TOPOLOGICAL OPTIMIZATION OF HOLLOW FIBER MEMBRANES TO ENHANCE HEMODIALYZER EFFICIENCY

International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol. 10, Issue 3, Jun 2020, 2397-2410 © TJPRC Pvt. Ltd.

TOPOLOGICAL OPTIMIZATION OF HOLLOW FIBER MEMBRANES TO ENHANCE HEMODIALYZER EFFICIENCY AMARESWARA PRASAD CHUNDURU Student, J.R.N. Rajasthan Vidyapeeth University, Udaipur, Rajasthan, India ABSTRACT Amongst the most common issues in kidney disease is atypical decline of fluid elimination in the body, which raises acid levels and increases the healthy range of molecules such as uremic toxins, glucose, creatinine, β 2 - micro globulin.

Variables that characterize the dialyzer framework are very vital because they determine the overall Uremic toxin solute molecules clearance. Such contaminants can be eliminated by manufacturing membrane frameworks which are efficient, due to the wide availability of technologies in production of membranes and hollow fibers which can vastly improve dialyzer efficiency. Since system criteria and architecture of dialyzer determine the level of removal and also the hold of beneficial molecules in the blood, the layout of processing and designing hollow fibers is of paramount importance. In this paper, a study is performed on tweaking the geometrical parameters of hollow fibers namely inner diameter, length of fiber and their effects on solute (Uremic toxins) clearance. To validate this model simulations are performed on Matlab,

hemodialyzer and finding the trade-off values for optimal geometrical parameters that increase dialyzer productivity.

KEYWORDS: Hemodialysis, Dialyzer Membranes, Optimization, Mathematical Modelling & Simulation

Received: Jun 02, 2020; Accepted: Jun 22, 2020; Published: Jul 06, 2020; Paper Id.: IJMPERDJUN2020223

Original Article

Simulink and COMSOL software. The study also discusses about the limitations in designing hollow fibers for

1. INTRODUCTION Only one or two of every 100,000 children-who are 19 years old or younger-experience kidney failure every year.

In contrast, adults are 20 times more likely than children to experience kidney failure, with risks steadily increasing with age. In addition, African Americans are three times more likely to develop kidney failure in their late teens than Caucasians in the same age group, as well as diseases that destroy the small blood vessels in the kidney.

Furthermore, boys are almost twice as likely to experience kidney failure due to birth defects, polycystic kidney condition, or other recessive genetic disorders.

When the kidneys stop working effectively, dialysis is an effective treatment of kidney failure. Dialysis uses special devices to extract excess blood water and waste materials. It partially replaces good kidney function.

Dialysis conducts approximately 10–15% of good kidney function. Nevertheless, this is sufficient to ensure that the body continues to work. Work to enhance artificial renal replacement therapies differs across a hemodialysis system's many different parts. Research focuses primarily on developing a better dialyzer – the part that is primarily responsible for eliminating waste from the blood but the entire hemodialysis process is dedicated to less research.

From a systematic engineering design viewpoint, this study serves as a thorough investigation of the hemodialysis process. There has been a substantial amount of research on homogeneous dialyzer membranes.

This study explores the effects of a reduced radius of hollow fibers in dialyzers. The study uses Dynamic simulation softwares such as COSMOL, Matlab, Simulink for model validation.

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RESEARCH METHODOLOGY

The system model created is the primary aspect of this study in need of verification. Because this system design is used for forecasting different system configurations, its accuracy is crucial to this work's relevance.

The system model is validated in two ways for 1) Theoretically by using the physics (equations) that govern the dialyzer system 2) Virtually by using COMSOL, Matlab and Simulink software, for different radii of hollow fibers

2. MATHEMATICAL MODELLING OF BLOOD FLOW IN MODIFIED HEMODIALYZER 2.1 Hollow Fiber Packing A hemodialyzer's effectiveness largely depends on its potential to enhance diffusion between the blood and dialysate. The diffusion process can be compromised if there is a discrepancy between the flow distribution of blood and dialysate flow.

