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Regenerating re-absorption function of proximal convoluted tubule using microfluidics for kidney-on-chip applications

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Abstract

Human kidney is a sophisticated organ with 1 Million nephrons arranged in subtle form. Kidney has the most failure cases in the world compared to the rest of the body organs. Kidney failure is a severe problem, where cardiac blood output is not filtered. Dialysis is one available substitute for kidney failure, which seems to help the patient incompletely. There is a great necessity for a device (artificial kidney) that can be implanted into the body to resume the kidney function. In replicating kidney function there are many potential challenges, which must be addressed for faithful regeneration. This paper primarily focuses on regenerating the proximal convoluted tubule (PCT) size dependent re-absorption, mimicking this function using microfluidics is not reported earlier. Different structural changes in the design have been adopted and the accomplishments are discussed. It is observed that the total flow (the total of flow through all 1000 channels) in straight is 0.4 × 10−16 m3/s, in the diagonal channel is 0.4 × 10−16 m3/s, in step is 0.32 × 10−16 m3/s and in serpentine is 0.38 × 10−16 m3/s. The size-dependent re-absorption of solutes, proteins, and urea with the help of array of channels has been achieved. The dimensions of the main tubule and channel are selected to replicate cell–cell interactions. The re-absorption rate obtained is around 48%, which is closely reaching the PCT re-absorption rate. The increase in the number of channels shows increase in re-absorption rate. The novelty of reported work lies in regenerating the human kidney proximal tubule cell function of size and shape dependent re-absorption using microfluidics technology. The proposed device performance proves its prevalence in kidney-on-chip applications.

Introduction

The human kidney is the only organ in the body that can perform 30 distinct operations, of them solute clearance, blood purification, and blood pressure maintenance are of prime importance. Nearly 20–25% of heart pump output receives by kidneys, which is far larger than any other organ receive. Nephrons in the kidney are responsible for versatile and distinct operations. A nephron is composed of different parts such as glomerulus, proximal convoluted tubule (PCT), loop of Henle, distal convoluted tubule inner medullary collecting duct. Glomerulus and tubule network functions depending on size, shape, charge and fluid shear stress solutes passing through. Glomerulus purifies the incoming impure blood using ultra-filter action and PCT diversifies the solutes in lumen fluid by re-absorbing the required and excreting the impurities. The PCT is lined with epithelial cells, these cells act as receptors of solutes passing in lumen fluid to get re-absorbed back into the bloodstream [1]. There are many types of transports in nephron including Epithelial solute transport (Cellular and paracellular) and membrane transport (active, passive, diffusion and facilitated). The decline in solutes transportation in proximal tubule finally steers to damage of whole nephron function. Renal failure may affect a person for his diet, habits, daily routine, heredity, etc. A person in early stage of renal dysfunction cannot recognize his kidney disability as there will be no observable change (such as pain in urination, urine colour change, etc.). Once the working nephrons in the kidney fall below 25% of total normal kidney, the malfunctioning of the kidney starts to show up its effects. The advancement of stages will start to induce further effects by degrading health conditions, finally leading to End stage renal disease (ESRD). In this stage, the electrolytes and water excretion fail completely showing only 5% of normal renal function. ESRD patients with diabetes have less chance of survival without replacing the kidney function.

Dialysis is the first artificial replacement for failed human kidney, saving millions of lives from a long time. Dialysis is a painful process with frequent insertion of needles and sucking the blood out of the body for purification. The blood purification needs huge amount of water with bulkier equipment, motors and pressure sensors to ensure the process is running fine as intended. Dialysis for a kidney failure patient should be performed timely with a frequency of at least two times a week. The cost for dialysis per year is $53,000 (peritoneal) and $72,000 (haemodialysis), making very costly to afford. Another route for kidney failure treatment is kidney transplantation, but currently it is not widely in use because of lack of organ donors. Organ donation is a big restriction in some countries’ traditions and customs. There is a desperate need to develop solutions for the problems popping-up with dialysis and transplantation. The most promising solution is Organ-on-Chip the preceding technology to Lab-on-Chip.

