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The ESWL Neural Network

Portions of this document were adapted in part from our paper presented at the International Conference on Engineering Applications of Neural Networks (EANN '96) London, England, June 1996, and published in the conference proceedings:
Niederberger CS, Michaels EK, Cho L, Hong Y, Brown B, Ross LS, Golden RM: A neural computational model of stone recurrence after ESWL: Proceedings of the International Conference on Engineering Applications of Neural Networks: 423--426, 1996


What is ESWL?

In the past, treatment of large urinary stones required invasive surgery. Since the early 1980's, extracorporeal shock wave lithotripsy (ESWL) obviated surgery for over 90% of these patients. As with any new medical technology, the goals and efficacy of ESWL must be compared to those of previous methods. Shock wave phenomena were studied during the 1960s with the advent of high velocity air and space travel, and shock wave effects on biologic materials began in the 1970's. As little difference exists in acoustic impedance between body tissues and water, shock waves generated in water are transmitted through biologic tissues without significant energy loss. Acoustic impedance exists between a kidney stone (solid) and surrounding kidney tissue with urine (water density). Experiments demonstrated disintegration of the crystalline structure of stones when shock wave energy was focused on this acoustic interface.

Shock waves are generated from a spark-plug apparatus with opposing electrodes surrounded by a Faraday-like cage to electrically isolate the electric discharge. The underwater spark produces a plasma-like environment which vaporizes adjacent water molecules causing a primary shock wave and a secondary shock wave from collapse of gas bubbles (cavitation) formed during the spark discharge. Shock waves are focused by a rotationally symmetrical semi-ellipsoid so that maximum energy of approximately 10,000 psi is delivered in a cross-sectional area of approximately 2 cm. Fragmentation occurs when the initial force of the shock wave exceeds the compressive strength of the stone; as the shock wave travels through the stone, tensile forces are created perpendicular to the direction of the wave propagation. A tensile wave also results from reflection at the acoustic interface with water at the back side of the stone. Stone fragmentation also requires that the energy be delivered in microseconds so that superposition of entering and reflected waves are avoided.

Urinary stones form when nucleation of crystal-forming substance occurs in the collecting tubes of the kidney. Crystals form when various inorganic and organic materials exceed their solubility product in human urine, and depends on urinary pH as well as the presence or absence of inhibitors and promoters of crystal growth and aggregation. Risk factors for initial and recurrent stone formation include environmental and nutritional variables which result in urine low in volume, high in sodium, phosphate, or sulphate, or low magnesium. Metabolic risk factors include urine that are high in calcium, oxalate, uric acid or low in citrate, or which varies significantly from the normal pH of 6.4. The presence of urinary stasis due to abnormal anatomy or obstruction of the urinary tract, epithelial inflammation, infection, injury, or a foreign body provides a nidus which facilitates crystallization and aggregation. Attempts have been made to determine the relative importance of various risk factors based on analysis of the frequency distribution in the stone forming population and on discriminate analysis of results of medical treatment directed at specific risk factors.

ESWL will not cause stone disintegration, rather stone fragments must pass spontaneously from the urinary tract. Fragments after ESWL are documented in 10 to 50% of patients, and are a function of stone size, composition, location, and of urinary stasis due to abnormal anatomy. We sought to accurately model whether these fragments would form clinically significant stones in patients after ESWL, and to determine if any individual factor within a good model dictated the presence of stones at follow-up.

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Neural Network programming and training

Data were modeled using neUROn, a suite of programs we designed as a general purpose neural computational environment in C so that applications could be tailored to a specific problem. Sixteen input variables were encoded into 37 nodes in the input layer. These included (1) patient age, (2) gender, (3) and ethnicity, (4) stone chemistry, (5) location, (6) and configuration, (7) metabolic disease, (8) infectious disease, (9) time since last follow-up, (10) presence of fragments after ESWL, (11) other procedures, (12) medical therapy, (13) anatomic abnormality, (14) presence of catheter, (15) history of previous stone and (16) concurrent stones. Continuous variables, such as age, were normalized to -0.9 to +0.9. Binary variables, such as gender, were represented by -0.9 or +0.9. Categorical variables, such as ethnicity, were represented by a group of nodes with all nodes set at -0.9 except the representative node (such as `African-American') set at +0.9. A single output node was encoded, with its value set at 0 for no stone recurrence, and 1 for stone recurrence at follow-up patient evaluation.

Ninety-eight examples were randomly divided into a training set of 65, and a test set of 33 examples. Outcome frequencies representative of the whole set were preserved in the training and testing subsets. The test set was not used in training. One hidden node layer networks were built, and backpropagation was used to train the network. Training ceased when least mean squared changed < 10-4 after 1 iteration. While training, test set data was sampled, and used only to calculate network error in the test set. The hidden layer was reduced, one node at a time, and the network was retrained until test set error did not increase on further training (indicating overlearning), and training set error did not increase substantially with hidden node reduction. The final number of hidden nodes so determined was 5. To demonstrate presence of a local error minimum, final trained weights were randomly altered by small (<<1) increments, the network was retrained, and return to the original trained weight set was verified. the entire trained network is available as javascript code , which can be seen by view source in your JavaScript capable browser.

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Accuracy of the neural network compared to linear statistical tools

To compare neural network (NNET) performance to `linear' statistical classification tools (methods in which only one hyperplane separates decision space), we modeled the data set with linear and quadratic discriminant function analysis (LDFA and QDFA). As shown in the table below, classification performance for all tools was determined by classification accuracy (Class Acc), sensitivity (Sens), specificity (Spec), predictive value positive (PPV), predictive value negative (NPV) and ROC curve area (ROC Area).

Accuracy of the Neural Network compared with Discriminant Function Analysis
Method Train Class Acc Test Class Acc Sens Spec PPV NPV ROC Area
NNET 100% 90.9% 90.5% 91.7% 95.0% 85.0% 0.964
LDFA 32.3% 36.4% 0% 100% NaN 39.4% 0.524
QDFA 32.3% 36.4% 0% 100% NaN 39.4% 0.524
NNET: Neural Network
LDFA: Linear Discriminant Function Analysis
QDFA: Quadratic Discriminant Function Analysis
Acc: Accuracy ([correct/total] * 100%)
Sens: Sensitivity
Spec: Specificity
PPV: Positive Predictive Value
NPV: Negative Predictive Value
ROC Area: Receiver Operating Characteristic Curve Area

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