Medical Diagnosis Decision-Support System: Optimizing Pattern Recognition of Medical Data<br />W. Art Chaovalitwongse<br /...
Outline<br />Introduction<br />Classification: Model-Based versus Pattern-Based<br />Medical Diagnosis<br />Pattern-Based ...
Pattern Recognition:Classification<br />3<br />Supervised learning: A class (category) label for each pattern in the train...
Model-Based Classification<br />Linear Discriminant Function<br />Support Vector Machines<br />Neural Networks<br />4<br />
Support Vector Machine<br /><ul><li>A and B are data matrices of normal and pre-seizure, respectively
e is the vector of ones
 is a vector of real numbers
 is a scalar
u, vare the misclassification errors</li></ul>Mangasarian, Operations Research (1965); Bradley et al., INFORMS J. of Compu...
6<br />Pattern-Based Classification: Nearest Neighbor Classifiers<br />Compute Distance<br />Test Record<br />Training Rec...
7<br />Traditional Nearest Neighbor<br />    K-nearest neighbors of a record x are data points that have the k smallest di...
Drawbacks<br />Feature Selection<br />Sensitive to noisy features<br />Optimizing feature selection<br />n features, 2n co...
Multidimensional Time Series Classification in Medical Data<br />Positive versus Negative<br />Responsive versus Unrespons...
Ensemble Classification for Multidimensional time series data<br />Use each electrode as a base classifier<br />Each base ...
Modified K-Nearest Neighbor for MDTS<br />11<br />Normal<br />Abnormal<br />K = 3<br />D(X,Y)<br />Time series distances: ...
Dynamic Time Warping (DTW)<br />The minimum-distance warp path is the optimal alignment of two time series, where the dist...
Optimizing Pattern Recognition<br />13<br />
Support Feature Machine<br />Given an unlabeled sample A, we calculate average statistical distances of A↔NormalandA↔Abnor...
Two distances for each sample at each electrode are calculated:<br /><ul><li>Intra-Class:Average distance from each sample...
Inter-Class:Average distance from each sample to all other samples in different class at Electrode j
Averaging: If for Sample i (on average of selected electrodes)</li></ul>Averageintra-class distance over all electrodes<br...
Distance Averaging: Training<br />Industrial & Systems Engineering Rutgers University<br />16<br />∙∙∙<br />Sample i at Fe...
Majority Voting: Training<br />Industrial & Systems Engineering Rutgers University<br />17<br />Positive<br />Negative<br ...
Intra-Class<br />Inter-Class<br />SFM Optimization Model<br />Chaovalitwongse et al., KDD (2007) and Chaovalitwongse et al...
Averaging SFM<br />Maximize the number of correctly classified samples<br />Logical constraints on intra-class and inter-c...
Voting SFM<br />Maximize the number of correctly classified samples<br />Logical constraints: Must win the voting if a sam...
Support Feature Machine<br />21<br />
Support Vector Machine<br />Feature 3<br />Pre-Seizure<br />Feature 2<br />Normal<br />Feature 1<br />
Application in Epilepsy Diagnosis<br />23<br />
Facts about Epilepsy<br />About 3 million Americans and other 60 million people worldwide (about 1% of population) suffer ...
Simplified EEG System and Intracranial Electrode Montage <br />Electroencephalogram (EEG) is a traditional tool for evalua...
Scalp EEG Acquisition<br />18 Bipolar Channels<br />
Goals: How can we help?<br />Seizure Prediction<br />Recognizing (data-mining) abnormality patterns in EEG signals precedi...
Normal versus Pre-Seizure<br />28<br />
10-second EEGs: Seizure Evolution<br />Normal<br />Pre-Seizure<br />Post-Seizure<br />Seizure Onset<br />Chaovalitwongse e...
NormalversusPre-SeizureData Set<br />
Sampling Procedure<br />Randomly and uniformly sample 3 EEG epochs per seizure from each of normal and pre-seizure states....
Information/Feature Extraction from EEG Signals<br />Measure the brain dynamics from EEG signals<br />Apply dynamical meas...
Evaluation<br />Sensitivitymeasures the fraction of positive cases that are classified as positive. <br />Specificitymeasu...
Leave-One-Seizure-Out Cross Validation<br />P1<br />N1<br />SFM<br />Selected Electrodes<br />N2<br />P2<br />1<br />2<br ...
