M Buller1, K M Chapple1, C R Bird2. 1. From the Department of Neuroradiology, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, Arizona. 2. From the Department of Neuroradiology, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, Arizona. Neuropub@barrowneuro.org.
Abstract
BACKGROUND AND PURPOSE: Brain metastases are a common finding on brain MRI. However, the factors that dictate their size and distribution are incompletely understood. Our aim was to discover a statistical model that can account for the size distribution of parenchymal metastases in the brain as measured on contrast-enhanced MR imaging. MATERIALS AND METHODS: Tumor volumes were calculated on the basis of measured tumor diameters from contrast-enhanced T1-weighted spoiled gradient-echo images in 68 patients with untreated parenchymal metastatic disease. Tumor volumes were then placed in rank-order distributions and compared with 11 different statistical curve types. The resultant R 2 values to assess goodness of fit were calculated. The top 2 distributions were then compared using the likelihood ratio test, with resultant R values demonstrating the relative likelihood of these distributions accounting for the observed data. RESULTS: Thirty-nine of 68 cases best fit a power distribution (mean R 2 = 0.938 ± 0.050), 20 cases best fit an exponential distribution (mean R 2 = 0.957 ± 0.050), and the remaining cases were scattered among the remaining distributions. Likelihood ratio analysis revealed that 66 of 68 cases had a positive mean R value (1.596 ± 1.316), skewing toward a power law distribution. CONCLUSIONS: The size distributions of untreated brain metastases favor a power law distribution. This finding suggests that metastases do not exist in isolation, but rather as part of a complex system. Furthermore, these results suggest that there may be a relatively small number of underlying variables that substantially influence the behavior of these systems. The identification of these variables could have a profound effect on our understanding of these lesions and our ability to treat them.
BACKGROUND AND PURPOSE: Brain metastases are a common finding on brain MRI. However, the factors that dictate their size and distribution are incompletely understood. Our aim was to discover a statistical model that can account for the size distribution of parenchymal metastases in the brain as measured on contrast-enhanced MR imaging. MATERIALS AND METHODS:Tumor volumes were calculated on the basis of measured tumor diameters from contrast-enhanced T1-weighted spoiled gradient-echo images in 68 patients with untreated parenchymal metastatic disease. Tumor volumes were then placed in rank-order distributions and compared with 11 different statistical curve types. The resultant R 2 values to assess goodness of fit were calculated. The top 2 distributions were then compared using the likelihood ratio test, with resultant R values demonstrating the relative likelihood of these distributions accounting for the observed data. RESULTS: Thirty-nine of 68 cases best fit a power distribution (mean R 2 = 0.938 ± 0.050), 20 cases best fit an exponential distribution (mean R 2 = 0.957 ± 0.050), and the remaining cases were scattered among the remaining distributions. Likelihood ratio analysis revealed that 66 of 68 cases had a positive mean R value (1.596 ± 1.316), skewing toward a power law distribution. CONCLUSIONS: The size distributions of untreated brain metastases favor a power law distribution. This finding suggests that metastases do not exist in isolation, but rather as part of a complex system. Furthermore, these results suggest that there may be a relatively small number of underlying variables that substantially influence the behavior of these systems. The identification of these variables could have a profound effect on our understanding of these lesions and our ability to treat them.
Authors: Raúl A Ruggiero; Juan Bruzzo; Paula Chiarella; Oscar D Bustuoabad; Roberto P Meiss; Christiane D Pasqualini Journal: Cancer Res Date: 2012-02-07 Impact factor: 12.701
Authors: Raúl A Ruggiero; Juan Bruzzo; Paula Chiarella; Pedro di Gianni; Martín A Isturiz; Susana Linskens; Norma Speziale; Roberto P Meiss; Oscar D Bustuoabad; Christiane D Pasqualini Journal: Cancer Res Date: 2011-11-15 Impact factor: 12.701
Authors: M S O'Reilly; T Boehm; Y Shing; N Fukai; G Vasios; W S Lane; E Flynn; J R Birkhead; B R Olsen; J Folkman Journal: Cell Date: 1997-01-24 Impact factor: 41.582
Authors: M S O'Reilly; L Holmgren; Y Shing; C Chen; R A Rosenthal; M Moses; W S Lane; Y Cao; E H Sage; J Folkman Journal: Cell Date: 1994-10-21 Impact factor: 41.582