Multicomponent DS Fusion Approach for Waveform EKG Detection Nicholas Napoli University of Virginia njn5fg@virginia.edu August 10, 2013 Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 1 / 33
Overview 1 Goal 2 Current EKG Signal Detection An Ideal Employed EKG Algorithm Common Employed Approaches Downfalls 3 Dempster-Shafer (DS) Theory 4 Multicomponent DS Fusion Approach for Waveform EKG Detection Template Models and Windowing Windowing and Components Designing Evidence Model for DS Masses Visual Examination of Results: The Benefits of Fusion 5 Future Work Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 2 / 33
Objective The development and comparison of electrocardiography (EKG) algorithms for the detection of physiological conditions that will aid in the prediction of Medical Emergency Team (MET) calls. MET Calls: When a patient s physiology breach certain parameters that represent severe deterioration. EKG Interpretation: Finds the cause of symptoms of heart disease, such as shortness of breath, dizziness, fainting, or rapid, irregular heartbeats (palpitations) Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 3 / 33
An Ideal Employed EKG Algorithm 1 Should provide reliable detection of each cardiac cycle 2 The temporal reference location of the cycle should be accurate Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 4 / 33
Common Employed Approaches 1 Power Spectrum Analysis 2 Non-Syntactic Algorithm Differentiation Technique Thresholding 3 Template Matching Techniques Template Cross Correlation Template Subtraction Automata-Based Template Matching Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 5 / 33
Power Spectrum Analysis Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 6 / 33
Differentiation Techniques Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 7 / 33
Thresholding Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 8 / 33
Template Subtraction Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 9 / 33
Downfalls 1 Lead information can be unreliable 2 Typically we make a decision based on one designated lead 3 There is no uncertainty present in the decision Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 10 / 33
Conceptual Overview of Dempster-Shafer (DS) Theory DS Theory has an ability to handle imperfect data (Conflict) DS Theory is an approach to combining evidence Each part of Evidence has a degree of support between 0 and 1 0 No support is given to the evidence 1 Full support is given to the evidence It s a generalization of probability theory The axiom of additivity is relaxed in DS theory Belief in the evidence and its complement do not need to sum to 1 Both values can be 0 (Therefore no evidence for or against the fact) DS theory allows supports to be assigned to the complete power set of possibilities It s framework handles uncertainty Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 11 / 33
DS Theory: Frame of Discernment or Power Set Set of possible conclusion: Θ Θ = {θ 1, θ 2,... θ n, } where: Θ is the set of possible conclusions to be drawn Each θ i is mutually exclusive: at most one has to be true Θ is exhaustive: At least one θ i has to be true Differences between Bayes and DS Theory: Bayes was concerned with evidence that supported single conclusions (e.g., evidence for each outcome θ i in Θ ) D-S Theory is concerned with evidences which support subsets of outcomes in Θ, e.g., {θ 1, θ 2, θ 3 } Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 12 / 33
DS Theory: Frame of Discernment or Power Set The frame of discernment (or Power set) of Θ is the set of all possible subsets of Θ: E.g., if Θ = {θ 1, θ 2, θ 3 } Then the frame of discernment of Θ is: {, θ 1, θ 2, θ 3, {θ 1, θ 2 }, {θ 2, θ 3 }, {θ 1, θ 3 }, {θ 1, θ 2, θ 3 }}, the empty set, has a probability of 0, since one of the outcomes has to be true. Each of the other elements in the power set has a probability between 0 and 1. The probability of Θ = {θ 1, θ 2, θ 3 } is 1.0 since one has to be true Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 13 / 33
Basic Probability Assignment (BPA) The mass function (m(a))or BPA is a given member of the power set. Theorem (Basic Probability Assignment (BPA)) m( ) = 0; m(a i ) = 1. (1) A i 2 Ω Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 14 / 33