EEG Classification<br />Support Vector Machine [Chaovalitwongse et al., Annals of OR (2006)]<br />Project time series data...
Performance Characteristics:Upper Bound<br />37<br />NN -> Chaovalitwongse et al., Annals of Operations Research  (2006)<b...
Separation of Normal and Pre-Seizure EEGs<br />From 3 electrodes not selected by SFM<br />From 3 electrodes selected by SF...
Performance Characteristics:Validation<br />39<br />SVM-> Chaovalitwongse et al., Annals of Operations Research  (2006)<br...
Epilepsy versus Non-Epilepsy<br />40<br />
Epilepsy versusNon-EpilepsyData Set<br /><ul><li>Routine EEG check: 25-30 minutes of recordings ~ with scalp electrodes
Each sample is 5-minute EEG epoch (30 points of  STLmax values).
Each sample is in the form of 18 electrodes X 30 points </li></li></ul><li>Leave-One-Patient-Out Cross Validation<br />N1<...
Voting SFM: Validation<br />43<br />
Averaging SFM: Validation<br />44<br />
1    Fp1 – C3<br />16      T6 – Oz<br />17      Fz – Oz<br />
Other Medical Diagnosis<br />46<br />
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  • Here is the outline of this talk.The focus of this talk will be on epilepsy and brain disordersFirst I will try to convince the audience why this problem is important and those patients need our helpThen I will identify the research goals, then I’ll talk about how to acquire and process the data from the brain – specifically try to predict seizuresThe second research challenge is how to use optimization and data mining techniques to recognize/or classify normal and abnormal brain data – this framework can be applied to other medical data or data in other real life problems.
  • m = number of samples for class 1n = number of samples for class 2Bradley, Fung and Mangasarian revamped this idea – using this robust optimization model – it is very fast and scalable
  • For multidimensional time series, it is ideal to do multivariate analysis – but it is computationally impossible in our applicationIn our work , we use univariate analysis – perform classification on each electrode at a time.Then we use the idea of ensemble classification to make the final decision.
  • Most ensemble deal with how to sample the data Bagging, Bootstrapping Boosting, - here we use the idea of voting and averaging/or accumulating prediction scoreHere I give an example why we use ensemble classification
  • Today about 3 million americans and other 60 million people worldwide have epilepsy. Epilepsy is the second most common brain disorder after stroke. It causes recurrent seizures, which appear to occur spontaneously and randomly.What happens when someone has a seizure – in his or her brain, there is a massive group of neurons hypersynchronized in a highly organized rhythmic patterns – which lasts about 20 seconds to a few minsThis brain disease causes our country so much money – in 1995 estimate, it imposes an economic burden of $12.5 billions – no just healthcare cost - including job loss, productivityPer patient, the healthcare cost ranged from 4k to almost 140k per year – and these numbers are more than 10 years ago.By now I hope I’ve convinced the audience that we should do something about this disease – next I will discuss standard diagnosis, treatment, (acquired data) and how we can help these patients.
  • Given multi-dimensional time series and a set of events/episodes (if you will). How can we predict the eventClassification of medical data (normal and abnormal) for guiding the future diagnosisFeature selection -&gt; initiating events – most differentiable
  • First we implement a modified support vector machine, which is one of the most commonly used classification technique. The main idea is to
  • Overfitting the dataSample sizeCPU time
  • The issue is not just to get 100% classification – rather we focus more on why we get that kind of results and understand the data.For example, we look at the selected electrodes that help in distinguishing epilepsy and non-epilepsy patients. We found 3 electrodes that play a major role – when we went back to the neurologists and talked to him. He was very surprised to see.One would not expect to see that the selected electrodes would be involved in epilepsy mechanisms.Again it could be the scalp electrode – one focus on the left but electrodes on the right pick up first.
