0018-9294 (c) 2015 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TBME.2015.2403266, IEEE Transactions on Biomedical Engineering IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. XX, NO. X, MONTH 2015 1 Nonlinear Dynamic Modelling of Platelet Aggregation via Microfluidic Devices Miguel E. Combariza, Member, IEEE, Xinghuo Yu*, Fellow, IEEE, Warwick S. Nesbitt, Arnan Mitchell, Member, IEEE, and Francisco J. Tovar-Lopez Abstract—The recent application of new microfluidic tech- nologies and methods has facilitated significant progress in the understanding of the fundamental mechanisms governing blood platelet function and how these parameters affect pathological thrombus formation. In-line with these new bioengineering ap- proaches, the application of nonlinear dynamic systems analysis holds particular potential to extend our understanding of the complex interplay between mechanical and biochemical factors that underlie this complex biological phenomenon. In this paper we propose a simple mathematical model of the main dynamics of platelet aggregation/disaggregation observed experimentally in a novel microfluidic device that approximates a severe arterial stenosis. We apply dynamic systems theory (system identification) to explore the dynamics of the biomechanical platelet aggregation response to a range of shear stress rates, inhibiting blood- born chemical pathways of platelet activation (ADP, TXA2 and thrombin). We demonstrate that the proposed model is able to replicate experimental results with low variation, and suggest that the reduced set of model parameters has the potential to be used as a simplified way to evaluate the biomechanical dynamics of platelet aggregation. The proposed model has application to the development of automatic controllers within the context of microfluidic systems that may show great utility in the clinical assessment of platelet hyperfunction. Index Terms—Blood, diagnosis, disturbed flow, microfluidics, platelet aggregate, platelet function, shear rate, system identifi- cation I. I NTRODUCTION P LATELETS play a key role in the arrest of bleeding (haemostasis) and subsequent vascular repair. This is achieved through their adhesion and aggregation at sites of blood vessel damage. However, alterations of normal blood Manuscript received August 15, 2013; revised December 09, 2014; accepted January 20, 2015. Asterisk indicates corresponding author. This paper has supplementary downloadable material available at http://ieeexplore.ieee.org, provided by the authors. This includes one multime- dia AVI format movie clip, which shows epi-fluorescence images of platelet aggregation/disaggregation in response to different shear rate conditions, and one PDF file, containing the Supplementary Information: SI Appendix 1 presents details on the image processing algorithm employed in this study, SI Appendix 2 shows Computational Fluid Dynamics simulations demonstrating the presence of a flow vortex proximal to the aggregate when it reaches a particular size, and SI Appendix 3 presents a summary of the operational parameters of microfluidics device employed for this study. This material is 12 MB in total size. ME. Combariza, FJ. Tovar-Lopez and A. Mitchell are with the Microplatforms Research Group, School of Electrical and Computer Engineering, RMIT University, Melbourne, VIC 3001, Australia (e- mails: miguel.combariza@rmit.edu.au; francisco.tovarlopez@rmit.edu.au; ar- nan.mitchell@rmit.edu.au). *X. Yu is with the Platform Technologies Research Institute, RMIT University, Melbourne, VIC 3001, Australia (e-mail: x.yu@rmit.edu.au). WS. Nesbitt is with The Bionics Institute Australia, East Melbourne, VIC 3002, Australia (email: wnesbitt@bionicsinstitute.org ). flow at sites of atherosclerotic plaque rupture or vessel narrow- ing (stenosis), can significantly amplify the platelet response leading to pathological platelet aggregation and thrombo- sis. Despite decades of research into the underlying platelet functional parameters that put patients at risk of thrombotic disease, the underlying mechanisms by which mechanical and biochemical parameters affect platelet function remain difficult to observe and analyse. Existing clinical testing relies on functional screens that are time consuming and fail to account for the integration of both mechanical and biochem- ical parameters. The application of advanced microfluidic technologies and the use of control engineering methods to platelet functional analysis offer new opportunities for the development of point of care diagnostics. Recent work suggests that under conditions of blood flow disturbance current anti-platelet therapies may be ineffective in limiting platelet aggregation. These studies have demonstrated a major role for shear rate micro-gradients in the initiation and maintenance of platelet aggregation [1]. A conceptual model of this process is illustrated in Fig. 1, in which initial platelet aggregation and thrombus development are regulated by two distinct, complementary processes [2]. These new insights into the mechanisms of platelet aggregation have motivated the development of flow-based devices for measuring platelet function that consider shear stress and blood flow distur- bances [3]–[11]. Several spatial-temporal mathematical models of platelet ag- gregation have benefited from new experimental microfluidic platforms available, and focused their analysis on the impact of blood flow on thrombus formation [12]–[19]. Microfluidic devices have evident advantages over traditional parallel-plate chambers, and cone-and-plane viscometery methods [20], such as precise control of blood flow parameters, and the ability to perform multiple experiments with small blood sample volumes, and high throughput [9]. Further, due to the enhanced precision, complexity and parallelism that is possible with these platforms, there is the potential to evaluate multiple aspects of platelet function and thrombus formation simulta- neously [3]. Evaluation of platelet function under flow conditions typ- ically consists of analysing the time dependent adhesion and aggregation profile. Analyses are commonly represented by parameters such as: lag time, aggregation rate, maxi- mum thrombus size, or total aggregation, for each shear rate tested [8]. The result is often a set of data of considerable size and large coefficient of variation. Furthermore, post-processing of experimental results can be time consuming and are often