PREDICTING THE EFFECTIVENESS OF HYDROXYUREA IN INDIVIDUAL SICKLE CELL ANEMIA PATIENTS Homayoun Valafar, Faramarz Valafar, Alan Darvill and Peter Albersheim, Complex Carbohydrate Research Center and the Department of Biochemistry and Molecular Biology, University of Georgia, 220 Riverbend Road, Athens, GA 30602 Abdullah Kutlar, Kristy F. Woods, and John Hardin, Department of Medicine, Medical College of Georgia, Augusta, GA 30912 Journal of Artificial Intelligence in Medicine, 18 (2): 133-148, February 2000 Abstract
Treatment with hydroxyurea (HU) partially alleviates disease symptoms in many
patients with sickle cell anemia. The study described in this paper was undertaken todevelop the ability to predict the response of sickle cell patients to HU therapy. Weanalyzed the effect of HU on the values of 23 parameters or characteristics of each of83 patients. A Student T-test was used to confirm9 at the 0.001 level that treatmentwith HU increases the proportion of red blood cells containing fetal hemoglobin (HbF),and that HU also increases the average corpuscular volume (MCV) of the red bloodcells.
Correlation analysis failed to establish a statistically significant relationship
between any of the 23 parameters and the magnitude of the HbF response. Linearregression analysis also failed to predict a patient’s response to HU. On the otherhand, artificial neural network (ANN) pattern recognition analysis of the 23 parameterspredicts, with 86.6% accuracy, those patients that respond positively to HU and thosethat do not.
Furthermore, we have found that the values of only 10 of the 23
parameters are sufficient to train ANNs to predict which patients will respond to HU. Based on analyses with ANNs, the most important parameters in predicting a patient’sresponse to HU are the duration of treatment with HU, red blood cell size, white bloodcell count, platelet count, mean cell volume, neutrophil count, patient weight, Senegal(SEN) haplotype, reticulocyte count, and patient gender. A trained ANN accuratelypredicted HU response for ~85% of the patients included in the analyses. Introduction
ANN-based pattern recognition techniques have had great success in identifying
patterns or complex relationships that man, unassisted by computers, is unable toperceive14,15,18,31,35,38,40. ANN technology involves extensive training of a computer toenable it to distinguish a pattern from many patterns that closely resemble each other. It is often difficult to identify the features an ANN uses to classify patterns (e.g. aresponder versus a non-responder). It may be the presence or absence of a particularfeature that enables an ANN to classify its patterns. Experimenting to find an effectiveANN architecture and algorithm is a process that requires considerable time on apowerful computer. But once an ANN is selected and trained, its ability to identify newdata is nearly instantaneous and requires only a PC.
ANNs have begun to be used for many different purposes in medicine16-35.
believe there is enormous potential for ANNs to be applied widely in data analysisincluding assisting in diagnoses and in analyzing the characteristics of individualpatients to identify the most effective treatment. The research project described in thismanuscript was designed to assist physicians in predicting the response to HU therapyin patients with sickle cell anemia.
Adult hemoglobin (HbA) is a tetrameric protein composed of two α-chains and
two β-chains (α2β2). Sickle cell anemia is an inherited disease in which the two β-chains of normal adult hemoglobin are replaced by two mutated chains each of whichhas a single nucleotide substitution (GAG -> GTG) in the genes encoding the β-chainsof HbA1. The abnormal β-chains (βs) contain a hydrophobic valyl residue in place of anegatively-charged glutamyl residue at position 6. Deoxygenated hemoglobin of sicklecell patients (HbS or α2βs2) is less soluble than deoxygenated HbA. Under conditionswhere HbS is depleted of oxygen, HbS aggregates, causing the erythrocytes to deforminto the sickle shape that tends to block capillaries, the characteristics of the disease2-4.
Treatment with HU alleviates the clinical course in many patients with sickle cell
anemia9. The beneficial effect of HU is believed to depend on its ability to increase theexpression of the γ chains of HbF (α γ
Most patients respond to HU with an increase in the HbF
concentration of blood by either increasing the amount of HbF in their F-cells and/or byincreasing the proportion of F-cells. The response to HU varies from patient to patient. If the magnitude of the HU-elicited increase in the %HbF (with respect to the total Hb)of the patient’s blood could be predicted, “non-responders” could be identified. Thiswould provide useful data for clinicians, including the ability to differentiate non-responding patients from those that are non-compliant as well as the ability to predictwhether a patient’s sickle cell symptoms will be significantly reduced by HU therapy. Materials and Methods
• Eligibility Criteria and HU Dosage
Sickle cell anemia (α2βs2) patients at least 16 years of age were offered HU if
they had one or more of the following: a minimum of three vaso-occlusive crises peryear; severe anemia/hyperhemolysis (Hb <6.5 g/dl and bilirubin >4.0 mg/dl); fatigue;history of acute chest syndrome; or leg ulcers. The risks and benefits of HU therapywere discussed with each patient, and the patients were given written informationdescribing HU and its effects.
