They are multiplied together to obtain a volume correction factor.

When applied to volume estimation, 3 correction factors are required, corresponding to the 3D of the object. The correction factor acquired in equation 4 is a length correction. When object size was larger than a certain threshold (about 3σ), FWHM size underestimated object size, ie the correction factor was greater than 1. FWHM size did not always overestimate object size. This curve serves as a reference table from which a correction factor can be obtained for a given image object based on FWHM size and the PSF. The correction factor was plotted as a function of FWHM size ( fig. In 3D a uniform sphere with a diameter of d and an isotropic 3-dimensional Gaussian PSF are assumed and the correction factor is defined as (equation 4) correction factor (3D) = d/FWHM.īased on these assumptions, the correction factor can be calculated for objects with different FWHM sizes. This method can be extended to 3D, which is the scenario for CT imaging. Measured FWHM size is multiplied by this correction factor to provide a more accurate estimation of the true size of the imaged object. The object size estimated using this method is referred to as FWHM size and this method is referred to as the FWHM method.īased on the relationship between object size and FWHM size a correction factor can be defined as (equation 3) correction factor (1D) = a/FWHM. To achieve an error of less than 5% the object size must be larger than 3.8 for 1D. However, as the size of the object decreases, the difference between object size and FWHM size increases dramatically. When the object is large enough, FWHM is a good estimator of object size. Since this relationship depends only on the ratio of the size to the SD of the PSF, 19 all data were scaled to σ. B, dimensional correction factor curve for sphere as function of FWHM size. Imaged FWHM deviates from object size when object becomes smaller. FWHM size of object equals object size for all sizes (dashed line). To achieve this goal we propose a volume estimation method, which was developed based on the recovery coefficient method and applied to stone volume measurement.Ī, relationship between object size and FWHM size in 1D.

We sought to increase the accuracy of volume measurement for small objects to provide an accurate, reproducible method to measure stones of any size. 19 However, since these methods require the true object diameter, the accuracy of the recovery coefficient is limited for small objects, of which the true size is difficult to measure. 19– 22 The recovery coefficient is modeled as a function of the true object diameter, which is estimated in images, eg using registered CT images, 23, 24 the threshold method 19, 25, 26 or regions of interest in the PET images. A practical method that has been extensively studied and validated is to calculate a recovery coefficient from the PSF. For PET the PSF is used to correct partial volume averaging and restore pixel values in PET images. Efforts have been made to improve spatial resolution and measurement accuracy in images using information about the PSF. However, a limitation of this method is that the measurement error increases rapidly with decreasing object size.Ī major source of error in size or volume measurement is blurring caused by the imaging system, which can be quantified by the PSF. 17, 18 The general conclusion of these studies was that a threshold equal to half the CT number of the object tended to provide a relatively accurate size or volume. 10 Similar threshold methods were used with CT images to quantify the size or volume of vascular calcifications, 13, 14 pulmonary nodules 15, 16 and the cortical shell of vertebral bones. 7, 9– 12 Demehri et al noted that the variable threshold method provided more accurate results than fixed threshold methods to estimate stone volume. Several groups have quantified stone volume from CT images using threshold based methods. However, this estimation method is not highly accurate or reproducible due to the complex 3-dimensional shape of kidney stones. Kidney stone size is usually quantified as the mean diameter of each stone, 5, 6 which is often measured subjectively using digital calipers.

Information on stone size can be extracted from CT images and used as a major consideration when selecting stone treatment. 3, 4 It is the diagnostic test of choice for nephrolithiasis. 2 Unenhanced CT is a fast, accurate method to diagnose urolithiasis in patients with acute flank pain. 1 Nephrolithiasis is a recurrent disease with a relapse rate of about 50% at 5 to 10 years. Between 19 nephrolithiasis developed in 5.2% of the American population between ages 20 and 74 years.

Actual kidney stone size chart in mm