  • We envision the outcome of our research in medical diagnosis as a tool or apparatus to process medical data signalThis is just my vision but we still have a long way to go.We have started off with neurophysiological signals like electroencephalograms or fMRI –Then use the tools developed over the course of my research as an automated decision support systems for physicians to helpRecognize abnormal data or abnormal patterns in medical dataTry to localize the source of abnormalityRecommend the diagnosis outcome – rather improve the confidence in the diagnosis
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    1. 1. Medical Diagnosis Decision-Support System: Optimizing Pattern Recognition of Medical Data<br />W. Art Chaovalitwongse<br /> Industrial & Systems Engineering<br /> Rutgers University<br /> Center for Discrete Mathematics & Theoretical Computer Science (DIMACS)<br /> Center for Advanced Infrastructure & Transportation (CAIT)<br /> Center for Supply Chain Management, Rutgers Business School<br />This work is supported in part by research grants from NSF CAREER CCF-0546574, and Rutgers Computing Coordination Council (CCC).<br />
    2. 2. Outline<br />Introduction<br />Classification: Model-Based versus Pattern-Based<br />Medical Diagnosis<br />Pattern-Based Classification Framework<br />Application in Epilepsy<br />Seizure (Event) Prediction<br />Identify epilepsy and non-epilepsy patients<br />Application in Other Diagnosis Data<br />Conclusion and Envisioned Outcome<br />2<br />
    3. 3. Pattern Recognition:Classification<br />3<br />Supervised learning: A class (category) label for each pattern in the training set is provided.<br />Positive Class<br />Negative Class<br />?<br />
    4. 4. Model-Based Classification<br />Linear Discriminant Function<br />Support Vector Machines<br />Neural Networks<br />4<br />
    5. 5. Support Vector Machine<br /><ul><li>A and B are data matrices of normal and pre-seizure, respectively
    6. 6. e is the vector of ones
    7. 7.  is a vector of real numbers
    8. 8.  is a scalar
    9. 9. u, vare the misclassification errors</li></ul>Mangasarian, Operations Research (1965); Bradley et al., INFORMS J. of Computing (1999)<br />
    10. 10. 6<br />Pattern-Based Classification: Nearest Neighbor Classifiers<br />Compute Distance<br />Test Record<br />Training Records<br />Choose k of the “nearest” records<br />Basic idea:<br />If it walks like a duck, quacks like a duck, then it’s probably a duck<br />
    11. 11. 7<br />Traditional Nearest Neighbor<br /> K-nearest neighbors of a record x are data points that have the k smallest distance to x<br />
    12. 12. Drawbacks<br />Feature Selection<br />Sensitive to noisy features<br />Optimizing feature selection<br />n features, 2n combinations  combinatorial optimization<br />Unbalanced Data<br />Biased toward the class (category) with larger samples<br />Distance weighted nearest neighbors<br />Pick the k nearest neighbors from each class (category) to the training sample and compare the average distances.<br />8<br />
    13. 13. Multidimensional Time Series Classification in Medical Data<br />Positive versus Negative<br />Responsive versus Unresponsive<br />Multidimensional Time Series Classification<br />Multisensor medical signals (e.g., EEG, ECG, EMG)<br />Multivariate is ideal but computationally impossible<br />It is very common that physicians always use baseline data as a reference for diagnosis<br />The use of baseline data - naturally lends itself to nearest neighbor classification<br />Normal<br />Abnormal<br />?<br />9<br />
    14. 14. Ensemble Classification for Multidimensional time series data<br />Use each electrode as a base classifier<br />Each base classifier makes its own decision<br />Multiple decision makers - How to combine them?<br />Voting the final decision <br />Averaging the prediction score<br />Suppose there are 25 base classifiers<br />Each classifier has error rate,  = 0.35<br />Assume classifiers are independent<br />Probability that the ensemble classifier makes a wrong prediction (voting):<br />10<br />
    15. 15. Modified K-Nearest Neighbor for MDTS<br />11<br />Normal<br />Abnormal<br />K = 3<br />D(X,Y)<br />Time series distances: (1) Euclidean, (2) T-Statistical, (3) Dynamic Time Warping<br />