The potential teratogenic effects of the drug were
emphasized. Patients undergoing treatment with HU were advised against pregnancyor fathering a child.
The sickle cell patients were treated with a daily, oral dose of HU (15-28 mg/Kg
of body weight), with the dose increasing over time. The dose was increased whenHbF levels stabilized in two consecutive monthly visits. If there was evidence of bonemarrow suppression, the HU was withheld and, when the marrow had recovered (~oneweek), HU treatment was resumed at a lower dose. Only patients who had receivedHU for 8 months or longer were included in the ANN studies, although some patientsfirst became positive responders well after 8 months of continuous treatment. The datafrom eighty three patients met this criterion.
• Collection and Analysis of Blood Samples
Blood samples were obtained and analyzed monthly.
parameters (see Table 1) for each of the 83 patients were recorded for a minimum of 8months and a maximum of 98 months. The parameters analyzed for each patient arethose normally included in a ‘Complete Blood Count” (CBC), ‘Chemistry Profile’ (SMA-18)’ serial HbF levels (absolute and percent), DNA analyses for β globin genehaplotype and number of α genes, treatment duration, weight, age, and gender. Thevalues of these parameters were used to train ANNs and for statistical analyses
• Statistical Analyses
One-tailed student T-test (a function of Microsoft Excel 7. 0) was applied to the
results of statistical analyses to confirm that the observed variation in concentration ofHbF as well as other results were due to the HU administered and not due to randomevents. A confidence level of 0.001 was the minimum value accepted as significant inthe results of Student T-tests.
Patients lacking values for critical parameters were
eliminated from this study. For example, in studies of the correlation between final HbFconcentration and mean cell volume, all patients were excluded for whom the ‘meancell volume’ or the ‘final HbF concentration’ was missing. Table 1. A description of the 23 parameters for which data was obtained from the patients. Parameter Description
Duration of treatment a patient received to
*The actual values were 0,1,or 2, but zero could not be used (see last paragraphunder ANN Analyses).
• ANN Analyses
Several options are selected for the design and operation of each ANN. The two
neural network models used for the experiments reported in this manuscript are one-and two-stage, fully connected, feed-forward topology with a back-propagation (Deltarule, in the case of the single stage network) learning algorithm. We used a step sizeof 0.01 with no momentum term38.
The first of the two different neural network
architectures used for this project consisted of 23 input neurons and one output neuron(no hidden neurons) (23-1) and the second network consisted of 23 inputs, 4 hiddenneurons and one output neuron (23-4-1). The first network architecture was used topredict whether treatment with HU results in a doubling of the HbF concentration in thepatient’s blood.
The second network architecture was used to predict whether
treatment with HU would raise the HbF concentration in the blood above apredetermined threshold.
Three neural network simulation programs were used in the experiments
described in this paper. The first software package was developed in house and iscopyright protected. If desired, a copy of the executable version of the software forULTRIX, DIGITAL UNIX, and SGI’s IRIX 6.4 can be acquired by contacting the authors. The two other software packages are NeuroShell 2.0 and Partek 2.0 (by Ward systemsgroup, Inc. [Fredrick, MD] and Partek Inc.[St. Charles, MO], respectively).
packages were used to help ensure that we were not using irreproducible software-specific features. The results of each of the three software packages are comparable.
NeuroShell 2.0 and Partek 2.0 were used to train ANNs and to select those
parameters that had an observable impact (when omitted from the training) on theability of the ANNs to predict a patient’s HbF response to HU. NeuroShell 2.0 selectedthe “most influential parameters” by monitoring, during training of ANNs, the relativeactivity and strength (weight) of the connections between the neurons; thoseparameters that had active neurons and strong connections are considered importantcontributors to the training. All NeuroShell experiments were repeated five times toeliminate the effects of random initialization.
greatest impact by training a series of ANNs, each time removing a different one of the23 parameters from the training set. The influential parameters were identified by theeffect that removing the parameter had on the ability of the ANN to correctly predict theresponse to HU, that is, how much did the predictive ability of the trained ANNdeteriorate in the absence of the parameter; the greater the degradation in the abilityof the ANN, the more influential the parameter. Partek experiments were repeated withtwo different seeds for the random number generator which we used to create the initialcondition of the ANNs.