Microfluidics is a technology where fluid dynamics can be handled accurately in microvillithe micrometre level. Owing to the advantages in microfluidics, it finds numerous applications, primarily Lab-on-Chip devices, µTAS, in printing heads for droplet formation, etc. Recently, Organ-on-Chip (Body-on-Chip) is providing auxiliary room to test, diagnose and replace traditional medical equipment. The reviews focusing on the microfluidics and their usage in cell-based microchip systems and their extension to drug screening is presented [2, 3]. An insight into future Nanofluidic technology was introduced in [4]. Organ-on-chips useful for drug discovery and disease modelling has been reviewed, pointed the current challenges and future aspects [5]. A microfluidics chip for drug toxicity testing developed with multiplexed microchannels for maintaining hepatocytes [6]. For ensuring the development of liver cells efficiently has experimented [7]. Another microfluidics chip for regenerating lung function is developed; it is revealed that cyclic mechanical strain stimulates toxic and inflammatory responses in lungs [8]. The importance for extension of applications of Organ-on-Chip in cancer treatment has been identified and experimentally attempted [9]. Nephrotoxicity screening using microfluidics suitable for in vitro using biomarker is reported [10], the toxicity in the kidney is faithfully achieved. The drug interactions have been clearly understood by looking at the fluid interactions, the same has been achieved through Kidney-on-Chip [11]. Human kidney cells cultured in micro-channels for lively environment for perfusion, trapping of these biological cells in micro-channels is predicted using experimental analysis [12]. Utilizing the trapping forces generated by gradients, blood waste trapping in a Blood cleaner-on-Chip system is developed [13].

The phenomenon behind how these kidney cells are able to sense the solutes is still unknown, but there are some predictions showing their relevance. The mechanosensory function of kidney cells (microvilli) inside the proximal tubule has been studied [14, 15], where the authors hypothesized that flow dependent reabsorption inside the kidney is auto regulated. The flow in any form poses countable stress on the surface it is flowing on. The fluid shear stress modulates endocytosis, affects the phenotype and cell cytoskeleton [16, 17]. The literature discussed so far uses direct live human dissected kidney cells, limited life time of these cells is a tight aspect to look at. The continuous change of cells will not help if the artificial kidney once implanted inside the body. There is available literature that contributed to kidney-on-chip, but unfortunately no manufactured or marketed device is available till now.

This can be avoided by realizing an artificial kidney cell, where a single kidney cell (epithelial cell lining inside the PCT) operation is achieved on a chip. A disease model developed for diabetic nephropathy dependent on the size and shape of molecules is described [18, 19], experimentation proves that size dependent separation is highly useful in biological systems regeneration. By taking this phenomenon as a reference kidney proximal tubule can be mimicked, which seems to be constructive thought in achieving Kidney-on-Chip, as it will avoid the use of live kidney cells.

This paper is organized as follows, second sections describing briefly kidney structure the working theory behind the proposed device working. Also, it elaborates on the proposed device structure with dimensions and shape. The results section provides an understanding of the results obtained with the proposed structures and the changes in the structure for optimal design. The forth section concludes by highlighting the merits of the presented work and extendibility of the idea.

Proposed design: structure and dimensions

Blood enters the nephron through afferent arteriole and gets filtered in glomerulus passes into efferent arteriole. After ultra-filtration in the glomerulus, lumen fluid enters Bowman’s capsule situated around glomerulus which will be further directed into nephron a long unbranched tubule network lined up with epithelial cells. The solutes, proteins, blood sugar and water in the lumen fluid get re-absorbed into efferent arteriole bloodstream while perfusing through the tubule system, the nephron internal structure is shown in Fig. 1. The tubules in the nephron entirely surrounded by capillary network of efferent arteriole. The majority part of the kidney functions is performed by the proximal convoluted tubule (The epithelial cells inside the PCT). Cells in PCT continuously face the flow of lumen fluid. Cells react to the fluid flow and perform different operations such as secretion, excretion, most importantly re-absorption. The complex packing of PCT into cylindrical shape with about 1 mm long and 250 microns across makes the flow objected all the time allowing more re-absorption. The exact phenomenon behind the cell’s operation is still unknown and is under study. The fluid shear stress (FSS), size and shape of the solutes contribute to the re-absorption as reported in published work [18, 19].