    16. 16. Dynamic Time Warping (DTW)<br />The minimum-distance warp path is the optimal alignment of two time series, where the distance of a warp path W is: <br /> is the Euclidean distance of warp path W.<br /> is the distance between the two data point indices <br /> (from Liand Lj) in the kth element of the warp path.<br />Dynamic Programming:<br />The optimal warping distance is<br />12<br />Figure B) Is from Keogh and Pazzani, SDM (2001)<br />
    17. 17. Optimizing Pattern Recognition<br />13<br />
    18. 18. Support Feature Machine<br />Given an unlabeled sample A, we calculate average statistical distances of A↔NormalandA↔Abnormalsamples in baseline (training) dataset per electrode (channel). <br />Statistical distances: Euclidean, T-statistics, Dynamic Time Warping<br />Combining all electrodes, A will be classified to the group (normal or abnormal) that yields <br />the minimum average statistical distance; or<br />themaximumnumber of votes <br />Can we select/optimize the selection of a subset of electrodes that maximizes number of correctly classified samples<br />14<br />
    19. 19. Two distances for each sample at each electrode are calculated:<br /><ul><li>Intra-Class:Average distance from each sample to all other samples in the same class at Electrode j
    20. 20. Inter-Class:Average distance from each sample to all other samples in different class at Electrode j
    21. 21. Averaging: If for Sample i (on average of selected electrodes)</li></ul>Averageintra-class distance over all electrodes<br />Averageinter-class distance over all electrodes<br /><<br />We claim that Sample i is correctly classified.<br />SFM: Averaging and Voting<br /><ul><li>Voting: If for Sample i at Electrodej (vote)</li></ul>Intra-class distance < Inter-class distance (good vote)<br />Based on selectedelectrodes, if # of good votes > # of bad votes, then Sample iis correctly classified.<br />Chaovalitwongse et al., KDD (2007) and Chaovalitwongse et al., Operations Research (forthcoming)<br />
    22. 22. Distance Averaging: Training<br />Industrial & Systems Engineering Rutgers University<br />16<br />∙∙∙<br />Sample i at Feature 1<br />Sample i at Feature 2<br />Sample i at Feature m<br />Select a subset of features ( ) such that<br /> as many samples as possible.<br />
    23. 23. Majority Voting: Training<br />Industrial & Systems Engineering Rutgers University<br />17<br />Positive<br />Negative<br />Negative<br />Positive<br />i<br />Feature j<br />Feature j<br />i’<br /> (Correct) if ; (Incorrect) otherwise. <br />
    24. 24. Intra-Class<br />Inter-Class<br />SFM Optimization Model<br />Chaovalitwongse et al., KDD (2007) and Chaovalitwongse et al., Operations Research (forthcoming)<br />
    25. 25. Averaging SFM<br />Maximize the number of correctly classified samples<br />Logical constraints on intra-class and inter-class distances if a sample is correctly classified<br />Must select at least one electrode<br />Chaovalitwongse et al., KDD (2007) and Chaovalitwongse et al., Operations Research (forthcoming)<br />
    26. 26. Voting SFM<br />Maximize the number of correctly classified samples<br />Logical constraints: Must win the voting if a sample is correctly classified<br />Must select at least one electrode<br />Precision matrix, A contains elements of <br />Chaovalitwongse et al., KDD (2007) and Chaovalitwongse et al., Operations Research (forthcoming)<br />
    27. 27. Support Feature Machine<br />21<br />
    28. 28. Support Vector Machine<br />Feature 3<br />Pre-Seizure<br />Feature 2<br />Normal<br />Feature 1<br />
    29. 29. Application in Epilepsy Diagnosis<br />23<br />
    30. 30. Facts about Epilepsy<br />About 3 million Americans and other 60 million people worldwide (about 1% of population) suffer from Epilepsy.<br />Epilepsy is the second most common brain disorder (after stroke), which causes recurrent seizures (not vice versa). <br />Seizures usually occur spontaneously, in the absence of external triggers.<br />Epileptic seizures occur when a massive group of neurons in the cerebral cortex suddenly begin to discharge in a highly organized rhythmic pattern. <br />Seizures cause temporary disturbances of brain functions such as motor control, responsiveness and recall which typically last from seconds to a few minutes.<br />Based on 1995 estimates, epilepsy imposes an annual economic burden of $12.5 billion* in the U.S. in associated health care costs and losses in employment, wages, and productivity.<br />Cost per patient ranged from $4,272 for persons** with remission after initial diagnosis and treatment to $138,602 for persons** with intractable and frequent seizures.<br />*Begley et al., Epilepsia (2000); **Begley et al., Epilepsia (1994).<br />24<br />