The experiment was repeated five times for each seed to
ensure reproducibility. The average of these ten runs constituted the results of Parteksoftware. Only the results of the NeuroShell software are listed in this report since bothsoftware produced similar results.
Some patients did not have data for all 23 parameters. Since the presence of a
zero at the input during the training causes the backpropagation algorithm not toupdate the first stage weights connected to that input, we decided to substitute a zerofor each missing parameter. In other words, the weight updating (learning) of the firststage is done only based on the value of the nonzero input parameters. This providedaway of reducing the effects of the missing data on the overall learning results.
Patients with three or more missing parameters were excluded from the
analyses. Since ANNs associate a special meaning (wild card) with the number zero,all of the parameters which may have a valid measurement of zero were shifted by one(add 1 to the value). For example the number of SEN haplotypes may be zero. In suchcases the number of haplotypes presented to the ANN are all shifted (increased) byone. The shifting principle is applied to all four β globin haplotypes (Bantu, Benin,Cameroon, Senegal) and to nucleated red blood cell counts (NRBC).
algorithm looks for differences between input values; therefore, the differencesbetween 1, 2, and 3 are equivalent to the differences between 0,1,and 2.
procedures, in conjunction with other considerations (e.g. duration of treatment),resulted in the database of 83 patients.
• Statistical Analysis
Some interdependent biological phenomena interact in a nonlinear manner,
while other interactions exhibit a linear relationship. The existence and strength oflinear relationships can be determined by correlation coefficient analysis, a statisticalmethod40, 41.
The results of correlation coefficient analysis fall between +1 and -1,
where values close to +1 or -1 are indicative of a strong linear relationship between thephenomena being examined, and values close to 0 indicate a weak or non-existentlinear relationship.
Correlation coefficient analysis was used to determine whether, in sickle-cell
patients administered HU, a linear relationship exists between the magnitude of theincrease in HbF concentration and the change in the value of each of the otherparameters taken independently. The results of these analyses (Table 2) revealed thatthere are no significant linear relationships between the HU-induced increase in HbFconcentration and any of the other parameters.
appears to correlate most strongly with the length of time patients are treated with HU,even the value of this correlation coefficient, 0.45, is too small to be significant; asignificant correlation in this study has an absolute value of 0.8 or higher. Furthermore,there is not even a linear relationship between the HbF concentration of patients priorto HU treatment and the HbF concentration following HU treatment (Figure 1). Perusalof the data presented in Figure 1 reveals that the magnitude of the increase in HbFconcentration in response to HU therapy is unrelated to the concentration of HbF in thepatient’s blood prior to HU therapy. Thus starting with a low concentration of HbF isnot a disadvantage in reaching an HbF concentration of 15% of total Hb, and startingwith a high concentration of HbF is likewise no advantage in this regard. Figure 1. The % of total Hb accounted for by HbF in the blood of 83 sickle cell patients before HU treatment (filled circles) is unrelated to the %HbF after HU treatment (open circles) . Those patients whose HbF concentration did not exceed 15% prior to HU treatment and that did exceed 15% HbF after HU treatment are considered responsive.
The absence of linear relationships between the HbF concentration and one or
more of the parameters examined (Table 2) suggests that either the values of theparameters are not related to the effect of HU treatment on HbF concentration or thatthe parameters are related in a nonlinear manner (e.g., exponential, or higher orderpolynomial38).
ANNs are particularly well suited to analyze complex, nonlinear
This attribute of ANNs assisted us in the discovery, in sickle cell
patients, of non-linear relationships between the magnitude of the HU-induced increasein HbF concentration and the values of other parameters (Table 1). Table 2. Correlation coefficients between the increase in HbF concentration following HU treatment and the effect of HU on the value of the indicated parameter (sorted in descending order).
