specific tubule resistance is defined as ΔP/LQ calculated as 8μ/πr⁴. The assumptions used for this model are as follows: 1) the density and viscosity of the tubule fluid are those of water, 2) the flow within the renal tubules is at a steady state, 3) each renal tubule segment can be modeled as a right circular cylinder.

Table 1.

Variables and parameters with units

Variable	Symbol	Units
Diameter	D	µm
Length	L	µm
Viscosity	µ	mPa s
Volumetric flow rate	Q	nl/min
Density	ρ	g/ml
Reynolds number	Re	unitless
Pressure	ΔP	mmHg
Resistance	R	mmHg/mm

Anatomical parameters are given in Table 2. Diameter measurements were taken from Sperber (29), except for the inner medullary collecting ducts (14) and the thin limbs of Henle’s loops (15, 18). Tubule lengths were estimated from Sperber (29) and from zonal thicknesses given by Sperber (29) and Knepper (14). The full Sperber work has been made available through a posting on a public web site (https://esbl.nhlbi.nih.gov/Databases/Sperber/). Zonal thicknesses used were (in mm): cortex, 2.9; outer medulla, 2.1; inner medulla, 4.7; and inner stripe of outer medulla, 1.5. Zonal thicknesses provided estimates for the length of the short-loop descending limb, the long-loop descending limb, the thin ascending limb, the medullary thick ascending limb, the cortical thick ascending limb (assumed half of cortical thickness), the cortical collecting duct, and the outer medullary collecting duct. The total number of nephrons per kidney was taken as 38,000 for rats (14). Seventy-two percent of these have short loops of Henle that bend in the outer medulla, and 28% have long loops of Henle that bend at various levels in the inner medulla (29). The model takes into account the convergence of renal tubules in the connecting tubule arcades of the cortex [assumes six nephrons merge to form one initial collecting tubule (14)] and in the inner medulla [uses morphometric data from (23)]. The distribution of loop bends in the inner medulla were estimated from Knepper (14).

Table 2.

Tubule anatomical parameters for root calculations

Segment	Inner Diameter, μm	Length, μm	Count	References
Proximal tubule (short-looped nephrons)	22.9	9,886	26,980	(29)
Proximal tubule (long-looped nephrons)	23.1	11,077	11,020	(29)
Thin descending limb (short-looped nephrons)	15.0	1,500	26,980	(15, 29)
Thin descending limb (long-looped nephrons)	15.0	6,200	11,020	(15, 29)
Thin ascending limb (long-looped nephrons)	15.0	4,700	11,020	(15, 29)
Cortical thick ascending limb	25.4	1,450	38,000	(29)
Medullary thick ascending limb	29.0	2,100	38,000	(29)
Distal tubule* (superficial)	39.0	1,452	26,980	(29)
Distal tubule* (deep)	43.0	1,650	11,020	(29)
Cortical collecting duct	24.0	2,900	6,000	(14, 29)
Outer medullary collecting duct	24.0	2,100	6,000	(14, 29)
Inner medullary collecting duct	23.5	variable	variable	(14)

^*Distal tubule, combination of distal convoluted tubule and connecting tubule.

Volumetric flow rates at the beginning of each segment are given in Table 3. Flow rates in water diuresis and antidiuresis were estimated from single-nephron glomerular filtration rate measurements and tubule fluid/plasma (TF/P) inulin measurements from micropuncture studies (11, 12, 28). Because the number of tubules changes in the inner medullary collecting duct, this segment was split into 92 subsegments. The pressure drops were summed to calculate the total pressure drop along the inner medullary collecting duct. In general, a similar segmentation was not done for the other segments. Instead, for these segments the volumetric flow rates used for the calculations were the values at the midpoint of the segment. Examination of TF/P inulin values (inverse of fractional reabsorption) from micropuncture studies indicates a nearly linear fall in flow rate with distance along the proximal tubule (7), justifying the assumption. This assumption was further validated by repeating the calculation after discretizing the proximal tubule into 10 subsegments, which showed no substantial difference in the calculated pressures (Supplemental Data Sheet S21).

Table 3.