Fig. 1
figure1

The internal structure of nephron

Considering the FSS, size and shape dependence solute clearance for designing the bioreactor for artificial kidney seems to be convincing plan. PCT is responsible for Sodium (Na), Chlorine (Cl), Potassium (K), Calcium (Ca), Albumin and Urea re-absorption. The dimensional findings of different solutes are given in Table 1.

Table 1 The structural size of solutes in lumen fluid

As stated earlier, the proposed design follows approximately proximal tubule. The dimensions of the proposed design are 6 mm in length and 100 µm width. PCT is wounded into a small circle, accordingly design shapes are to be changed for better reabsorption and ease of fabrication. Regenerating kidney function for a small portion (Unit) is associated with much effort than integrating the developed parts (replication and connecting back to back), for this the size of the design is scaled down to nanometre level.

As shown in Fig. 2, for all the shapes there will be two blood carrying tubules parallelly aligned with a main tubule carrying lumen fluid. The design uses two blood tubules for improving the re-absorption rate. As the two sides of the tubule are connected out, there is more room for the fluid to diffuse out. There will be channels connecting the lumen tubule and blood tubule to transfer the solutes. The width of the channel could be selected starting from 0.25 nm and till 4 nm, but for fluid dynamics 4 nm is preferred. The novelty in the proposed structure is it can reabsorb 50% of the lumen fluid that is passing into the main tubule.

Fig. 2
figure2

The schematic of proposed structure. a The top view and b the front view

Material selection is predominantly important in MEMS/Microfluidic structures. Materials are accountable for faithful working and reliability of the device. The proposed device is considered with Silicon for its high bio-compatibility. The bio-compatibility of silicon is proved to be very high, as it doesn’t show any observable reactions with body fluids and cells. The SiO2 layer over the Silicon prevents the reaction to take place. The fabrication of silicon structure is a neat walkway. The proposed structure has nanometre dimension, Si fabrication help in achieving the smallest size.

The structure is placed parallel to the ground, where the influence of the gravitational force is not present. This is because of the reason that in the parallel flow the flow diversion is much easier as compared to vertical structures. The channels are sized uniformly at 4 nm, because the solutes with small size will flow in without any obstruction. Furthermore, with uniform size the fabrication can be easier.

Theoretical parameters governing the re-absorption

Proximal Tubule is lined by epithelial cells that are continuously in action to excrete, secrete and re-absorb the solutes. The re-absorption rate depends on the number of cells that are in fine working state. There will be no reaction taking place in the proximal tubule for the re-absorption, only pick and drop of solutes by the cells is going on.

The flow in the tubule is considerably low, because by the time blood reaches the glomerulus it will be flowing through capillaries.

The velocity of the fluid is given as

$$V = \emptyset_{f} /A_{c}$$
(1)

where \(\emptyset_{f}\) is Flow rate and Ac is Area of the channel. The flow causes fluid shear stress which can be formulated as

$$\tau = \mu \frac{du}{dx}$$
(2)

where u is Viscosity of fluid, u is velocity and x is distance.

The straight channel in the proposed design is shown as follows. The flow of solutes from main tubule to blood tubule through transferring channel is pictured in Fig. 3.

