This paper presents a vision-based method to model a precision loadcell with artificial neural networks. The proposed model is used for measuring the applied force to a spherical biological cell during micromanipulation processes. The devised vision-based method is most useful where force feedback is required while integrating a force sensor into a cell micromanipulation setup is a challenging job. The proposed neural network model is used in conjunction with a methodology to track and characterize the cell deformation by extracting a geometric feature referred to as the 'dimple angle' directly from images of the cell micromanipulation process. The neural network is trained and used for the experimental data of zebrafish embryos micromanipulation. However, the proposed neural network is applicable for indentation of any other spherical elastic object. The results demonstrate the capability of the proposed method. The outcomes of this study could be useful for measuring force in biological cell microinjection processes such as injection of the mouse oocyte/embryo.