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Quantification of tumour response to radiotherapy

¹ Magnetic Resonance and Image Analysis Research Centre (MARIARC), ² Department of Medical Imaging, ³ Department of Neurosurgery, Walton Centre for Neurology and Neurosurgery, ⁴ Centre for Medical Statistics and Health Evaluation, University of Liverpool, Liverpool, UK, ⁵ Department of Mathematics, Statistics and Computation, University of Cantabria, Santander, Spain and ⁶ Department of Oncology and Radiotherapy, Hammersmith Hospital, London, UK

View larger version (110K): [in a new window]   Figure 1. Sample images for case 1. (a) T2 map; (b) magnetization transfer ratio (MTR) map; (c) pre-contrast 3D T1 weighted image; (d) post-contrast 3D T1 weighted image. T2 map (e) and MTR map (f) are thresholded so that the total abnormality is seen within the red shading. Note that stereological test systems for point counting are overlain on the enhancing abnormality (d), T2 total enhancing abnormality (e) and MTR total abnormality (f) with a uniform random position to obtain unbiased volume estimation. Each red cross (+) signifies one test point. Details of the calculation of tumour volume and precision are given in the text.

View larger version (73K): [in a new window]   Figure 2. (a) 3D T1 weighted images of patient 1 showing examples of the volume measurement corresponding to (i) the Cavalieri method (left and middle columns) and (ii) the calliper method (right column), where the first and second rows correspond to the third time point, and the third and fourth rows to the fourth time point. (i) A stereological test system for point counting, available in ANALYZETM software, is overlain in four Cavalieri sections with uniform random position to obtain the enhancing abnormality (EA) volume estimation. (ii) Calliper measurements were made using the calliper device in ANALYZETM software. The measurement of the EA included the greatest diameter found on the axial images (red line), the diameter perpendicular to it on the same image (blue line), and the greatest diameter on a coronal image (green line). Details of the calculation of tumour volume and the precision of the Cavalieri method are given in the text. (b) Graph illustrating the mathematical analysis of tumour volume change between two time points according to the Cavalieri and calliper methods (spherical and ellipsoidal models), see worked example. Error bars indicate an approximate confidence interval for the true volume obtained as the Cavalieri volume estimate±twice the predicted standard error (we have assumed that the Cavalieri estimator is normally distributed, however its distribution is still an open problem).

View larger version (19K): [in a new window]   Figure 3. Volume estimates of the enhancing abnormality obtained by the Cavalieri and calliper methods (spherical and ellipsoidal models).

View larger version (20K): [in a new window]   Figure 4. Graphs showing serial changes in volume of the enhancing abnormality (EA), T2 non-enhanceing abnormality (NEA) and magnetization transfer ratio (MTR)-NEA for Patient 1 (top left), Patient 2 (top right), Patient 3 (bottom left) and Patient 4 (bottom right). The horizontally shaded bar on the x-axis represents the period of radiotherapy.