Fig. 3
figure3

The transfer of solutes from the main tubule to blood tubule

Transport of solutes from proximal tubule to blood channel has certain parameters involving directly and indirectly. The Bernoulli equation comes in, where pressure and density are inversely proportional, density affecting the velocity of the fluid. According to Darcy Equation pressure loss due to wall friction is given by [20,21,22,23],

$$h_{f} = \frac{{f_{d} }}{2g} \times \frac{{v^{2} }}{D}L$$
(3)

The continuity equation of fluid flow expressing the conservation of mass is given by subtracting the net inlet from the net efflux

Finally, the velocity of a fluid in the channel is calculated as follows:

$$V = \frac{{4h^{2} \Delta p}}{{\pi^{3} \eta L}}\mathop \sum \limits_{n}^{\infty } \frac{1}{{n^{3} }}\left[ {1 - \frac{{\cos n\pi \frac{y}{h}}}{{\cos n\pi \frac{w}{2h}}} } \right]$$
(4)

L is the length of the channel, w is the width of the channel, h is the height of the channel, \(\Delta p\) is the pressure differential applied, \(\eta\) is the dynamic shear viscosity factor.

Results and discussion

Fluid shear stress (FSS) inside the kidney tubules will support the functioning by altering the cytoskeleton of the cells. The FSS is observed to vary between 1 dyne to 5 dynes. For this reason, we prefer the flow rate as low as possible, 10−4 nl/min is the flow rate that is scaled down to fit the downscaled structure. The PCT is packed into small cylinder shape in the kidney, the flow has to face additional turns all the time, and these obstructions allow more reabsorption. If a part of the PCT is regenerated, in the same way whole PCT can be regenerated easily by integrating all the individual parts. For this a 500 × 200 nm of length and width tubule is considered. It is analysed for all the shapes of main tubule considering the literature fact that cross sectional shape has no effect on the flow [1].

Structure optimization

Rectangular proximal tubule

To determine the channel transport properties a rectangular tubule with transporting channels is created. The distance between each channel is uniform as well as dimensions. The inlet is supplied with water of low flow rate 10−4 nl/min. It is observed that the channels are having heavy flow compared to actual tubule which is satisfying the theoretical laws. If the fluid flowing area is small the flow will be very high. The average flow velocity inside all the channels observed is the same and its value is 9.1 × 10−3 ml/min. The whole setup is simulated in COMSOL Multiphysics. The simulated results are shown in Fig. 4. The uniformity in the channel flow has allowed us to calculate the total flow with ease of effort. The total flow through the channels is found to be 1.32 × 10−16 m3/s. A comparison of theoretical and simulated results is presented in Fig. 5. It shows that the curves are nearly correlated. The fabrication of this structure is not complicated as there are no curves in the design.

Fig. 4
figure4

a Flow through rectangular tubule with uniform channels and b A single channel possessing heavy flow

Fig. 5
figure5

The graphs plotted between flow rate and a shear stress and b pressure difference

Diagonal proximal tubule

As discussed earlier PCT is packed into cylinder like structure. Likewise, the idea is to make our structure to look in the same manner. The structural design of the diagonal PCT tubule is shown in Fig. 6. In this setup also, the tubule is supplied with 10−4 nl/min of in-flow rate.

Fig. 6
figure6

Diagonal channel and its effect on flow at different places

The channel dimensions are the same as in rectangular PCT tubule. The results show some interesting facts, at the face and outlet (at the ends) of main tubule the flow is slow. It is identified that the channels that are nearer to the corners possess more flow. Cumulatively transport channels possess more flow than main tubule despite end or corner in comparison with the rest of the shapes. The problem arises in fixing the angle of the bending and fabrication. Optimization of the structure is not possible for this shape. The theoretical understanding behind the working of diagonal tubule is very complex involving lengthy differential equations. As there is no uniform flow the total flow calculation was little complicated involving some assumptions. The total flow through the channels is calculated to be 2.51 × 10−16 m3/s. A graph plotted in origin pro plotter for flow velocity at selected pointed on the dimension is shown in Fig. 7, where it shows maximum flow at the centre.

Fig. 7
figure7

The change in flow velocity to the length scale. Reaching maximum at the diagonal

Step and serpentine structures

The step and serpentine structures are shown in Fig. 8. The step structure exerts more blockages to the flow. As the fluid goes through 90° of bending, where there is less possibility for the liquid to flow along the steep rise. In the same way serpentine structure also has the same problem. But comparatively serpentine structure is more suitable.

Fig. 8
figure8

The flow in a step structure and b serpentine structure

The flow comparison of different structures is plotted in Fig. 9.