    31. 31. Simplified EEG System and Intracranial Electrode Montage <br />Electroencephalogram (EEG) is a traditional tool for evaluating the physiological state of the brainby measuring voltage potentials produced by brain cells while communicating<br />25<br />
    32. 32. Scalp EEG Acquisition<br />18 Bipolar Channels<br />
    33. 33. Goals: How can we help?<br />Seizure Prediction<br />Recognizing (data-mining) abnormality patterns in EEG signals preceding seizures<br />Normal versus Pre-Seizure<br />Alert when pre-seizure samples are detected (online classification)<br />e.g., statistical process control in production system, attack alerts from sensor data, stock market analysis<br />EEG Classification: Routine EEG Check<br />Quickly identify if the patients have epilepsy<br />Epilepsy versus Non-Epilepsy<br />Many causes of seizures: Convulsive or other seizure-like activity can be non-epileptic in origin, and observed in many other medical conditions. These non-epileptic seizures can be hard to differentiate and may lead to misdiagnosis.<br />e.g., medical check-up, normal and abnormal samples<br />27<br />
    34. 34. Normal versus Pre-Seizure<br />28<br />
    35. 35. 10-second EEGs: Seizure Evolution<br />Normal<br />Pre-Seizure<br />Post-Seizure<br />Seizure Onset<br />Chaovalitwongse et al., Annals of Operations Research (2006)<br />29<br />
    36. 36. NormalversusPre-SeizureData Set<br />
    37. 37. Sampling Procedure<br />Randomly and uniformly sample 3 EEG epochs per seizure from each of normal and pre-seizure states.<br />For example, Patient 1 has 7 seizures. There are 21 normal and 21 pre-seizure EEG epochs sampled.<br />Use leave-one(seizure)-out cross validation to perform training and testing.<br />Normal<br />8 hours<br />8 hours<br />8 hours<br />8 hours<br />Pre-seizure<br />30 minutes<br />30 minutes<br />Seizure<br />Seizure<br />Duration of EEG<br />
    38. 38. Information/Feature Extraction from EEG Signals<br />Measure the brain dynamics from EEG signals<br />Apply dynamical measures (based on chaos theory) to non-overlapping EEG epochs of 10.24 seconds = 2048 points.<br />Maximum Short-Term Lyapunov Exponent<br />measure the stability/chaoticity of EEG signals<br />measure the average uncertainty along the local eigenvectors and phase differences of an attractor in the phase space<br />Pardalos, Chaovalitwongse, et al., Math Programming (2004)<br />
    39. 39. Evaluation<br />Sensitivitymeasures the fraction of positive cases that are classified as positive. <br />Specificitymeasures the fraction of negative cases classified as negative. <br />Sensitivity = TP/(TP+FN)<br />Specificity = TN/(TN+FP)<br />Type I error = 1-Specificity<br />Type II error = 1-Sensitivity<br />Chaovalitwongse et al., Epilepsy Research (2005)<br />
    40. 40. Leave-One-Seizure-Out Cross Validation<br />P1<br />N1<br />SFM<br />Selected Electrodes<br />N2<br />P2<br />1<br />2<br />3<br />4<br />5<br />6<br />7<br />.<br />.<br />.<br />2324<br />25<br />26<br />N3<br />P3<br />N4<br />P4<br />N5<br />P5<br />Training Set<br />Testing Set<br />34<br />N – EEGs from Normal State<br />P – EEGs from Pre-Seizure State<br />assume there are 5 seizures in the recordings<br />
    41. 41. EEG Classification<br />Support Vector Machine [Chaovalitwongse et al., Annals of OR (2006)]<br />Project time series data in a high dimensional (feature) space<br />Generate a hyperplane that separates two groups of data – minimizing the errors<br />Ensemble K-Nearest Neighbor [Chaovalitwongse et al., IEEE SMC: Part A (2007)]<br />Use each electrode as a base classifier<br />Apply the NN rule using statistical time series distances and optimize the value of “k” in the training<br />Voting and Averaging<br />Support Feature Machine [Chaovalitwongse et al., SIGKDD (2007); Chaovalitwongse et al., Operations Research (forthcoming)]<br />Use each electrode as a base classifier<br />Apply the NN rule to the entire baseline data<br />Optimize by selecting the best group of classifiers (electrodes/features) <br />Voting: Optimizes the ensemble classification<br />Averaging: Uses the concept of inter-class and intra-class distances (or prediction scores)<br />35<br />
    42. 42.