Volumetric flow rates at beginning of individual segments during antidiuresis and water diuresis

Segment	Volumetric Flow Rate (nl/min)
Proximal Tubule of Short-Looped Nephrons (SNGFR)	40.9
Proximal Tubule of Long-Looped Nephrons (SNGFR)	39.7
Thin descending limb (short-looped nephrons)	26.4
Thin descending limb (long-looped nephrons)	26.3
Thin ascending limb	8.0
Thick ascending limb (short-looped nephrons)	8.1
Thick ascending limb (long-looped nephrons)	8.0
Distal tubule (short-looped nephrons)	6.0
Distal tubule (long-looped nephrons)	6.0
Cortical collecting duct, antidiuresis	4.7
Cortical collecting duct, diuresis	14.4
Outer medullary collecting duct, antidiuresis	4.7
Outer medullary collecting duct, diuresis	14.4
Inner medullary collecting duct	See supplemental data

Calculated from single-nephron glomerular filtration rate measurements and TF/P inulin measurements obtained in micropuncture studies (11, 12, 28). SNGFR, single-nephron glomerular filtration rate.

In additional simulations, we considered the elasticity of the tubules. The compliance value used for the collecting duct was 0.833 µm/mmHg (22). The compliance value used for the proximal tubule and loop of Henle was 0.133 µm/mmHg (9, 20). Because of the lack of compliance data, the distal tubule was assumed to be inelastic. We assumed a given segment of the renal tubule expanded equally across its length, and we used the pressure at the center of the segment to calculate expansion. Consideration of compliances resulted in three equations which were solved simultaneously using the Gauss-Seidel method,

$$r=r_0+P_{center}C$$

$$\Delta P=\frac{\Delta P_0{r}_0^4}{r^4}$$

$$P_{center}=P+\frac{\Delta P}{2}$$

where P_center is the pressure at the center of the tubule, r is the compliant radius, r₀ is the rigid radius, ΔP is the pressure drop across the compliant tubule, ΔP₀ is the rigid tubule pressure drop, P is the pressure at the end of the tubule, and C is the compliance.

RESULTS

Calculations with the rigid-tube model identify thin limbs of Henle and inner medullary collecting ducts as the major sites of flow resistance along the renal tubule.

The maximum Reynolds number for the renal tubule is 0.06 (Supplemental Data Sheets S2 through S12a), well below the threshold for turbulence in a circular tube (8), justifying the use of the Hagen-Poiseuille equation to calculate the pressure drop along the renal tubule. Figure 1 shows the calculated pressure profile in the superficial nephron and collecting duct referenced to the collecting duct outlet (i.e., the end of the inner medullary collecting duct). The estimated pressure at the glomerular capsule is 8.6 mmHg. For comparison, hydrostatic pressure in Bowman’s capsule of superficial nephrons or Munich-Wistar rats gave values in the range 8–9 mmHg (3), but later studies suggested that this value was higher when measured in well-hydrated, volume-replete Munich-Wistar rats, namely 12–13 mmHg (1). Based on our calculations (Fig. 1) the greatest pressure drop is seen in the early part of the loop of Henle (corresponding to the thin descending limb) and the inner medullary collecting duct. The large pressure drop in the thin descending limb is owing to its small diameter and the resulting high specific tubular resistance (Fig. 2). The large pressure drop in the inner medullary collecting duct is owing to the presence of multiple junctions that markedly reduce the number of collecting ducts toward the papillary tip, thereby increasing the volumetric flow rate in each. Specific tubular resistance is not exceptionally high in the inner medullary collecting duct (Fig. 2). The calculations are consistent with the findings of Marsh et al. (22) who noted the majority of the pressure drop in the collecting ducts was in the inner medulla. When the calculations were repeated under water diuretic conditions (increased flow in collecting duct), the glomerular capsular pressure increased to 15.8 mmHg, which exceeds the measured values reported above (Fig. 1). Although these results exceed reported values, Marsh et al. (22) reported the pressure drop over the collecting ducts was 3.8 and 3.2 times greater under mannitol diuresis and saline diuresis, respectively, when compared with antidiuresis; therefore, the predicted glomerular capsular pressure in this model is not surprising.

Fig. 1.

Gauge pressure relative to papillary tip vs. position for superficial nephron for three models: antidiuresis with rigid renal tubule, water diuresis with rigid renal tubule, and water diuresis with elastic tubule wall.

Fig. 2.

Specific tubular resistance of individual tubule segments. Thin limbs of Henle’s loop have the highest resistance because of a small diameter.

Renal tubule elasticity is critical in the prevention of high glomerular capsule back pressure during water diuresis.