Usually fibers are packed in a dialyzer without any particular pattern as these are cost efficient and typically observed in low cost or conventional dialyzers. Studies such as macroscopic and densitometric evaluation indicate that the distribution of flow in a patterned packaging was homogeneous compared to standard packaging. Consider a fiber casing of 500cm and fibers of radius 45cm (hypothetically) and are packed with Standard, Hexagonal and Square patterns as shown below: From the cross-section diagrams of casings, it is observed that standard pattern has non-homogeneously distributed intrinsic spaces through which the dialysate flows while the hexagonal and square patterns has homogeneous distribution. According to “Circle packing equation” the empty, filling fraction and maximum number of fibers that can be packed are calculated.

Table 1: Space occupied by Fibers for Different Packings Circle Packing Method Max. Fibers Filled Fraction Empty Fraction Standard 100 81.42% 18.58% Hexagonal 96 78.17% 21.83% Square 82 66.77% 33.23%

Figure 1: Packing of Hollow Fibers in Different Circle Packing Patterns Standard, Hexagonal and Square (Left to right).

2.2 Standard Packing: It is observed that a fiber casing can accommodate maximum number of fibers using this method with high filled fraction. But due to its uneven distribution of intrinsic spaces the flow distribution in non-homogeneous that could cause turbulent flow and bubbles in the dialyzer.

2.3 Hexagonal Packing: It is observed that it could accommodate ~3% less the number of fibers compared to standard packing but its uniform distribution of intrinsic spaces leads to uniform flow of dialysate with a laminar flow and its high filled fraction depicts the effective usage of space available in the casing. The packing density is high in hexagonal packing compared to square packing.

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2.4 Square Packing: It is observed that with this packing pattern the fibers that a fiber casing can accommodate is least in comparison with the other methods. Large empty fraction leaves inadequate dialysis.

2.5 Kinetic Modelling of Dialyzer Characteristics with Various Packing Patterns To investigate the efficiency of hemodialysis, the whole patient dialyzer system can be described by a kinetic model incorporating fluid mechanics and mass transport. In essence, kinetics defines a physical entity's change in time (characterized by a time constant) according to a driving force such as mass and energy. A Simulink model of a Hemodialyzer is designed to calculate the Kinetic modelling characteristics (Performance) of dialyzer.

Boundary Conditions An appropriate boundary conditions are required for solving fluid dynamic equations especially in flow field. At dialyzer inlet a uniform flow and velocity is presumed. The boundaries of the domain are modeled either as a wall where no-slip occurs or as planes of symmetry if only part of a symmetric structure is modeled. At fixed walls no-slip conditions are applied. There are no-velocity components perpendicular to symmetry plane and tangential stress being zero. The concentration can be specified on certain part of the field boundary, while a zero perpendicular variance is prescribed on symmetry planes.

Method of Modelling In this work, clinical parameters are collected from a patient who attends hemodialysis sessions twice a week. These parameters applied to the performance characteristic equations of dialyzer with standard, hexagonal and square fiber packing to show the performance of dialyzer under different packings. The reference dialyzer used for the work is Fresenius FX 60.

Table 2: Model Patient Parameters Model Patient Parameters Patient Name xxxxx Body weight 70kg Age >30 Hematocrit 35% Weight Gain 4kg Treatment time 3hrs Body temperature 370C Arterial Urea Concentration 95 mg/dL Venous Urea Concentration 25 mg/dL Pre-pump arterial pressure -120 mmHg Table 3: Model Dialyzer Parameters Model Dialyzer Parameters Fiber Length 25cm Fiber inner radius 190 microns Fiber outer radius 205 microns Fiber wall thickness 15 microns Casing radius 2.02 cm Blood Viscosity 0.0352g/(cm-s) Dialysate Viscosity 0.687 mPa-s t (packing density) Dense = 0.88, Hexagonal = 0.90, Square = 0.7 Pressure drop 15 mmHg UF rate 1333.33mL/hr www.tjprc.org

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These sample parameters are used to observe the kinetic characteristic equations of dialyzer mentioned in table below:(Sigdell, n.d.)

