Novel applications of intelligent computing paradigms for the analysis of nonlinear reactive transport model of the fluid in soft tissues and microvessels

  • Iftikhar Ahmad
  • Hira Ilyas
  • Aysha Urooj
  • Muhammad Saeed AslamEmail author
  • Muhammad Shoaib
  • Muhammad Asif Zahoor Raja
Original Article


This article presents a methodology to solve a one-dimensional steady-state nonlinear reactive transport model (RTM) that is meant for fluid and solute transport model of soft tissues and microvessels. The methodology integrates the artificial neural network (ANN), genetic algorithms (GAs), and pattern search (PS) aided by active-set technique (AST) and interior-point technique (IPT). The RTM is represented with nonlinear second-order system based on the boundary value problem of ordinary differential equation. The ANN modeling is used for governing expression of RTM to form a fitness function in mean square sense, and optimization solvers based on the GA, PS, GA-AST, GA-IPT, PS-AST, PS-IPT are used for viable learning of weights. Proposed techniques are applied to different nonlinear RTMs based on variation in the characteristic reaction rate and half-saturation concentration. The proposed stochastic numerical solutions are compared with state-of-the-art solvers in order to check the accuracy and convergence based on sufficient large multiple runs of the algorithms.


Nonlinear reactive transport model Artificial neural networks Genetic algorithms Pattern search Interior-point technique Active-set technique 


Compliance with ethical standards

Conflict of interest

All the authors of the manuscript declared that there are no potential conflicts of interest.

Human and animal rights

All the authors of the manuscript declared that there is no research involving human participants and/or animal.

Informed consent

All the authors of the manuscript declared that there is no material that required informed consent.


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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GujratGujratPakistan
  2. 2.School of Electrical and Electronic EngineeringUniversity of AdelaideAdelaideAustralia
  3. 3.Department of MathematicsCOMSATS University IslamabadAttockPakistan
  4. 4.Department of Electrical and Computer EngineeringCOMSATS University IslamabadAttockPakistan

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