Although the calculated pressure in the glomerular capsule of superficial nephrons during water diuresis is higher than measured, the initial model did not consider possible dilation of the tubules, which would reduce flow resistance. Consequently, we modified the model to account for reported values for renal tubule compliance (elasticity) (see methods). See Supplementary Data set for specific calculations. For water diuresis, the model estimated an increase (in μm) in inner diameter of the proximal tubule from 22.9 to 23.3, the thin descending limb from 15.0 to 15.3, the thick ascending limb from 25.4 to 25.5, the cortical collecting duct from 24.0 to 24.9, the outer medullary collecting duct from 24.0 to 24.3, and the inner medullary collecting duct from 23.5 to 30.3. The elastic model predicted a decreased pressure drop along the renal tubule relative to the rigid model (Fig. 1). The introduction of elastic behavior reduced the estimated glomerular capillary pressure from 15.7 to 11.4 mmHg, well within the reported range of values. We concluded the compliances of the renal tubule walls are critical for luminal flow dynamics.

Effect of longer thin limb lengths on flow resistance in deep nephrons is countered by larger luminal diameter.

In superficial nephrons, the flow resistance is greatest in the thin descending limb because of its small diameter. In deep nephrons with long loops of Henle that extend into the inner medulla, the thin limbs are much longer. This raises the question, “what is the predicted glomerular capsular pressure for long-looped (deep) nephrons?” Figure 3 shows the results using the elastic tubule model for two nephrons extending different distances into the inner medulla (i.e., with loops that bend 1 mm and 5 mm into the inner medulla). The predicted glomerular capsular pressures are considerably higher than for superficial nephrons: 18.3 mmHg for the outer-most and 20.5 mmHg for the inner-most long-loop nephrons. The glomerular capsular pressures in long-looped nephrons are difficult to measure because these glomeruli cannot be reached from the surface of the kidney. Measurements in juxtamedullary glomeruli exposed by longitudinally bisecting the kidney gave a mean glomerular capsular pressure of 17.8 mmHg (5), which is not far from our estimates. However, because the glomerular capsular pressure is a negative determinant of single-nephron glomerular filtration rate (GFR), the glomerular capsular pressures in deep nephrons are unlikely to be substantially higher than in superficial nephrons given that the single-nephron GFR in deep nephrons is equal to or greater than in superficial nephrons (25). Thus, the calculated glomerular capsular pressure is 6–8 mmHg seemingly higher than the likely actual value. This leaves an apparent discrepancy. One possible explanation would be that the diameters of the thin limbs of long loops are greater than those of short loops, thus compensating for the longer lengths. Indeed, Kriz (16) has reported the thin descending limb diameter can be substantially greater in the long-looped nephrons than in short-looped nephrons. Consequently, we repeated the pressure calculations with 1.5× and 2× increases in the diameters of the thin descending and ascending limbs of the long-looped nephrons (Fig. 4). As seen, with larger diameters the predicted glomerular capsular pressure fell to 7.7–10.5 mmHg, which is in the range of measured values in superficial nephrons. This confirms the critical role of the thin limbs of Henle as a determinant of the pressure drop along the nephron and the glomerular capsular pressure.

Fig. 3.

A: gauge pressure relative to papillary tip vs. position. Deep nephron with long-loop length to 5-mm depth. Elastic tubules with antidiuresis. B: deep nephron with long-loop length to 1-mm depth. Elastic tubules with antidiuresis.

Fig. 4.

Effects of increased diameter in thin limbs of long-loop nephrons on pressure profile along renal tubule to 5-mm depth (A) and 1-mm depth (B). Calculations from Fig. 3 were repeated with a 1.5× and 2× diameter.

Sensitivity analysis.

Sensitivity to parameter estimates was tested by varying length, diameter, and volumetric flow rate and calculating pressure profiles. As expected based on the laminar flow equation, variability in the diameter had the greatest effect. In the rigid water diuresis model, a 1.5×-difference in length or volumetric flow rate results in an increase in the net pressure drop along the renal tubule of 7.4 mmHg, and a 0.5×-difference would result in a decrease of 8.0 mmHg. Conversely, a 1.5×-difference in diameter would result in a 12.7-mmHg decrease in the net pressure, and a 0.5×-difference would result in an increase in the net pressure drop of 232.3 mmHg. These findings confirm the importance of the diameter measurements and how variations in the estimates of these values can cause significant changes in the estimated pressure drop.

Effect of solute diuresis in short- and long-looped nephrons.

Agents that inhibit salt and water reabsorption in the proximal tubule, such as acetazolamide, can be expected to increase back pressure in Bowman’s capsule by virtue of increased flow rate in the thin limbs of Henle and the inner medullary collecting duct. Indeed, acetazolamide administration in rats was associated with an increase in pressure in the proximal tubule of ~2 mmHg in association with a decrease in whole kidney GFR (21). Figure 5 shows predicted glomerular capsular pressures for different percent increases in flow out of the proximal tubule. Indeed, increased flow out of the proximal tubule is predicted to increase glomerular capsular pressure by 1%–5%.