Table 4: Performance or Characteristic Equations Parameter Characteristic equation ∆P QB = 8μL x N Blood flow rate (

Dialyzer clearance Dialyzer efficiency Kt/V Ultra-filtration reate Transmembrane pressure

πr4

)

Qc = QB (1KoA =

Cbe Cbi

)

k 1− d

QB QD QB − QD

ln[

QB

k 1− d

]

QD

Kt/V W∗1000 QF = TMP =

t UFR KUF

Simulink Model A Simulink model of a Hemodialyzer is designed to calculate the Kinetic modelling characteristics (Performance) of dialyzer.

Figure 1: Image of Simulink Model for Characteristic Equations The results of this simulation are discussed in results section.

Dialyzer membrane and Effects of Radius Reduction in Solute Clearance The purpose of this study is to establish an illustration of a hollow fiber dialyzer that is a critical component of any method of hemodialysis. This is done to enhance understanding of the processes of mass transportation and fluid dynamics occurring within the dialyzer that affect end-stage renal disease (ESRD) patients ' dynamic homeostasis. The Virtual model depicts the dialyzer unit and processes using a computer-generated model via COMSOL. This study uses biophysical equations to simulate the dialytic process to demonstrate the effect of changing dialyzer parameters on the process of treatment. For instance, how the membrane radius adjustment affects toxin extraction and dialysis duration. The simulation largely emphases on modeling the steady state diffusive flux of Uremic toxins across the dialyzers through semi-permeable membrane due to the concentration gradients fashioned across it.(Ogore et al., n.d.)

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Figure 3: Domain model of hollow fiber inside dialyzer The blood flows via these artificial capillary channels (membranes) while the dialysate passes over the shell across the capillaries in a counter-current fashion similar to a heat exchanger (shell and tube type). The flow of blood and dialysate is laminar in this simulation.

Governing Equations The subsequent condensed Partial Differential Equations explains the processes of convection and diffusion in the blood and dialysate. ∇. (−𝐷𝑖 ∇𝑐𝑖 + 𝑐𝑖 𝑢) = 0 Where ci represents the uremic toxins (mol/m3) concentration in the corresponding phase, D represents the diffusion coefficient (m2/s) in the liquid phase and u denotes the velocity (m/s) in the liquid phase.

The Diffusion coefficient varies among toxins based on their molecular weights. For this simulation we consider only Urea. The diffusion coefficient is calculated using 𝐷 = 1.62 × 104 (𝑀𝑊)−0.552 Where MW represents the molecular weight of toxin. For Urea MW = 60 Da Diffusion coefficient of Urea = 1690.35x10 -8 cm2/sec Inlet velocity of blood along the axial direction is given by VB = (

2𝑄𝑏 𝜋𝑅12 𝑛

𝑟

2

) [1 − ( ) ] 𝑅1

Where QB is the blood volume flow rate, R1 is the hollow fiber inner radius r is the radial coordinate, and n is the fiber count.

For simulating diffusion phenomena through porous membrane, the below equation is used ∇. (−𝐷𝑒,𝑖 ∇𝑐𝑖 ) = 0 Where De is effective diffusive coefficient of toxin in porous medium. The effective diffusivity is given by 𝐷𝑒 = 𝐷. 𝑓(𝑞). 𝑆𝑑 . 𝐴𝑘

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𝑞=

𝑓(𝑞) =

𝑟𝑠 𝑟𝑝

1 − 2.1050𝑞 + 2.0865𝑞 3 − 1.7068𝑞 5 + 0.72603𝑞 6 1 − 0.75857𝑞 5

SD = (1 - q)2 Where f(q) is the friction coefficient, SDthe steric hindrance factor for pore inlet in diffusion, Akthe membrane porosity, q is the ratio of solute radius rsto pore radius rp.(Ronco& Clark, 2018) Model Geometry For simulation, the scaling factor is used in the COMSOL interface to model the entire length of a hollow fiber using geometry of a smaller size. Such length scaling has a direct effect on the velocity fields and the diffusive and convective transportation along this scaled range. As considering the fact that the real radial dimension is kept the same while the length is scaled.

