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The increasing number of imaging studies and the prevailing application of positron emission tomography (PET) in clinical oncology have led to a real need for efficient PET volume handling and the development of new volume analysis approaches to aid the clinicians in the clinical diagnosis, planning of treatment, and assessment of response to therapy. A novel automated system for oncological PET volume analysis is proposed in this work. The proposed intelligent system deploys two types of artificial neural networks (ANNs) for classifying PET volumes. The first methodology is a competitive neural network (CNN), whereas the second one is based on learning vector quantisation neural network (LVQNN). Furthermore, Bayesian information criterion (BIC) is used in this system to assess the optimal number of classes for each PET data set and assist the ANN blocks to achieve accurate analysis by providing the best number of classes. The system evaluation was carried out using experimental phantom studies (NEMA IEC image quality body phantom), simulated PET studies using the Zubal phantom, and clinical studies representative of nonsmall cell lung cancer and pharyngolaryngeal squamous cell carcinoma. The proposed analysis methodology of clinical oncological PET data has shown promising results and can successfully classify and quantify malignant lesions.

Positron emission tomography (PET) volume analysis is vital for various clinical applications including artefact reduction and removal, tumour quantification in staging, a process which analyses the development of tumours over time, and to aid in radiotherapy treatment planning [

The main challenges associated with PET are the statistical noise and the low resolution which results in a significant partial volume effect. This effect should be reduced to the minimum level so that the required information can be precisely extracted from the analysed volume. Analysing and extracting the proper information from PET volumes can be performed by utilising analysis and classification approaches which provide rich information compared to what can be extracted from visual interpretation of the PET volumes alone. The need for accurate and fast analysis approaches of imaging data motivated the exploitation of artificial intelligence (AI) technologies. Artificial neural network (ANN) is one of the powerful AI techniques that has the capability to learn from a set of data and construct weight matrices to represent the learning patterns. The ANN is a mathematical model which emulates the activity of biological neural networks in the human brain.

ANNs had great success in many applications including pattern classification, decision making, forecasting, and adaptive control [

Many other approaches were used for medical image segmentation. A fuzzy locally adaptive Bayesian (FLAB) segmentation for automatic lesion volume delineation has been proposed in [

This paper aims to develop a robust PET volume analysis system using ANN combined with Bayesian information criterion (BIC). The initial investigation of this system was published in [

This paper is organised as follows. Section

Bayesian information criterion (BIC) is employed to approximate the Bayes factor which is consequently used to compare a series of rival theories. BIC is one hypothesis testing approach which uses Bayesian inference. BIC has gained notoriety as a significant approach for model selection and has been used in contexts varying from image processing and analysis [

The ratio of posteriors,

where

where

Although the absolute value of the BIC is not individually informative due to comparison with the null hypothesis, the disparity between BIC values for competing models provides evidence specifying the use of one model against another.

Expectation maximisation (EM) algorithm is used to find the maximum likelihood estimation for each class in the processed PET volume. The maximum likelihood estimation of

where

The maximum likelihood estimation for each segment is finally obtained utilising this probability beside the histogram of each level in the processed slice. The mean and standard deviation, for each class are also calculated based on histogram calculation, and according to these statistical details mthe signal-to-noise ratio (SNR) for each class is obtained as well to evaluate the level of the signal in each segment [

Competitive neural networks can learn to detect regularities and correlations in their input and adapt their future responses to that input accordingly. The neurons of competitive networks learn to recognise groups of similar input vectors. Self-organising maps learn to recognise groups of similar input vectors in such a way that neurons physically near each other in the neuron layer respond to similar input vectors.

CNN consists of a single layer, the

The learning rule used for CNN is based on Kohonen rule [

where the learning rate

Learning vector quantisation neural network is a hybrid network, it uses unsupervised and supervised learning to form the classification. LVQNN has two layers: the first layer calculates weighted inputs using negative Euclidean distance approach. The second layer has neurons with pure-line activation function and calculates weighted input using dot product weight approach. There are no biases used in LVQNN. LVQ learning in the competitive layer is based on a set of input/target pairs. Each target vector has a single 1, and the rest of its elements are 0. The 1 tells the right classification of the associated input.

LVQNN is more efficient than CNN in case of large number of inputs. The optimisation procedure implicitly in this network yields the class means by estimating optimised assignment for each class [

The learning rule in LVQNN combines competitive learning with supervised learning approach [

The proposed medical volume analysis system is illustrated in Figure

Proposed system for oncological PET volume analysis.