Fig. 5.

The glomerular capsular pressure is predicted to increase when proximal tubule volumetric flow increases.

Another class of agents with similar effects are SGLT2 inhibitors, which block transport by the SGLT2 expressed in early portions of the renal proximal tubule. These agents are widely utilized to treat diabetes mellitus. They can lower blood glucose by increasing glucose excretion. Because the transport is coupled to sodium absorption, these inhibitors decrease sodium and fluid reabsorption in the proximal tubule (17, 30). They have also been found to decrease GFR (17, 30), presumably through the tubuloglomerular feedback mechanism. The calculations in Fig. 5 suggest these inhibitors may decrease GFR in another way, namely by increasing hydrostatic pressure in Bowman’s space.

Applications to other species.

Using the Sperber data, L/r⁴ ratios were calculated for a variety of different species and are shown in Table 4 (29). L/r⁴ is proportional to the resistance to flow and across all species considered, the highest value was in the thin descending limb. This finding suggests the conclusions regarding the pressure profile along the nephron, drawn from the rat, are likely applicable to other species. In the collecting duct, a convergence of collecting ducts appears to be a general feature in many mammals (14), including humans (24) leading to the conclusion that a large pressure drop in the inner medullary collecting duct is likely not unique to the rat.

Table 4.

L/r⁴ was calculated for various species in the different segments of the nephron using Sperber’s data

		L/r4 (µm−3 × 1,000)
Species	Common name	Proximal tubule	Thin limb	Thick limb	Distal tubule
Epimys rattus	Rat	1.6	332	10.2	0.5
Urus arctos	Brown bear	2.2	138	6.3	2.5
Antechinomys laniger	Kultarr	2.1	170	11.3	0.8
Erinaceus europeaus	Hedgehog	0.9	254	6.6	0.7
Pteropus edulis	Flying fox	1.1	216	15.0	0.5
Mus musculus	Mouse	1.3	189	11.6	0.7
Felis catus	Cat	3.0	193	22.7	1.3
Bos taurus	Cow	6.8	501	90.9	4.0
Pipistrellus nilssoni	Northern bat	1.2	160	1.8	0.9
Oryctolagus cuniculus	Rabbit	1.8	265	11.4	1.0

Sperber’s data found in (29). L, length; r, radius.

DISCUSSION

The objective of this paper was to calculate the pressure drop along the different segments of the nephron and determine the points of highest flow resistance. The calculations described here focus solely on physical flow resistance and do not attempt to take into account active biological elements such as tubuloglomerular feedback and glomerulotubular balance mechanisms. The calculations reported in this paper indicate the hydrostatic pressure drop along the renal tubule is greatest in the thin limbs of Henle’s loops and in the inner medullary collecting duct. These segments represent the chief flow resistances that determine the back pressure at the level of Bowman’s capsule. The resistance in the thin limbs of Henle is high because of the small diameter, and pressure drop in a tube is proportional to the inverse of the radius raised to the fourth power. The large pressure drop in the inner medullary collecting ducts is due to the convergence of tubules that channel tubule fluid flow into fewer and fewer collecting ducts toward the papillary tip, resulting in around 6–8 ducts of Bellini in the rat (31). Although there are quantitative variations in the relative radii and lengths of various segments among various mammalian species, it is likely that the resistance is highest in the descending limb in most species (Table 4). The work of Oliver (24) on the structure of the human nephron suggests that this is likely to be true in humans as well. Thus, the diameter, length, and flow rate in the thin descending limbs and inner medullary collecting ducts are important determinants of the hydrostatic pressure in Bowman’s space by the resulting back pressure.

Jensen et al. (13) performed mathematical modeling with the glomerulus and nephron, which estimated pressure profiles along the renal tubule. These studies found the total pressure drop along the nephron is between 13 and 23 mmHg, which is comparable for the values presented here. However, these authors did not draw a specific conclusion regarding the points of greatest resistance and did not evaluate the effects of tubule elasticity and increased flow because of diuretic agents.

