Laurent Simon, Ph.D. - Providing more effective and affordable healthcare.

Collaborative Partnerships
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Our group is interested in working with both academicians and private-sector researchers.
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Software Tools

Education is key to ongoing success of scientific discovery in this area. The Simon group uses its research activity to enhance and elevate the educational process for the scientists of tomorrow...the students enrolled in our high schools and universities. Software tools, using mathematical modeling, have been and are continuing to be developed to assist in this endeavor. The implementation of these tools will help create an environment where a symbiosis between practicality and fundamental knowledge becomes the norm and students will be able to devote more time understanding the relevancy of engineering in every day life.

Linear Mixed-Effects Models in Mathematica®

The codes are based on the book: "Mixed-Effects Models in S and S-Plus" written by José C. Pinheiro and Douglas M. Bates.

Evaluation of Stress in Rails (Devore, 2000): rail.nb, railres.nb, rail.dat
Radioimmunoassay of IGF-I Protein (Davidian and Giltinan, 1995): ifg.nb, igfres.nb, igf1.dat

Transdermal Drug-Delivery Systems

The codes are developed to simulate drug transport across the skin.

Models of transdermal drug delivery - analytical and orthogonal collocations-based solutions: transderm.nb
Models of transdermal drug delivery - analytical and orthogonal collocation on finite elements (OCFE)-based solutions: transOCFE.nb

webMathematica Applications

webMathematica examples and applications are provided.

2D graph (example introduced by Wolfram Research, Inc.): 2D Plotting
Analytical integration (example introduced by Wolfram Research, Inc.): Function integration
Drug transport across the skin: Drug released
Heat-aided transdermal drug delivery: Heat drug released
Iontophoretic drug transport across the skin: Ionto drug released
Two-pathway transdermal drug-delivery model: Two-pathway drug released
Two-compartment pharmacokinetic model with Michaelis-Menten kinetics (contribution by Kwangseok Kim, Ph.D. candidate): PhKin
Transdermal drug-delivery model - Epidermal turnover: Turnover
Optimum drug dosage regimen: Multiple iv boluses plus infusion (contribution by Kwangseok Kim, Ph.D. candidate): OptKin
In vitro drug release from microspheres (contribution by Kwangseok Kim, Ph.D. candidate): Microsphere
Estimation of one-compartment pharmacokinetic parameters (contribution by Kwangseok Kim, Ph.D. candidate): One-Compartment PhKin
Optimum drug dosage regimen in one-compartment models (constant dosing interval): Multiple iv boluses: Onephk
Optimum drug dosage regimen in one-compartment models (two treatment strategies are compared): Multiple iv boluses: Onephkkim1