One of the interests of the Biotransport and Metabolic Monitoring Laboratory (PI: Dr. Dale A. Baker) within the Department of Bioengineering at UCSD is the role of oxygen and lactate concentration in health and various disease states. Lactate and oxygen are key metabolites of interest to medical professionals and exercise physiologists. The concentrations of these metabolites have importance in conditions related to hypoxia, ischemia, acidosis, and anaerobic metabolism. Such situations occur in shock and resuscitation, heart disease, vascular occlusive disease, pulmonary insufficiency and stroke in various organs, but most notably the brain. Lactate and oxygen concentration also show marked changes with exercise and during sports such as running, swimming and diving. To measure the concentration of lactate and oxygen in vivo and continuously with time, the members of our laboratory have been developing an implantable biosensor based on the enzyme electrode principle for real time and continuous monitoring. This presentation will show research on the role of the transport phenomena and catalysis/enzymatic reaction in a continuous in vivo sensor for lactate and oxygen. By using fundamental chemical engineering analysis of mass transfer and reaction in this immobilized enzyme system, the basic physical parameters (equilibrium, kinetic and diffusive transport) that influence the sensor response can be shown. To better characterize these parameters, investigations with a membrane-covered von Karman spinning disc have been conducted and will be highlighted in this presentation. The membrane-covered von Karman spinning disc is also known as the membrane-covered rotated disc electrode by researchers in electrochemistry. The basic momentum transport or fluid mechanics were described for the rotated disc by Theodore von Karman in 1921. The basic electrochemical phenomena of this rotated disc as an electrode were described by Veniaamin G. Levich in his book entitled, Physicochemical Hydrodynamics, in 1962. Our laboratory has used this unique rotated disc electrode and electrochemical methods for the characterization of the transport and reaction in membranes containing immobilized enzymes. Membranes containing the enzyme, lactate oxidase, the most common oxidase enzyme used for making enzymatic lactate sensors, have been made by crosslinking the enzyme and support matrix/protein with glutaraldehyde. Transport of lactate, oxygen and hydrogen peroxide in the membranes can be analyzed in quantitative detail taking into account the external mass transfer resistance. Techniques have been developed for determining the kinetic constants and intrinsic activity of the immobilized enzymes using the rotated disc electrode and will be discussed. These techniques permit non-destructive determination of the activity of the enzyme in the immobilized state. Additionally, repeated kinetic determinations can be made on membranes stored at 37^o C under near physiologic conditions to simulate enzyme inactivation, giving the rate constants for inactivation of lactate oxidase. The mechanisms of enzyme inactivation can also be determined with this system by looking at membrane performance on the rotated disc electrode over days, weeks or months. The sensor signal should remain relatively constant while the enzyme activity is high and the sensor operates in a diffusion-limited mode, but when activity drops below a critical value, the membrane/electrode system operates in a reaction-limited mode and the signal can then decay rapidly. The apparatus and mathematical models of transport and reaction allow determination of the necessary loading above the critical value to ensure proper sensor signal stability and extension of the useful lifetime of the sensor. Mathematically, the lactate/oxygen sensor can be described by a coupled set of second-order partial differential equations that account for the nonlinear, two-substrate reaction-diffusion processes that are involved. The equations are derived based on the classical methods of species conservation, proper description of the boundary and initial conditions, non-dimensionalization and appropriate scaling. This yields a reaction/diffusion model, which is solved numerically. This model is used in conjunction with the kinetic sensor parameters, which are determined by the rotated disc electrode experimental studies described above. The numerical simulations will be presented to show the parameters that affect the steady state and un-steady state response of the sensor system. Discussion of the experiments to verify the model simulations for the transient and steady state cases will also be presented. The role of internal and external mass transfer resistance as revealed by the appropriate Biot numbers will be shown. The dimensionless Biot numbers provide information for designing lactate/oxygen sensors for use in the two biological environments of interest to medical researchers: the bloodstream and the tissue (subcutaneous, cutaneous, etc.). The use of fundamental chemical engineering principles for conceptualization, design, analysis and testing (in vitro and in vivo) of this enzymatic biosensor system has allowed systematic progress toward the development of implantable biosensor and bio-instrumentation for measurement of lactate and oxygen concentrations in animals and humans.

Keywords: Transport Phenomena, Mass Transfer, von Karman, Levich, Physicochemical Hydrodynamics, Biot, Enzyme-Electrode, In vivo Biosensor, Implantable Sensors, Modeling, Simulation, Bioinstrumentation, Lactate, Oxygen