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Analytical solution using computer algebra of a biosensor for detecting toxic substances in water

机译：使用生物传感器的计算机代数检测水中有毒物质的分析解决方案

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In a relatively recent paper an electrochemical biosensor for water toxicity detection based on a bio-chip as a whole cell was proposed and numerically solved and analyzed. In such paper the kinetic processes in a miniaturized electrochemical biosensor system was described using the equations for specific enzymatic reaction and the diffusion equation. The numerical solution shown excellent agreement with the measured data but such numerical solution is not enough to design efficiently the corresponding bio-chip. For this reason an analytical solution is demanded. The object of the present work is to provide such analytical solution and then to give algebraic guides to design the bio-sensor. The analytical solution is obtained using computer algebra software, specifically Maple. The method of solution is the Laplace transform, with Bromwich integral and residue theorem. The final solution is given as a series of Bessel functions and the effective time for the bio-sensor is computed. It is claimed that the analytical solutions that were obtained will be very useful to predict further current variations in similar systems with different geometries, materials and biological components. Beside of this the analytical solution that we provide is very useful to investigate the relationship between different chamber parameters such as cell radius and height; and electrode radius.
机译：在相对较新的论文中，提出了一种基于生物芯片作为整个细胞的用于水毒性检测的电化学生物传感器，并对其进行了数值求解和分析。在此类论文中，使用特定酶促反应方程和扩散方程描述了小型电化学生物传感器系统中的动力学过程。数值解与测量数据显示出极好的一致性，但是这种数值解不足以有效地设计相应的生物芯片。因此，需要一种分析解决方案。本工作的目的是提供这种分析解决方案，然后给出代数指导来设计生物传感器。使用计算机代数软件（特别是Maple）获得分析溶液。解决方法是具有Bromwich积分和残差定理的Laplace变换。最终解决方案由一系列Bessel函数给出，并计算了生物传感器的有效时间。据称，所获得的分析解决方案对于预测具有不同几何形状，材料和生物成分的类似系统中的进一步电流变化将非常有用。除此之外，我们提供的分析解决方案对于研究不同腔室参数（例如细胞半径和高度）之间的关系非常有用。和电极半径。

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