The first data set used in this study is obtained using the NEMA IEC image quality body phantom which consists of an elliptical water filled cavity with six spherical inserts suspended by plastic rods of volumes 0.5, 1.2, 2.6, 5.6, 11.5, and 26.5 mL. The inner diameters of these spheres are 10, 13, 17, 22, 28, and 37 mm. The PET image volume consists of

To choose the optimal number of classes for each slice in the processed PET phantom volume, different values of

Plot of BIC values for experimental phantom data set, scaled by a factor of 1000.

The mean standard deviation, SNR, and class probability (CP) for each slice have been calculated to analyse all the recommended classes in each slice. Table

Statistical information about the best class number for experimental phantom data set.

CN | SNR | CP | ||
---|---|---|---|---|

1 | 1.000986 | 0.250000 | 4.003944 | 0.469466 |

2 | 3.528585 | 1.602465 | 2.201973 | 0.240734 |

3 | 13.024477 | 7.048304 | 1.847888 | 0.247406 |

4 | 57.982584 | 45.253936 | 1.281271 | 0.042394 |

The second data set consists of Monte Carlo simulations of the Zubal anthropomorphic model where two volumes were generated. The first volume contains a matrix with isotropic voxels, the size of this volume is

Tumours characteristics for the second data set with 2 types of voxels.

Tumours | Isotropic voxels | Nonisotropic voxels | ||

Position | Size | Position | Size | |

1 | Slice 68 | 2 voxels | Slice 142 | 2 voxels |

2 | Slice 57 | 3 voxels | Slice 119 | 3 voxels |

3 | Slice 74 | 2 voxels | Slice 155 | 2 voxels |

For isotropic voxels in simulated phantom data set, the optimal class number obtained from BIC plot is 5 classes, as shown in Figure

Plot of BIC values for isotropic phantom data set, scaled by a factor of 1000.

Table

Statistical information about the best class number for the simulated phantom data set, tumour 1.

CN | SNR | CP | ||
---|---|---|---|---|

1 | 1.003849 | 0.250000 | 4.015396 | 0.409114 |

2 | 16.288944 | 6.399162 | 2.545480 | 0.247941 |

3 | 26.890255 | 9.694972 | 2.773628 | 0.197655 |

4 | 48.774962 | 18.579216 | 2.625243 | 0.120429 |

5 | 137.468019 | 57.911212 | 2.373772 | 0.024862 |

Statistical information about the best class number for the simulated phantom data set, tumour 2.

CN | SNR | CP | ||
---|---|---|---|---|

1 | 1.003102 | 0.250000 | 4.012408 | 0.399154 |

2 | 14.181862 | 6.814574 | 2.081107 | 0.207690 |

3 | 26.481251 | 9.468495 | 2.796775 | 0.227157 |

4 | 51.409594 | 19.963755 | 2.575146 | 0.142332 |

5 | 133.638905 | 56.426063 | 2.368389 | 0.023667 |

Analysing the statistical details about tumour 3 shows that there is a small difference between the SNR values calculated for classes 2, 3, 4, and 5, as presented in Table

Statistical information about the best class number for the simulated phantom data set, tumour 3.

CN | SNR | CP | ||
---|---|---|---|---|

1 | 1.002889 | 0.250000 | 4.011556 | 0.407105 |

2 | 14.616784 | 6.508255 | 2.245883 | 0.207151 |

3 | 25.914234 | 8.984076 | 2.884462 | 0.223710 |

4 | 47.367310 | 18.536074 | 2.555412 | 0.136315 |

5 | 141.792551 | 60.934125 | 2.326980 | 0.025720 |

SNR and CP for tumours 1, 2 and 3 in the simulated phantom data set with nonisotropic voxels.

CN | Tumour 1 | Tumour 2 | Tumour 3 | |||

SNR | CP | SNR | CP | SNR | CP | |

1 | 4.016184 | 0.407899 | 4.013160 | 0.402693 | 4.012848 | 0.396036 |

2 | 2.504101 | 0.239490 | 2.110565 | 0.190559 | 1.962133 | 0.176196 |

3 | 2.814225 | 0.205216 | 2.846712 | 0.222405 | 2.965170 | 0.237096 |

4 | 2.671825 | 0.123275 | 2.557056 | 0.158497 | 2.515199 | 0.161232 |

5 | 2.488246 | 0.024121 | 2.286361 | 0.025846 | 2.224181 | 0.029441 |

The optimum chosen class number is fed to both CNN and LVQNN, where both have clearly classified all spheres in experimental phantom data set, as illustrated in Figure

Experimental phantom data set: (a) original PET image and (b) classified image.