Fig. 9
figure9

The flow comparison of different structural shape main tubules

Fluid shear stress analysis

The stress that is exerted by the fluid on the surface it flows is termed as Fluid Shear Stress (FSS). As discussed earlier, the FSS is responsible for kidney functioning. FSS judges the solute re-absorption, excretion, secretion and alters the cell cytoskeleton. The flow in the channel is observed to be varying along the whole width. The pressure is varying from high to low from face to end of the channel Fig. 10a, b. The FSS generated with this flow is shown in Fig. 10b, d. Where the stress at the boundaries of the channel is high and in the middle it is low.

Fig. 10
figure10

The pressure distribution in the channel a at the end b at the face. c, d the FSS distribution along the channel at different pressure ranges

Channel selection

The channel selection is based on the size of the solute particles. Now the number of channels needs to be finalized for convincible reabsorption. For this, the flow in the channel, area of the channel, flow into the main tubule and area of the tubule are governing parameters. The PCT will absorb 60% of the lumen fluid. For a rectangular main tubule, for satisfying the above condition to reabsorb 60% of lumen fluid there is a need to calculate the number of channels required (Fig. 11). The theoretical calculations we made indicates, for a channel with 500 nm of length and 200 nm of width requires 168 number of channels. The same has been finalized and simulated which shows good correlation with theoretical calculations. Different dimensions of channels are also studied starting from 4 nm, but flow restriction was not allowing the solutes to flow into the channels, for this reason the small dimensions are deliberately avoided. As hypothesized the flow through all the channels was uniform, but the total flow is high as the number of channels was high. The structure has been simulated and presented in Fig. 12.

Fig. 11
figure11

The flow through single channel depicted 3 dimension

Fig. 12
figure12

The finalized main tubule with the required number of channels showing good flow velocity

Conclusion

This paper proposed and analysed different structures for mimicking proximal tubule re-absorption. The size and shape dependent diversification of kidney cells is considered as predominant phenomenon at a particular fluid shear stress. The identical concept is utilized in designing different structural shapes. The design considers an analogy of proximal convoluted tubule (PCT) cell function and its transport to design the structure. The dimensions of the proposed design are adopted based on proximal tubule dimensions in the human body. The PCT tubule is a helical structure which is winded into cylindrical shape, for this reason different shape changes were applied.

As discussed, the size of the channels is kept to a uniform size where most of the small solutes can be re-absorbed back. The main proximal tubule is connected to blood to tubule through these Nanochannels. As estimated the flow in the channels is very high than the flow in the main tubule the importance of shear stress for re-absorption is clearly understood. Different structural changes have been studied. The rectangular tubule has uniform flow; diagonal tubule has very high flow because of drifting of solutes. The serpentine has considerably same flow as the straight channels; because of big obstructions step structure is undesirable. The diagonal channels associated with high toughness in fabrication aspect, which seems impractical. The total flow in the diagonal main channels is 2.51 × 10−16 m3/s and the flow through the rectangular channels is 1.32 × 10−16 m3/s, the comparison is shown in Table 2. By calculation it is found that 168 channels per 500 nm are required for faithful re-absorption. In the future, the integration of present model to form a full proximal convoluted tubule (artificial bio-reactor) can be attempted. The association of ultra-filter and bio-reactor will fully satisfy the kidney. The proposed design is having advantages that make it suitable for use in Kidney-on-Chip applications.

Table 2 Comparison table between theoretical and simulated results

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Acknowledgements

The authors would like to thank NMDC@NIT Silchar supported by National Institute of Silchar for providing financial assistance and computer tools.

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Correspondence to Jasti Sateesh.

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Sateesh, J., Guha, K., Dutta, A. et al. Regenerating re-absorption function of proximal convoluted tubule using microfluidics for kidney-on-chip applications. SN Appl. Sci. 2, 39 (2020) doi:10.1007/s42452-019-1840-2

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Keywords

  • Kidney-on-chip
  • Microfluidics
  • Proximal tubule
  • Fluid shear stress