Usually the toxin in the blood stream must dissolve into the membrane during hemodialysis before the dialysate can carry it out. A dimensionless partition coefficient K is therefore used to describe this interaction between the membrane and the fluids.(Islam & Szpunar, 2013) 𝐾=

𝑐𝑀𝐵 𝑐𝑀𝐷 = 𝑐𝐵𝑀 𝑐𝐷𝑀

The boundary layers of the concentration simulation were then defined as follows: The symmetry condition of the Bwall and Dwall were isolated. Bout and Dout, modeled as convection flux regions that contribute greatly to conversion rather than diffusion. Bin was a model with a fixed concentration of inlet c0.Din was a design with a fixed concentration of 0 inlet.

Bin had a condition of inlet velocity in the y-direction defined in the following equation as shown below: ( 𝑉𝐵 =

2𝑄𝐵 𝜋.𝑅12 .𝑛

𝑦

2

) [1 − ( ) ] 𝑅1

𝑠𝑐𝑎𝑙𝑒

Din has model with a condition of inlet velocity in the y-direction defined in the equation below: 𝑉𝐷 =

4. 𝜋(𝑅34

8. 𝑄𝐷 𝑦 2 [𝑟 2 − 𝑅22 − 2. 𝑅32 . 𝑙𝑛 ( ) ] 4 ). 𝑅2 − 𝑅2 𝑛. 𝑠𝑐𝑎𝑙𝑒

Under these circumstances, the application mode of COMSOL's Chemical Engineering Module Incompressible Navier-Stokes can simulate the flow fields on both sides of the membrane. First, the viscosity and density of the fluid subdomain property is determined by the values shown below.

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Table 5: Diffusion Properties of COMSOL Model User Defined in [mm] Inner Radius Hollow Fiber 0.205[mm] Outer radius hollow fiber 0.7[mm] Approximate radius unit cell 250[mm] Fiber length 7 Axial coordinate scale factor SCOPUS Indexed Journal

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h_max D Dm M K c0 v1_max A

0.1 × R1 3.017e-11[m2/s] 4.505e-11[m2/s] 1e4[m/s] 0.7 0.01582[mol/liter] 1.4696e5[mm/s] -2e3[1/(m*s)]

Maximum mesh element size Diffusion constant, Urea Diffusion constant Stiff-spring velocity Partition coefficient Inlet concentration Maximum velocity Permeate velocity

2403

liquid phases membrane

dialysate dialysate

The results of this simulation are discussed in results section.

Effect of Urea clearance due to Fiber Radius Reduction The concentrations profile across the dialyzer length was examined. The following formula is created by conducting a mass balance over a small length of the blood vessel: 𝑉

𝑑𝐶 = 𝑄𝐵 𝐶|𝑧 − 𝑄𝐵 𝐶|𝑧+∆𝑧 − (𝐴𝐽|𝑟= 𝑅𝑖 ) 𝑑𝑡

In which V is the blood vessel's volume QB is the blood volumetric flow, A is the blood vessel's surface area, and J is the blood vessel's wall flux.It is presumed that the concentration within the blood vessel is constant in every slice of z.In other words, within the blood vessel, there is no radial aspect of C.The blood volumetric flow rate, volume of blood vessel and area of vessel can be further broken down in terms of Δz.(Chen, Fong, & Kumar, n.d.)