Simulated phantom data set (tumour 1): (a) original PET and (b) classified image.

Better performance has been achieved using LVQNN rather than CNN; however, the required time for classifying each slice in the processed volume using LVQNN is higher than the time required for processing each slice using CNN.

Two performance metrics have been employed to evaluate the performance of the proposed ANNs. A confusion matrix is a visualisation tool typically used in supervised and unsupervised learning approaches. Each row of the matrix represents the instances in a predicted class, while each column represents the instances in an actual class. One benefit of a confusion matrix is that it is easy to see if the system is confusing two classes: (the tumour and the remaining tissues in case of clinical PET data sets). The other performance metric approach is receiver-operating characteristic (ROC). This approach can be represented by plotting the fraction of true positives rate (TPR) versus the fraction of false positives rate (FPR), where the perfect point in the ROC curve is the point (0,1) [

Clinical PET volume of patient with histologically proven NSCLC (clinical Stage Ib-IIIb) who has undertaken a diagnostic whole-body PET/CT scan was used for assessment of the proposed classification technique. Patient fasted not less than 6 hours before PET/CT scanning. The standard protocol involved intravenous injection of ^{18}F-FDG followed by a physiologic saline (10 mL). The injected FDG activity was adjusted according to patient’s weight using the following formula:

The optimal number of classes obtained from BIC plot for clinical PET volume of nonsmall cell lung cancer patient is 5 classes, as illustrated in Figure

Statistical information about the best class number for clinical PET volume of nonsmall cell lung cancer patient.

CN | SNR | CP | ||
---|---|---|---|---|

1 | 1.000840 | 0.250000 | 4.003360 | 0.509741 |

2 | 2.911473 | 1.142062 | 2.549312 | 0.163043 |

3 | 9.035780 | 4.213254 | 2.144608 | 0.146897 |

4 | 32.665878 | 16.455158 | 1.985145 | 0.078470 |

5 | 167.509276 | 52.633532 | 3.182558 | 0.101848 |

Plot of BIC values for clinical PET volumes of nonsmall cell lung cancer patient, scaled by a factor of 1000.

Clinical PET data: (a) original PET image and (b) classified image.

The second clinical data set used in this study is PET volumes from seven patients with T3-T4 laryngeal squamous cell carcinoma. Prior to treatment, each patient underwent an FDG-PET study. Patients were immobilised with a customised thermoplastic mask (Sinmed, Reeuwijk, The Netherlands) fixed to a flat table-top to prevent complex neck movements. First, a 10 min transmission scan was obtained on the Siemens Exact HR camera (CTI, Knoxville, USA). Immediately after intravenous injection of 185–370 MBq (5–10 mCi) of FDG, a 1h dynamic 3D emission scan was performed. It consisted of eight frames with variable duration ranging from 90 to 600 s. All images were corrected for dead time, random, scatter attenuation and decay and then reconstructed using a 3D OSEM algorithm, as used in the clinics for patients with head and neck tumours [

In the case of clinical data set, the plot of BIC values flattens to an approximate plateau at

Using the proposed approach the optimum CN for each patient has been chosen. According to Figure

Plot of BIC values for clinical PET data set 2, scaled by a factor of 1000.

All the statistical information about each class in this data set has been calculated, Figure

Clinical PET data set 2: the

Clinical PET data set 2 (patient 1): (a) original PET (

An artificial intelligent statistical approach based on CNN and LVQNN was proposed for 3D oncological PET volume analysis. Experimental, simulated, and clinical PET studies of nonsmall cell lung cancer and pharyngolaryngeal squamous cell carcinoma were used to evaluate the performance of the proposed system. BIC and EM approaches were deployed to obtain the optimal number of classes, which was used by CNN and LVQNN to classify each slice in the processed PET volume. The mean, standard deviation, signal-to-noise ratio, and class probability were also calculated for each class. A detailed objective assessment together with subjective evaluation based on clinical knowledge was performed to characterise the performance of the proposed approach. Promising results were obtained, and the system appears to successfully classify and quantify lesions from clinical oncological PET studies.

This paper was supported by the Swiss National Science Foundation under Grant SNSF 31003A-125246, Geneva Cancer League, and the Indo Swiss Joint Research Programme ISJRP 138866.