Dempster Shafer Evidence Evidence is required in order to develop a mass function. Evidence is then fused to dynamically update the mass function. Aids in the mass functions reduction of uncertainty Aids in the redistributing the mass to the propositions. Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 15 / 33
Combining Evidence Dempster s Combination Rule (DCR) m 1 (A p ) m 2 (A q ) A p A q=a i m(a i ) = m 1 (A p ) m 2 (A q ), (2) A p A q= where the evidence provided by the mass functions m 1 and m 2 are combined to get the fused mass function m. This is usually denoted as m = m 1 m 2. (3) Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 16 / 33
DS Application to Patient Diagnostics Consider a medical diagnosis problem in which we have four mutually exclusive hypotheses: C(Common Cold) F(flu) M(Meningitis) N(No Problem) Thus, the Power Set is Θ = {C, F, M, N}. Fever Evidence: m1(x ) Let us assume the evidence provided is from medical cases that support: m 1 ({C, F }) =.5 m 1 ({M}) =.2 m1({θ}) =.3 Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 17 / 33
DS Application to Patient Diagnostics Nausea Evidence 2: m 2 (X ) Let us assume additional evidence provided and that it is supported from previous medical cases: m 2 ({C, F, N}) =.7 m 2 ({Θ}) =.3 Since, new information is provided we can make a better informed decision by applying an evidence fusion technique(dcr). m 1 BPA m 2 BPA Intersection Product { C,F }.5 { C,F,N }.7 { C,F }.35 { C,F }.5 { Θ }.3 { C,F }.15 { M }.2 { C,F,N }.7 { }.14 { M }.2 { Θ }.3 { M }.06 { Θ }.3 { C,F,N }.7 { C,F,N }.21 { Θ }.3 { Θ }.3 { Θ }.09 Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 18 / 33
DS Application to Patient Diagnostics New BPA: m 3 = m 1 m 2. Provided by the empty set the normalizing factor is 1.14 =.86 m3({c, F }) = (.35+.15).86 =.581 m3({m}) = (.06).86 =.07 m3({c, F, N}) (.21).86 =.244 m3({θ}) (.09).86 =.104 If further evidence was provided m 4, such as possible blood results we could then produce an additional new BPA, where m 5 = m 3 m 4. (4) Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 19 / 33
Multicomponent DS Fusion Approach for Waveform EKG Detection 1 Develop a Template 2 Develop a Windowing Scheme 3 Determine a Fusion Method 4 Develop a Evidence Model Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 20 / 33
Template Modeling Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 21 / 33
Template Modeling Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 22 / 33
Template Models Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 23 / 33
Windowing Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 24 / 33
Windowing and Components Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 25 / 33
The Fundamental Concept of Uncertainty Assignment Table : Assignment of Uncertainty with Regards to P and N. P N M(Θ) 1 128 0 32 128.25 64 128.50 96 128.75 128 128 1.0 Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 26 / 33
An Overview of DS Framework for Correlation Coefficients Example i: V = [0.01, 0.03, 0.12, 0.98] T M(V 1 ) M(V 2 ) M(V 3 ) M(V 4 ) = M(Θ) 0 0 0 0.9081 0.0919 (5) Example ii: V = [0.98, 0.83, 0.40, 0.30] T M(V 1 ) 0.2303 M(V 2 ) M(V 3 ) M(V 4 ) = 0.1120 0 0 M(Θ) 0.6577 Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 27 / 33
Thresholding Example iii: V = [0.31, 0.32, 0.43, 0.44] T M(V 1 ) 0 M(V 2 ) M(V 3 ) M(V 4 ) = 0 0.0158 0.0191 M(Θ) 0.9652 Example iv: V = [0.31, 0.32, 0.73, 0.74] T M(V 1 ) 0 M(V 2 ) M(V 3 ) M(V 4 ) = 0 0.0998 0.1061 M(Θ) 0.7942 Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 28 / 33
Visual Examination of Results: The benefits of Fusion Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 29 / 33
Visual Examination of Results: The benefits of Fusion Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 30 / 33
Complexity: Real Time? Time Series Length Beats TicToc 70.09 secs 131 21.74 secs 105.09 secs 197 32.38 secs 163.42 secs 267 51.60 secs Table : Processing Time: Evaluation After Filtering 98.3 % Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 31 / 33
Future Work 1 Fusion using Multi-Dimensional Windowing (Wavelets?) 2 Hidden Markov Model for Phase/Cardiac Style Detection 3 Add Templates of Disease Cardiac Cycles Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 32 / 33
The End Nicholas Napoli (UVa) Multicomponent EKG Fusion August 10, 2013 33 / 33