Follow Up of a subject with Hemiparetic stroke using Interval - PowerPoint PPT Presentation

“ Follow Up of a subject with Hemiparetic stroke using Interval Computations ” Jorge Garza-Ulloa Electrical & Computer Engineering Doctoral Program The University of Texas at El Paso jgarzaulloa@miners.utep.edu uno@computecworld.com EE313 HUMAN LAB 1 (#)

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa Motivation Real Case for the Follow-Up: We have a subject that had a Hemiparetic stroke. Information about the Stroke Patient  37 year old female  Hemiparetic Stroke  First visit: February 2010  Second visit: April 2010  Symptoms: Right hemiparetic  Treatment: Hydrotherapy “the best tools for balance evaluation in patients with stroke are still under debate.” Volume 45 Number 8, 2008 Journal of Rehabilitation Research & Development Can we do something to help? 2

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa Outline 1.Introduction to: Interval Computations & Hemiparetic stroke 1. Treadmill Bortec to get data from subjects 2.Understanding the Human Gait Cycle . 3.Specification from the follow-up of the subject 4.Information of 2 visits of the subject 5.Defining Coefficients for follow-up 7. Conclusions 3

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa 1.- Introduction to Hemiparetic stroke Stroke is a sudden impairment in brain function. Usually, this is caused by the blockage, or the rupture, of a blood vessel Hemiparesis is muscle weakness on only one side of the body. When Hemiparesis happens as a result of a stroke, it commonly involves muscles in the face, arm, and leg. Hemiparesis is the most frequent neurological deficit after stroke . 4

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa How can we test a subject with Hemiparetic stroke? The treadmill analysis, it’s a split -belt instrumented treadmill (Bertec Corp.) measuring the Ground Reaction Forces (GRFs) of the subject. 5

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa What are we measuring ? Gait Cycle Ground Reaction Forces and Phases 33

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa 1.- Introduction to Interval Computations Basic Math Operations: Example: Besides computational existence and uniqueness, interval arithmetic provides several other elementary but powerful tools. The most prominent, already 7 mentioned, is bounding the ranges of functions .

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa 1.- Introduction to Interval Computations Application of Interval: • Linear Systems _ Bounding the solution set of an interval linear system is as fundamental in interval computations as in traditional point computations. An interval linear system is a system of the form AX = B; • Nonlinear Systems/Optimization _ Because of interval arithmetic’s power to bound ranges of functions, interval arithmetic has arguably been most successful in solution of nonlinear systems and global optimization. In global search algorithms for nonlinear systems of the form. • Quadrature _ Adaptive quadrature is another area in which interval methods have much to offer. • Initial Value Problems _ provide enclosures for errors in the initial values, mathematical truncation, and roundoff errors, so that, for each time point ti, intervals are produced that contain the actual solution . • Boundary Value Problems and Partial Differential Equations _ in principle, be converted to systems of ordinary differential equations or linear or nonlinear algebraic systems. 8 • Integral Equations and more

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa 4.- Specification from the follow-up of the subject Test: Ground Reaction Forces from the subject First Visit 2-Feb-2010 She made the test a very slow Speed only 2 cycles on 500 unit times Second Visit 28-Apr-2010 She made the test medium slow Speed only 3.5 cycles on 500 unit times How can we compare both charts for Follow up? 9

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa Ranges - First Visit First Visit 2-Feb-2010 She made the test a very slow Speed only 2 cycles on 500 unit times Obtaining the ranges of Visit 1 10

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa Ranges of second Visit First Visit 2-Feb-2010 She made the test a very slow Speed only 2 cycles on 500 unit times Obtaining the ranges of Visit 2 11

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa Defining Coefficients for follow-up Healthy Subject has a Delta very small and the subject with stroke has a big delta Average of Delta Max_Delta First Visit _Subject 0.032746 .212285 Second Visit_ Subject 0.0188 0.1027 Normal Health Subject 0.007027 0.039825 How can we compare the next charts for Follow up if they have different speed? 12

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa Defining Coefficients for follow-up GRC We need to define a new term On Human Gait Cycle to adjust speed: GRC ( G ait R elative Coefficient )= actual speed/Normal speed of the subject Speed ( m/s ) GRC ( G ait R elative Coefficient ) First Visit _Subject 0.25 0.2632 Second Visit_ Subject 0.5 0.5263 Normal Healthy Subject .95 1 The GRC must be applied on the Unit Time 13

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa Coefficient CF of Gait Cycle How can we differentiate when a subject is doing a good Gait cycle independent of speed? Answer: During gait cycle the normal is 60% stance 40% swing Based on this we need a R elative C oefficient F actor (CF): RCF=ARC/ERC Where ERC is the E xpected R ate C ycle and ARC the A ctual R ate C ycle RCF RCF using X_Med (CF) Coefficient ranges First Visit _Subject 3.0 [2.96,3.04] Second Visit_ Subject 2.0 [1.97,2.03] Normal Healthy Subject 1.0 [0.99 1.01] 14

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa 6. Conclusions We have 3 parameters to measure the follow-up of a subject using his Gait Human Cycle: Relative Coefficient Factor (CF), GRC ( G ait Relative Coefficient Max_Delta of Ranges best RCF (C oefficient F actor GRC ( G ait R elative Max_Delta of x_med Coefficient ) Normal Healthy 1.0 1.0 0.039825 Subject Second Visit_ 2.0 0.5263 0.1027 Subject First Visit 3.0 0.2632 .212285 _Subject On this case She is improving with the Rehabilitation 15

Follow Up of a subject with Hemiparetic stroke using Interval Computations Jorge Garza-Ulloa 7. Conclusions for the future “It is not over, now that we obtain: The Get Relative Gait Cycle using data using Interval Computations theory We will have to prove it …” 16