Method and system for fetal weight estimation

A method for fetal weight estimation, comprising the following steps:

• a) ultrasonically measuring fetal biometric parameters for a plurality of sample cases;
• b) determining physiological and phenomenological pregnancy parameters for each sample case of said plurality of sample cases;
• c) determining a fetal weight for each of the sample cases by precision weighing at birth;
• d) creating a database of the sample cases in which each record associated to each known case comprises the fetal biometric parameters, the physiological and phenomenological pregnancy parameters and the fetal weight as determined at birth;
• e) generating mathematical prediction models from the database of the sample cases;
• f) ultrasonically measuring said fetal biometric parameters of a case under examination for which fetal weight is to be predicted;
• g) determining further physiological and phenomenological pregnancy parameters of the case under examination;
• h) predicting the fetal weight of the case under examination by using the mathematical prediction models generated in step e), wherein a multinormal probabilistic model is used as the mathematical model, said predicting step providing an estimation of a most probable fetal weight, as a multinormal probabilistic model maximizing value over all the fetal weights, wherein said multinormal probabilistic model is governed by the following function which provides a probability density of the measured fetal biometric parameters and one or more of the physiological and phenomenological pregnancy parameters, the probability density is conditioned by information relating to the physiological and phenomenological pregnancy parameters and the fetal weights of the sample cases:
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• where:
• x is an observation vector, including the measured ultrasound biometric parameters of the fetus and one or more physiological and phenomenological pregnancy parameters, wherein the observation vector comprises, as components, variables xi, i=1,2, . . . n, each relating to one of the measured ultrasound biometric parameters of the fetus and of the one or more physiological and phenomenological pregnancy parameters,
• w is a data vector containing, as components, the variables wj, j=1,2, . . . ,k, each being composed of the weight at birth and of one of the other physiological and phenomenological pregnancy parameters,
• d is a dimension of a multidimensional space of the measured ultrasound biometric parameters of the fetus, and one or more physiological and phenomenological pregnancy parameters which form components of the vector x, with d=n,
• μ(w) and Σ(w) are a mean vector and a covariance matrix, respectively, of the mean value xim of the components xi of the data vector x, as functions of said data vector w, the mean vector μ(w) and the covariance matrix Σ(w) are determined using non linear predictive algorithms that are trained with the data of the database of sample cases, the predictive algorithms are three artificial neural networks comprising a first artificial neural network (ANNm) for estimating the mean vector μ(w), a second artificial neural network (ANNv) for estimating the variances (diagonal elements) of the covariance matrix Σ(w) and a third artificial neural network (ANNc) for estimating the covariances of the same covariance matrix Σ(w);
• i) training the first artificial neural network (ANNm) with the data of the database of sample cases, to estimate the components of the mean vector μ(w), by presenting thereto the components of the data vector w as input data and the components of the observation vector x as output data, and determining synaptic weights ω(w,x) and activation thresholds α(w,x) depending on the components of the observation vector x, the first artificial neural network (ANNm) having an input;
• j) on the basis of such synaptic weights ωm, and neuron activating thresholds αm, using the first artificial neural network (ANNm) for estimating the components of the mean vector μ(w) to determine the estimates of the mean values of the components of the observation vector x by presenting to the input of said first artificial neural network (ANNm), the values of the components of the data vector w;
• k) determining deviations between each component of the observation vector x and the mean value of the corresponding component of the observation vector x as determined by the first neural network, that was trained in the previous steps;
• l) squaring said deviations and placing them at an output of the second artificial neural network (ANNv) for variance estimation, which is trained by presenting to its input the components of the corresponding data vector w;
• m) multiplying said deviations together and placing them at an output of the third artificial neural network (ANNc) for covariance estimation, which is trained by presenting to its input the components of the corresponding data vector w, wherein said neural networks are used to estimate the components of the mean vector μ(w) and the covariance matrix Σ(w) of the multinormal probabilistic model from the ultrasound biometric parameters and one or more measured physiological and/or phenomenological pregnancy parameters, which form the components of the observation vector x, and the other measured physiological and/or phenomenological pregnancy parameters, which form the components of the data vector w to be added to the fetal weight value;
• n) computing a plurality of probability curves by the multinormal probabilistic model for at least one component of the observation vector x and at least one of the physiological and phenomenological pregnancy parameters that form the components of the data vector w;
• o) determining a set of most probable values of the ultrasound biometric parameters and at least one of the physiological and phenomenological pregnancy parameters;
• p) determining a set of deviations of the most probable values from the measured values of said ultrasound biometric parameters and at least one of the physiological and phenomenological pregnancy parameters, the deviations are expressed in terms of univariate probability of consistency with the most probable fetal weight;
• and
• q) displaying the probability curves, the most probable values and the deviations.