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𝜋𝑅2 ∆𝑧

𝜕𝐶(𝑧, 𝑡) 𝜕𝐶 = 𝜋𝑅2 𝑣𝑐(𝑧, 𝑡) − 𝜋𝑅2 𝑣𝑐(𝑧 + ∆𝑧, 𝑡) − 2𝜋𝑅∆𝑧(−𝐷 ) 𝜕𝑡 𝜕𝑟

Where v is the velocity of blood flow which is assumed to be constant in the radial direction.

Upon further simplification the diffusion equation is given by: C = A×ln(r) + B 𝐴=

− 𝐶 (𝑟 = 𝑅𝑖 ) 𝑅𝑒

ln ( )

,𝐵 =

𝑅𝑖

𝐶 (𝑟 = 𝑅𝑖 ) 𝑅

ln ( 𝑒)

× ln (𝑅𝑒 )

𝑅𝑖

The results of this simulation are discussed in results section.

Efficiency of Peristaltic Pump Peristaltic pumps are a particular type of positive-displacement rotating pumps used in hemodialysis machines. Working rollers compress a flexible pipe to increase pressure and speed. As only the liquid is exposed to the elastic pipe and not the pump's mechanical components, preserving sterility is very straight forward. The life of the pump is also satisfactory.

Equation of the Energy required for pumping blood is given by : (Roy, De, Roy, & De, 2017)

𝐸𝑝𝑢𝑚𝑝 =

2 16𝜋𝜇𝑁𝐿𝑑2 𝛾𝑤

128

; ➔Epump∝ d2

Where viscosity of blood (µ), Length of fiber (L), Number of fibers (N) and d be the inner diameter of fiber. The energy required by peristaltic pump Epump for pumping blood at required flow rate Q B is directly proportional to the square of the diameter i.e., lesser the diameter of hollow fiber lesser the energy required to pump blood and vice versa.

Design Limitations for Optimizing Hollow Fiber Dialyzer Flow Profile of Fluid in a Pipe Flow profile of blood inside fiber is an important aspect to be considered. If the flow is turbulent or transient it causes air bubbles inside the dialyzer which can be disturbance in efficiency of dialyzer as well as for the patient. A significant amount of air bubbles inside patient’s body can lead to “Air Embolism” which could lead to cardiac issues.

Reynolds number is defined by 𝑅𝑒 =

𝜌 × 𝑣 × 𝑙 𝜇

Where ρ is the density of blood (1060 kg/m3 @ 370C), v is the velocity, l being the length of the fiber and µ is the viscosity of blood (0.0035 Ns/m2).

Minimum Thickness of Hollow Fiber The hollow fiber in the hemodialyzer must be able to endure the TMP. When that the inner radius of the fiber, it should be kept in mind that if the inner radius is built to be below the minimum thickness, the fiber cannot withstand the TMP and fails.

Equation for minimum thickness of hollow fiber is given by

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𝑡=

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𝑃𝑑0 2(𝐻𝑠 + 𝑃)

Where P is the internal pressure (TMP), d 0 is the outer diameter, Hs is the hoop stress in the fiber wall.From the above equation it is clear that the minimum thickness required for a hollow fiber is inversely proportional to the hoop stress. While the hoop stress is directly proportional to the inner diameter of the fiber. Therefore, as the inner diameter is reduced it reduces the hoop stress. Once the hoop stress is reduced the minimum thickness is increased.

Back Filtration and Length of Fiber Back-filtration can be defined as a condition in which there is a transport of fluid from the dialysis fluid (side) to the blood side. This phenomenon usually arises in high-flux dialyzers. It primarily arises due to the excess UF through the first half of the dialyzer than the other half which follows a pressure drop in the secondary distal part of the dialyzer. It is the less desirable property in Hemodialysis therapy.

The pressure pattern along the hemodialyzer's length is clearly not linear. In fact, while the areas α and α 1 are the same, their shapes are different. Back-transport phenomenon occurring in hemodialysis from dialysate to blood. Back filtration is generated as a response to the equilibrium of the dialyzer pressure. A deviation of 9.6% was observed for a standard dialyzer with an effective fiber length of 230 mm, although fiber elongation by a factor of 1.5 or 2 results in a pressure drop of 15% lower than the rule of Poiseuille.