• Effect of HU on the HbF concentration in the blood
Examination of the concentrations of HbF and HbS and the volume of the red
blood cells of sickle cell patients provide a quick measure of how the patients areresponding to HU therapy. The mean values of these three parameters obtained from83 patients before and after treatment with HU are presented in Table 3. The HU-induced increase in HbF concentration and in the average volume of the red blood cellswere shown to be significant at the 0.001 level by a Student T-test. The same testindicated that the small difference in HbS concentration before and after HU treatmentis not significant. The increases in HbF concentration and mean volume of red bloodcells are in agreement with results of previous reports42,43,44,45. Table 3. Mean values. before and after treatment with HU, for three parameters of 83 sickle-cell patients.
The concentration of HbF in the blood of each of the 83 sickle-cell patients,
before and during treatment with HU, is plotted in Figure 2. The significance of thedifference in HbF concentration before and after HU treatment is made even moreapparent by the lack of an effect of HU treatment on the HbS concentration (comparethe data in Figure 2 with that in Figure 3). HU treatment increased the mean HbFconcentration of the 83 patients from 4.4 to 19.1 grams per liter (Table 3). The one-directional spread in the concentration of HbF following treatment with HU is evidencethat the individual members of the patient population do not respond equally to HU. Furthermore, since there are no reports of HU causing a decrease in the HbFconcentration of blood, it is reasonable to conclude (by observing the data in Figure 2)that some patients with low initial HbF levels (Figure 2) are weakly effected by HU andthus remain at the low end of the distribution. This conclusion is supported by the datain Figure 1. 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 HbF concentration (g/L) Figure 2. The distribution of the initial and maximum HbF concentrations of the 83 sickle cell patients prior to and after treatment with HU.
• Effect of HU on the concentration of HbS in red blood cells
HU increases the HbF concentration in the blood of sickle cell patients by
increasing the number of F-cells and/or the amount of HbF of individual
However, at the beginning of this study it was unclear whether HU also alters the HbSconcentration of the blood. An increase in the HbS concentration of blood would likelybe detrimental since it is this relatively insoluble form of hemoglobin that, in conditionsof low oxygen concentrations, aggregates causing the sickling of the erythrocytes.
The HbS concentration in the blood of the 83 patients, before and after HU
treatment, is summarized in Figure 3. The results establish that the HbS concentrationin the blood is not significantly affected by HU treatment. In summary, HU raises theHbF concentration of blood whereas HU has no apparent affect on the HbSconcentration. 100 105 110 HbS concentration (g/L) Figure 3. The distribution of the initial and final concentration of HbS in the blood of 83 sickle cell patients treated with HU.
• Effect of HU treatment on the average volume of the red blood cells of sickle cell patients
The mean cell volume (MCV) of erythrocytes of most but not all patients
increases significantly following treatment by HU (shown by a Student T-test to be asignificant increase). The mean cell volume of the erythrocytes of each patient, bothbefore and after at least eight months of HU therapy, is compared in Figure 4. Theaverage HU-induced increase in the volume of the red blood cells of the 83 patients is22%. This agrees with the results of an earlier report42,43,44,45. Thus monitoring theMCV may be a useful guide for determining compliance with HU treatment.
It is interesting to compare the HU-induced increase in HbF concentration with
the increase in MCV. If the relationship between the change of these two parameterswere linear, then the correlation coefficient would indicate the strength of thisrelationship.
However, since the increase in MCV is not linearly dependent on the
increase in HbF concentration (see above), the correlation coefficient is only a roughlinear estimate of the strength of the relationship. The data appear to approximate alogarithmic relationship (Figure 5). 95 100 105 110 115 120 125 130 135 140 145 150 155 Mean cell (erythrocyte) volume (Femtoliter) Figure 4. The distribution of average volume of the red blood cells of 83 sickle cell patients before and after treatment with HU. % change in HbF Figure 5. % change in HbF concentration versus % change in MCV measured before and after treatment with HU.
• Training and testing of ANNs to predict the effect of HU treatment on the HbF concentration of the blood of sickle cell patients
The data from the 83 participating patients needed to be separated, before
training ANNs, into a group that responds to HU and a group that does not respond. The criterion for responders was first defined as a doubling of the patient’s initial HbFlevel.
Thus a patient whose blood HbF concentration changed in response to
treatment with HU by increasing, for example, from an initial value of 0.5 g/L to a finalvalue of 1.0 g/L would be considered a “responder,” while a patient whose bloodconcentration of HbF increased from 20 to 35 g/L would be considered a non-responder.
Since the clinical correlation of a doubling in HbF is an ambiguous
criterion, we decided to distinguish responders from non-responders based on the HbFconcentration passing a threshold of 15% of total Hb. The selection of the threshold isbased on published reports that HbF has a beneficial effect at this concentration43,44,46. This threshold divides the 83 patients into 58% responders and 42% non-responders(Figure 6).