Because the net driving force for glomerular filtration is the mean glomerular capillary pressure minus the pressure in Bowman’s space, it can be inferred that flow resistances in the thin descending limbs and inner medullary collecting ducts are an indirect determinant of GFR. The chief element controlling GFR is thought to reside in the regulation of glomerular capillary pressure, largely through the tubuloglomerular feedback mechanism (28) and various neural and hormonal factors that affect afferent and efferent arteriolar resistance (4). However, successful control at this level probably requires the Bowman’s space pressure to remain relatively stable. The calculations presented in this paper suggest the ability of the tubules to dilate with increased intraluminal pressure, providing a passive mechanism whereby extraordinarily high back pressures in Bowman’s space are avoided when flow increases. We note the actual compliance values of most tubule segments have not been reported, and given the important role of tubule compliance in the function of the nephron inferred in this paper, such measurements could be considered a priority for future studies. Beyond the rapid, short-term effects of tubule dilation to regulate flow resistances, it seems possible that mechanisms exist for long-term adaptations that would allow descending limb cells to sense changes in luminal pressure and to respond by making more or less basement membrane, thereby producing fixed changes in diameter. Of interest, the mechano-sensor protein Piezo1 is selectively expressed in the thin limbs of Henle’s loop and medullary collecting ducts (19) (i.e., at the points of highest flow resistance along the renal tubule).

An additional issue is how long-looped nephrons, which have much longer thin limb segments, avoid high back pressures in Bowman’s capsule. The answer appears to be that the thin limbs in long-looped nephrons are not only longer but also have a greater diameter. This increased diameter equalizes the flow resistance in the two types of nephrons. A general question that has not yet been addressed is what determines the luminal diameter of a given nephron segment. In general, the overall diameter of a renal tubule is largely determined by the amount of basement membrane per unit tubule length present at steady state. It seems likely that the luminal diameter of various segments is regulated by the production of basement membrane components, regulation of degradation of basement membrane components, or both. As indicated above, this regulation is likely to be governed by luminal pressure, but the signaling pathways involved have not been explored.

One of the assumptions for the model used in this study is that flow is steady. This assumption provides a simple means to identify the chief sites of flow resistance. Dynamic pressure measurements, however, indicate that superimposed on the average pressure are variations in luminal pressure that may be periodic or chaotic (10, 27). These variations are believed to be due in part to the underdamped feedback afforded by the tubuloglomerular feedback mechanism. In addition, we speculate that pressure variations in the long-looped nephrons can occur because of periodic contractions of the renal pelvic wall, which squeezes the inner medulla, thereby altering fluid dynamics (26). We have made no attempt to assess these factors in the current work.

One challenge to the maintenance of GFR is increased renal tubule pressure in diuretic states. Our calculations suggest that during water diuresis, there is a tendency for pressure in Bowman’s space to increase because of an increased pressure drop, as a result of increased flow in the inner medullary collecting ducts. However, this effect is largely counteracted by tubule dilation not only in the collecting duct but throughout the nephron. Interestingly, studies that evaluated whole-kidney GFR in rats during antidiuresis versus water diuresis showed a significantly higher value in water diuresis (12) contrary to the predicted effect of increased back pressure.

Another relevant diuretic state is the one associated with inhibition of salt and fluid transport in the proximal tubule such as occurs with treatment with SGLT2 inhibitors or acetazolamide. Studies with acetazolamide demonstrated that increased flow out of the proximal tubule is associated with a substantial increase in luminal hydrostatic pressure (21), consistent with the calculated changes presented in this paper. Our results are also consistent with other studies that demonstrate maintenance of glomerular capsular pressure and GFR during vasodilation is affected by changes in proximal tubule pressure (2). It seems possible that the decrease in GFR seen with SLGT2 inhibitors is due in part to similar increases in hydrostatic pressure in Bowman’s space and is not solely because of tubuloglomerular feedback, as has been proposed (6). It is widely stated that SGLT2 inhibitors may have beneficial effects in diabetic kidney disease by decreasing glomerular hyperfiltration but direct measurements that support this view seem to be lacking.

GRANTS

The work was funded by the Division of Intramural Research, National Heart, Lung, and Blood Institute (Project Nos. ZIA-HL-001285 and ZIA-HL-006129, to M. Knepper). G. Gilmer was supported by the National Heart Lung Blood Institute Summer Internship Program (May–August 2017). V. Deshpande was a member of the Biomedical Engineering Student Internship Program supported by the National Institute for Biomedical Imaging and Bioengineering (June–August 2017).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

M.K. conceived and designed research; G.G.G. and V.G.D. performed experiments; G.G.G. and V.G.D. analyzed data; G.G.G., V.G.D., C.-L.C., and M.K. interpreted results of experiments; G.G.G. and V.G.D. prepared figures; G.G.G., V.G.D., and M.K. drafted manuscript; G.G.G., V.G.D., C.-L.C., and M.K. edited and revised manuscript; G.G.G., V.G.D., C.-L.C., and M.K. approved final version of manuscript.