Figure 4: Pressure Profile Across Length of Dialyzer

3. RESULTS AND DISCUSSIONS 3.1 Optimizing Geometrical Parameters of Hollow Fiber The efficacy of the dialyzer can be enhanced by lowering the inner radius of hollow fiber. The packing density of fibers can be boosted as the radius decreases (by coordinating them in hexagonal packing). This enhanced packaging density enhances dialyzer features such as clearance rate, blood flow rate, dialyzer efficiency, and Kt / V value.

Table 6: Performance of Dialyzer for Various Fiber Packings Parameter FX 60 Dense Packing Hexagonal Packing Number of fibers 9000 10,004 10,214 Packing Density 88.79% 90.6% Effective Surface area (m2) 1.4 2.63 2.685 Blood flow rate (mL/min) 300 700 715 Clearance Urea (mg/dL) 303 516 527 Dialyzer Efficiency (KoA) 967 1423 1512 Maximum dialysate flow rate (mL/min) 1000 1000 1000 TMP (mmHg) 29 15.15 14.8 UF – Coefficient (KUF) 46 88 90 www.tjprc.org

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It is evident from the above table that the dialyzer has more performance than standard or square packing for hexagonal packing.

Figure 3: Performance of Dialyzer Against Different Packing Methods 3.2 Dialyzer membrane and effects of Radius Reduction in Solute Clearance Decreasing the fiber radius can lead to increased solute clearance on the dialysate side. COMSOL blood and dialysate mass transport mechanism simulations were evaluated at different (inner) radii of hollow fibers (membrane) relative to their effecting mass transport system. The findings of the simulations were: It is apparent that the urea concentration on the dialysate side, i.e. clearance of urea and uremic toxins, has significantly increased with increased membrane thickness / reduction in the hollow fiber inner radius.

Figure 6: Graph for Urea Clearance Against Membrane Thickness The plot reaches its peak at 105 microns and drops to 115 microns as minimal as possible.A trade-off value between these two points must be quantified to determine at which thickness value of the membrane is suitable to obtain adequate dialysis. With in-vivo testing, this can be further conquered.

3.3 Reduced Radius of Fiber and Urea Clearance As the internal diameter of the fiber raises the concentration of decay in Urea and vice versa, it is clear from the graph above. Similarly, the concentration of Urea decreases as the fiber length increases. Therefore, a smaller internal fiber diameter (radius) and shorter length will provide Urea with efficient clearance to avoid back filtration.

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Figure 7: Increase in clearance of Uremic Toxins as Radius Decreases 3.4 Efficiency of Peristaltic Pump and Decreased Radius The amount of energy essential by peristaltic pump to pump blood at the necessary flow rate is directly proportional to the square of the diameter i.e. lower the diameter of hollow fiber less the energy needed to pump blood and vice versa.

However, hollow fiber membranes have the inherent advantage of the cheap cost of production, as no expensive spacers are needed to support the structure or fiber arrangement.

3.5 Design Limitations and Trade-off Point Chapter 3 points out that dialyzer efficiency is increasing as the inner radius of hollow fiber decreases. But Chapter 3.6.1 shows that as the radius diminishes Reynold's number of fluid increases resulting in fluid flow turbulence. Such movement will lead to air bubbles inside the blood lines, which could lead to air embolism accompanied by cardiac embolism when entering the patient's body.

As the length of hollow fiber increases, it is evident from the Chapter 3.6.3 that back-filtration occurs which could give rise to toxins entering the bloodstream by dialysis. But shorter hollow fiber length leads to rapid clearance of Urea.

Due to the axial load imposed by fluid flow, the effective length of the fiber must be considered.