An ANN using 23 input neurons, 4 hidden neurons, and one output neuron was
used for the 15% threshold experiment. This neural network produced an output valuehigher than 0.5 if the patient was predicted to be a responder and an output of lessthan 0.5 if the patient was predicted to be a non-responder. The individuals whoseinitial HbF concentration exceeded the 15% threshold were excluded from thatparticular experiment in order to maintain the coherence of the threshold criterion. Three patients were eliminated from these experiments based on this criterion, whichresulted in 83 patients qualifying for this experiment.
The threshold experiment was designed in such a way as to eliminate the
possibility that the ANN could simply “memorize” the values of the parameters of each
patient. This was accomplished by training ANNs with the parameter values of 82 ofthe patients, and then using the values of the patient whose parameters had not beenseen by the ANN to test the ANN. This procedure was repeated 83 times and eachtime an ANN was trained (a different patient was left out of the training). The result ofthis experiment is presented in Figure 6. Seventy patients were correctly classified asresponders or non-responders while 13 were misclassified.
responses were predicted correctly. This experiment was repeated five times with, onaverage, 86.6 correct predictions with a standard deviation of +/-2.0. Actual response PATIENTS Predicted response Figure 6. The prediction by ANNs of which patients would respond to HU by an increase in their HbF concentration to the point where it accounts for 15% or more of their total Hb. ANNs were trained with the values of the parameters of 82 patients and then tested with the values of the parameters of the patient that had not been used to train the ANN. This procedure was repeated 83 times, each time leaving out a different patient and training the ANN with the data from the other 82 patients to give the values in the figure. Patients whose HbF concentration did not reach 15% of the total Hb should have generated an ANN “output” of less than 0.5, while patients whose HbF concentration exceeded 15% of the total Hb should have generated an ANN output of more than 0.5.
• Contribution of each of the 23 parameters toward enabling ANNs to predict which sickle cell patients will respond to HU treatment by an increase of their HbF concentration to greater than 15% of total Hb.
This experiment was designed to identify which of the 23 parameters are most
important or influential in assisting ANNs to predict those patients that will respond to
Response, in this section is defined as the increase in HbF
concentration to more than 15% of total Hb. Determining the importance of each of the23 parameters was accomplished by employing two different methods.
method consisted of a recursive elimination process in which a different set ofparameters was taken out of the training set. The ANNs were trained with the values ofthe remaining parameters.
The software measures the degradation of performance
due to the missing parameters. This experiment is an exhaustive elimination process inwhich the removal of every combination of parameters (223-1=8,388,607 combinations)is evaluated.
The degradation (or importance) of the parameters observed are the
averages of 10 experiments (2 different seeds, and 5 runs per seed) performed onPartek software.
The final effect of removing each set of parameters is calculated by
averaging the performance degradation of the 10 ANNs trained without that set ofparameters.
The second method of parameters selection was implemented on the NeuroShell
This software performs a different method of parameter selection.
algorithm is initiated by setting equal values for each parameter. During the course oftraining, these values are updated to reflect the strength of the synaptic connectionassociated with the particular parameter as well as its contribution towards thediscovery of the correct answer. Thus at the end of the training the contribution of eachparameter reveals its importance in the solution of the problem. Each training sessionwas repeated 5 times to eliminate any random behavior of the system.
Although the above two methods are two distinctly different ways of parameter
selection, both algorithms produced similar in extracting the valuable parameters. Therefore, only the results of the NeuroShell parameter selection are shown in thisreport.
The 23 parameters and their scores, which are proportional to their contributions
in predicting the response to HU treatment, are listed in Table 4. This table containsthe averaged data for over 5 different training sessions. The lack of any particularlyinfluential contributors indicates that no one parameter contains most of the informationneeded to predict the response to HU. Therefore, based on the given contributions, itis reasonable to assume that the information needed for a successful classification isdistributed among a number of parameters, perhaps even a fairly large number ofparameters.