    43. 43. Performance Characteristics:Upper Bound<br />37<br />NN -> Chaovalitwongse et al., Annals of Operations Research (2006)<br />SFM -> Chaovalitwongse et al., SIGKDD (2007); Chaovalitwongse et al., Operations Research (forthcoming)<br />KNN -> Chaovalitwongse et al., IEEE Trans Systems, Man, and Cybernetics: Part A (2007)<br />
    44. 44. Separation of Normal and Pre-Seizure EEGs<br />From 3 electrodes not selected by SFM<br />From 3 electrodes selected by SFM<br />
    45. 45. Performance Characteristics:Validation<br />39<br />SVM-> Chaovalitwongse et al., Annals of Operations Research (2006)<br />SFM -> Chaovalitwongse et al., SIGKDD (2007); Chaovalitwongse et al., Operations Research (forthcoming)<br />KNN -> Chaovalitwongse et al., IEEE Trans Systems, Man, and Cybernetics: Part A (2007)<br />39<br />
    46. 46. Epilepsy versus Non-Epilepsy<br />40<br />
    47. 47. Epilepsy versusNon-EpilepsyData Set<br /><ul><li>Routine EEG check: 25-30 minutes of recordings ~ with scalp electrodes
    48. 48. Each sample is 5-minute EEG epoch (30 points of STLmax values).
    49. 49. Each sample is in the form of 18 electrodes X 30 points </li></li></ul><li>Leave-One-Patient-Out Cross Validation<br />N1<br />SFM<br />E1<br />Selected Electrodes<br />N2<br />E2<br />1<br />2<br />3<br />4<br />5<br />6<br />7<br />.<br />.<br />.<br />2324<br />25<br />26<br />N3<br />E3<br />N4<br />E4<br />N5<br />E5<br />Training Set<br />Testing Set<br />42<br />N – Non-Epilepsy<br />P – Epilepsy <br />
    50. 50. Voting SFM: Validation<br />43<br />
    51. 51. Averaging SFM: Validation<br />44<br />
    52. 52. 1 Fp1 – C3<br />16 T6 – Oz<br />17 Fz – Oz<br />
    53. 53. Other Medical Diagnosis<br />46<br />
    54. 54. Other Medical Datasets<br />Breast Cancer<br />Features of Cell Nuclei (Radius, perimeter, smoothness, etc.)<br />Malignant or Benign Tumors<br />Diabetes<br />Patient Records (Age, body mass index, blood pressure, etc.)<br />Diabetic or Not<br />Heart Disease<br />General Patient Info, Symptoms (e.g., chest pain), Blood Tests<br />Identify Presence of Heart Disease<br />Liver Disorders<br />Features of Blood Tests<br />Detect the Presence of Liver Disorders from Excessive Alcohol Consumption<br />47<br />
    55. 55. Performance<br />48<br />Training<br />Testing<br />
    56. 56. Average Number of SelectedFeatures<br />49<br />
    57. 57. Medical Data Signal Processing Apparatus (MeDSPA)<br />Quantitative analyses of medical data <br />Neurophysiological data (e.g., EEG, fMRI) acquired during brain diagnosis<br />Envisioned to be an automated decision-support system configured to accept input medical signal data (associated with a spatial position or feature) and provide measurement data to help physicians obtain a more confident diagnosis outcome. <br />To improve the current medical diagnosis and prognosis by assisting the physicians <br />recognizing (data-mining) abnormality patterns in medical data<br />recommending the diagnosis outcome (e.g., normal or abnormal)<br />identifying a graphical indication (or feature) of abnormality (localization) <br />50<br />
    58. 58. Automated Abnormality Detection Paradigm<br />Data Acquisition<br />Multichannel<br />Brain Activity<br />Optimization:Feature Extraction/ Clustering<br />Interface<br />Technology<br />Statistical Analysis:<br />Pattern Recognition<br />Nurse<br />Initiate a warning or a variety of therapies (e.g., electrical stimulation, drug injection) <br />Stimulator<br />User/Patient<br />Drug<br />
    59. 59. Acknowledgement: Collaborators<br />E. Micheli-Tzanakou, PhD<br />L.D. Iasemidis, PhD<br />R.C. Sachdeo, MD<br />R.M. Lehman, MD<br />B.Y. Wu, MD, PhD<br />Students<br />Y.J. Fan, MS<br />Other undergrad students<br />52<br />
    60. 60. Thank you for your attention!<br />Questions?<br />53<br />

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