4. CONCLUSIONS A comprehensive machine design was generated in Chapter 3 following the dialyzer physics. The design was further improved by criteria for geometry (topology) of dialyzers, ultrafiltration, trade-off factors, and excretion of uremic toxins.

Such supplementary inputs and requirements are important as the template is used under very stringent design constraints to design a system.

Because a revised method of hemodialysis will provide improved clearances, it is important to recognize the residual function of the kidney and other characteristics of the body. The scope in which they were developed is a key difference between the model developed in this research and established models essentially, most models were designed to replicate the traditional practice of hemodialysis. The prototype is unique in this research because it was developed to examine all the hemodialysis system design scenarios. Matlab Simulink's model increases and flexibility enabled a thorough experimentation of the paradigms of hemodialysis in Chapter 3 & 4.The design was studied and the inputs were set to develop notions that, through trial and error, would have the lowest inner diameter of hollow fiber. The prime www.tjprc.org

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constraint of a modified hemodialysis system is its hollow fiber topology. The notions created all were designed with the target of minimizing the total inner diameter (radius) and intensify the dialyzer's proficiency.

Basically, seeking a trade-off point is the ultimate solution to the design problem. A reduced dialyzer system with an internal diameter is not available on the market and would require substantial additional research. In Section's future work, its design development requirements are further mentioned.

5. FUTURE WORK 5.1 Sensitivity Analysis and System Optimization The simulation inputs implemented in this research were chosen with designer instinct. Furthermore, a rigorous analysis could be done which examined the nature of the relationship between all the different variables in a hemodialysis system which focused primarily on the relationship between blood and dialysis flow rates in this analysis. The model could be reversed, the developer would determine the requirements of his/her ideal output process, and the model would select the best inputs to achieve those goals.

5.2 Trade-off Point for Optimal Geometrical Parameters of Hollow Fiber The efficient trade-off point for geometrical quantities of fibers can be achieved through in-vivo testing using the model developed in Chapter 3.

The single greatest "future research" to bear in mind is the progression of a replacement renal system not relying on a dialyzer. While slavishly rejecting membrane dialysis should not be the goal, research seems to suggest that an alternative RRT needs to be created to dramatically improve the clearance of solutes from patients with CKD.

ACKNOWLEDGEMENTS I would like to thank Dr. Chinta Rama Krishna M.D, D.M (Nephrology), and Department of Nephrology Vedanta Hospitals, Guntur for their expert advice, suggestions throughout research.

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Chen, B. K., Fong, S., & Kumar, A. (n.d.). Modeling Dialysis.

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Islam, S., & Szpunar, J. (2013). Study of Dialyzer Membrane ( Polyflux 210H ) and Effects of Different Parameters on Dialysis Performance. 2013(September), 161–167.

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Mohammad Bajwa, “Nan medicine – The Futuristic Medicine”, International Journal of General Medicine and Pharmacy (IJGMP), Vol. 6, Issue 1,pp. 1-8

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Ogore, O., Sherpa, K., Baron, C., Zenouzi, M., Ph, D., Krishnan, S., & Ph, D. (n.d.). Design of a Simplified Hemodialysis Simulation. 1–12.

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Sengpasith Houngaloune, Naoki Hiroyoshi & Mayumi Ito, “Effect of Reaction Temperature on Schwertmannite Synthesis from Simulated Copper Heap Leach Solutions”, BEST: International Journal of Management Information Technology and Engineering (BEST: IJMITE), Vol. 5, Issue 10, pp. 27-34

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Roy, A., De, S., Roy, A., & De, S. (2017). State-of-the-Art Materials and Spinning Technology for Hemodialyzer Membranes State-of-the-Art

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AUTHOR PROFILE

Amareswara Prasad Chunduru currently a final year student of Bachelors of Computer applications at JRN Rajasthan Vidyapeeth University. He will be completing his undergraduate degree by 2020 and highly focused in research work and a competent academic career. He has done a notable interdisciplinary research related to Chaos theory and simulation algorithms.

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