The ANNs trained in Figure 6 used the values of all 23 parameters. A separate
experiment was carried out to determine if the values of just ten 10 of the 23parameters listed in the previous section could be used while maintaining the ANN’sfull ability to identify responders and non-responders. This experiment used the top 10parameters listed in Table 4. The ability to eliminate unnecessary parameters has thepotential for reducing the problem size by more than 50% and might assist inelucidating the mechanisms by which ANNs function. Table 4. The effectiveness of each of the 23 parameters to assist ANNs in predicting the response of patients to HU treatment. Parameter Discussion
Artificial neural networks capable of recognizing patterns can do so by
memorization or generalization38,40. Memorization occurs when the ANN can memorizeall or some of the training patterns exactly as they are. Generalization occurs when theANN is not large enough to memorize the training pattern(s) exactly, but rather learnsthe identifying feature(s) of each pattern. In cases such as predicting a drug response,memorization is not desired as it will cause the network to perform well in predicting theresponse of the patients included in the training set but will fail when tested withpatients not included in the training set (new patients). The type of ANN used for theexperiments described in this manuscript is, in theory, capable of memorizing thevalues of the 23 parameters for each of the 83 patients. We were concerned that wecould be mislead into thinking we were observing a feature detecting patternrecognition procedure when in fact the computer had memorized the 83 sets of data. We avoided the possibility of being mislead in this way by training an ANN with theparameter values of 82 patients.
The parameter values were obtained before the
patients were exposed to hydroxyurea, and then the trained ANN was tested with theparameter values, also obtained before exposure to hydroxyurea, of a single patientthat had been excluded from the training set so that the trained ANN had never seenthe patient’s parameter values and, therefore, could not have memorized them. Werepeated the training of 83 different ANNs, that is, each time we started with a differentANN that had been “initiated” by assigning random weights to the connections betweenits neurons, and each time we omitted the parameter values of a different patient andused the parameter values of that patient to test the system. This experiment wasrepeated in its entirety five times, that is, each repeat required training 83 ANNs. Thesystem was asked, for each of the 83 patients, whether treatment with hydroxyureawould increase the HbF concentration to greater than 15% of the blood’s total Hb. Thesystem, under these conditions, correctly predicts the response of 86.6±2.2% of thepatients.
Some misclassified patients in all likelihood had values that fell on the edge of
the envelope formed by the values of the 82 individuals in the training sets.
conclude this because, when the experiment was repeated five times, some of the 13patients miss-classified in the first experiment were correctly assigned in one or moreof the repeat experiments and vice versa. Since the starting weights of the connectionsbetween the neurons of the 83 training sets are randomized before each trainingsession, variations in the classification of a small percentage of the patients isexpected.
There are several factors that can be corrected or improved to increase the
accuracy of the ANNs. A larger data set (training set) would ensure a more robustpredictor.
A more accurate and complete data set would do likewise.
powerful pattern recognition engines if the data by which they are trained is robust. Weexpect the accuracy of the predictions made by ANNs vis-à-vis the response to HU toimprove if the ANNs can be trained with the parameter values obtained from a larger
number of appropriately treated sickle-cell patients and if the ANN architecture andalgorithm are optimized.
We have demonstrated that it is possible to identify
patients who will respond to HU therapy by an increase in their HbF such that it equals15% or more of the patient’s total Hb. . A separate study might refine the level of HbFneeded to result in a significant improvement in the clinical course of the disease. It ispossible that sickle-cell patients at different points in the progression of the diseaseand at different ages may require different levels of HbF for meaningful relief.
Training ANNs to distinguish responders from non-responders is of value
regardless of how the two classes are defined by the medical community. An importantcontribution of the research reported herein is that ANNs can be used to detectcorrelations between medical data that humans, without the assistance of computers,can not see. There are many areas in medicine where data analysis is likely to besubstantially improved by utilizing the power of pattern recognition software. A relatedcontribution of this research, and perhaps the most important for future studies is thatimportant, unforeseen information encrypted in the results of standard blood analysescan be deciphered by ANN-assisted analyses. References
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NICODOM IR Kidney Stones - List of spectra The infrared spectral library „NICODOM IR Kidney Stones“ contains 1668 FTIR spectra of kidney stones and related compounds. The spectra were collected in by transmission technique as KBr pellets using the FTIR Spectrometer Nicolet 740. The spectral library features resolution of 4cm-1 in the spectral range 400-4000 cm-1, measurement time 1 mi
Professor Salah Badawi Ahmed Doma Postal Address: El-Yasmin Village, El-Arish, North Sinai, Egypt. Academic Qualifications: B. Sc. Special degree in Mathematics (Distinction with honor), Faculty of Science, Alexandria University, Egypt, June 1966. M. Sc. in Applied Mathematics, Faculty of Science, Alexandria University, Egypt, January 1970. PhD. in Mathematical Physics, Tb