Idiopathic Intracranial Hypertension (IIH) Models:
In this research I am working with a group of mathematicians and neurosurgeons at the University of Vermont and a Neurologist in Cleveland (Case Western Reserve University). A down-stream starling like resistor has been incorporated into various intracranial models and the resulting dynamics mimic those observed in IIH patients and other pathological ICP patterns such as plateau waves (A-waves) and B-waves.  We believe we have discovered the cause of these disorders.

Four publications relating to this topic 

1) Stevens, Previte, Lakin, Thakore, Penar, and Hamschin: "Idiopathic Intracranial Hypertension and Transverse Sinus Stenosis: A Modeling Study". Mathematical Medicine and Biology 24(1) 85-109 (2007). Abstract

2) Lakin WD, Stevens SA, and Thakore NJ . "On the Pressure Dependence of a Starling-Like Resistor". International Journal of Pure and Applied Mathematics: 32(2) (2006) Abstract

3) S.A. Stevens, W.D. Lakin, N.J. Thakore, P.L. Penar and B.I. Tranmer: "A modeling study of idiopathic intracranial hypertension", In Modelling in Medicine and Biology VI, (Edited by M. Ursino et al.), WIT Press, Southampton, UK (2005), pps. 47-56. Abstract

4) Another manuscript is in-press with Neurological Research

Microgravity Models: 
We've spent quite a bit of time researching the effects of microgravity on the the cardiovascular and intracranial systems.  

The paper describing the whole-body model:
7) Lakin, Stevens, Tranmer, and Penar:  "A whole-body mathematical model for intracranial pressure dynamics." Journal of Mathematical Biology, 46: 347-383 (2003) Copyright holder: Springer-Verlag.     abstract and authors  PDF reprint   The original publication is available at http://link.springer.de or http://link.springer-ny.com. (protected) DOI: http://dx.doi.org/10.1007/s00285-002-0177-3 (protected)
 

The paper describing the intracranial response to microgravity:
Stevens SA, Lakin WD, and Penar PL: Modeling steady-state intracranial pressures in supine, head-down tilt, and microgravity conditions. Aviation, Space, and Environmental Medicine 76(4):329-338 (2005).
Reprints available upon request or go to the ASMA home page and order a reprint through Ingenta.
Abstract and Authors.

The paper describing systemic circulatory system dynamics:
Stevens SA and Lakin WD: "A mathematical model of the circulatory system with logistically defined nervous system regulatory mechanisms". Mathematical and Computer Modelling of Dynamical Systems. 12(6): 555-576 (2006). Reprints available upon request.  Abstract

Other papers describing intracranial fluid dynamics: 
1) Stevens and Lakin: "Local Compliance Effects on the Global CSF Pressure-Volume Relationship in Models of Intracranial Pressure Dynamics."  Mathematical and Computer Modeling of Dynamical Systems, 2000, Volume 6, Number 4, pp 445-465.     abstract and authors  or   PDF copy

2) Stevens: "Mean Pressures and Flows of the Human Intracranial System as Determined by Mathematical Simulations of a Steady-State Infusion Test."Neurological Research, 2000, 22, 809-814.       abstract and authors  or   PDF copy

International Heart Institute: 
1) Wolfgang A Goetz, Emmanuel Lansac, Hou-Sen Lim, Scott A Stevens, Patricia A Weber and Carlos MG Duran: " Kinking of the Atrioventricular Plane During the Cardiac Cycle". Asian Cardiovasc Thorac Ann. 14:394-398 (2006) Abstract

2) Stevens, Lakin, and Goetz: "A Differentiable, Periodic Function for Pulsatile Cardiac Output Based on Heart Rate and Stroke Volume" Mathematical Biosciences 2003, 182, 201-211  abstract and authors  or     PDF copy For a very slick copy with active links see: DOI: http://dx.doi.org/10.1016/S0025-5564(02)00200-6


Below is an animation of sonomicrometry crystals in the mitral valve and left ventricle of a sheep.  The left images illustrate the 3-D  structure of the valve and left ventricle.  The right images represent a 2-D view of the mitral valve annulus looking down into the left ventricle.  The units are in millimeters.  The light blue curve describing the mitral valve annulus was generated using cubic spline interpolation.   This is only 8 figures representing one cardiac cycle.  With a more refined movie playing device it is possible to view these images at "real time" of 200 frames per second. However, in order to accomodate web viewing,  the temporal resolution was reduced.  To view complete cardiac cycles of all the frames, view or download   mitral.avi  .   The files used to generate these animations are listed below.

MATLAB Files used to generate these images:

lisa.m   (the actual data from a sheep named lisa)
ann.m (builds the cubic spline of the mitral annulus.  called by runit.m)
coeffmatrix.m  (builds the matrix that generates the cubic spline. called by ann.m )
runit.m  (makes the movie.  calls lisa.m and ann.m)

Below, the interior of the left ventricle surface is generated by a B-Spline surface interpolation technique. The algorithm for approximation/interpolation of a cloud of points by a B-spline surface was designed by Professor George Wolberg  from The City College of New York. Many of the algorithms used in generating these images were provide by  Zoran Lazarevic  at Columbia University in New York.  The data came from   The International Heart Institute of Montana. Again, the temporal resolution was reduced to aid in web-viewing. To view complete cardiac cycles of all the frames, view or download   surface.avi.   To see the types of analysis with regards to left-ventricle pressure and volume as well as aortic pressure and flow, view or download pressvol.avi.