Stereology meets electron tomography: towards quantitative 3D electron microscopy

Stereological tools are the gold standard for accurate (i.e., unbiased) and precise quantification of any microscopic sample. The past decades have provided a broad spectrum of tools to estimate a variety of parameters such as volumes, surfaces, lengths, and numbers. Some of them require pairs of parallel sections that can be produced by either physical or optical sectioning, with optical sectioning being much more efficient when applicable. Unfortunately, transmission electron microscopy could not fully profit from these riches, mainly because of the large depth of field. Hence, optical sectioning was a long-time desire for electron microscopists. This desire was fulfilled with the development of electron tomography that yield stacks of slices from electron microscopic sections. Now, parallel optical slices of a previously unimagined small thickness (2-5 nm axial resolution) can be produced. These optical slices minimize problems related to overprojection effects, and allow for direct stereological analysis, e.g., volume estimation with the Cavalieri principle and number estimation with the optical disector method. Here, we demonstrate that the symbiosis of stereology and electron tomography is an easy and efficient way for quantitative analysis at the electron microscopic level. We call this approach quantitative 3D electron microscopy.

Unifying energy minimization and mutual information maximization for robust 2D/3D registration of X-ray and CT images

Similarity measure is one of the main factors that affect the accuracy of intensity-based 2D/3D registration of X-ray fluoroscopy to CT images. Information theory has been used to derive similarity measure for image registration leading to the introduction of mutual information, an accurate similarity measure for multi-modal and mono-modal image registration tasks. However, it is known that the standard mutual information measure only takes intensity values into account without considering spatial information and its robustness is questionable. Previous attempt to incorporate spatial information into mutual information either requires computing the entropy of higher dimensional probability distributions, or is not robust to outliers. In this paper, we show how to incorporate spatial information into mutual information without suffering from these problems. Using a variational approximation derived from the Kullback-Leibler bound, spatial information can be effectively incorporated into mutual information via energy minimization. The resulting similarity measure has a least-squares form and can be effectively minimized by a multi-resolution Levenberg-Marquardt optimizer. Experimental results are presented on datasets of two applications: (a) intra-operative patient pose estimation from a few (e.g. 2) calibrated fluoroscopic images, and (b) post-operative cup alignment estimation from single X-ray radiograph with gonadal shielding.

Reprint of "Stereology meets electron tomography: towards quantitative 3D electron microscopy" [J. Struct. Biol. 159 (2007) 443-450]

Stereological tools are the gold standard for accurate (i.e., unbiased) and precise quantification of any microscopic sample. The past decades have provided a broad spectrum of tools to estimate a variety of parameters such as volumes, surfaces, lengths, and numbers. Some of them require pairs of parallel sections that can be produced by either physical or optical sectioning, with optical sectioning being much more efficient when applicable. Unfortunately, transmission electron microscopy could not fully profit from these riches, mainly because of the large depth of field. Hence, optical sectioning was a long-time desire for electron microscopists. This desire was fulfilled with the development of electron tomography that yield stacks of slices from electron microscopic sections. Now, parallel optical slices of a previously unimagined small thickness (2-5nm axial resolution) can be produced. These optical slices minimize problems related to overprojection effects, and allow for direct stereological analysis, e.g., volume estimation with the Cavalieri principle and number estimation with the optical disector method. Here, we demonstrate that the symbiosis of stereology and electron tomography is an easy and efficient way for quantitative analysis at the electron microscopic level. We call this approach quantitative 3D electron microscopy.

An integrated system for 3D hip joint reconstruction from 2D X-rays: a preliminary validation study

The acquisition of conventional X-ray radiographs remains the standard imaging procedure for the diagnosis of hip-related problems. However, recent studies demonstrated the benefit of using three-dimensional (3D) surface models in the clinical routine. 3D surface models of the hip joint are useful for assessing the dynamic range of motion in order to identify possible pathologies such as femoroacetabular impingement. In this paper, we present an integrated system which consists of X-ray radiograph calibration and subsequent 2D/3D hip joint reconstruction for diagnosis and planning of hip-related problems. A mobile phantom with two different sizes of fiducials was developed for X-ray radiograph calibration, which can be robustly detected within the images. On the basis of the calibrated X-ray images, a 3D reconstruction method of the acetabulum was developed and applied together with existing techniques to reconstruct a 3D surface model of the hip joint. X-ray radiographs of dry cadaveric hip bones and one cadaveric specimen with soft tissue were used to prove the robustness of the developed fiducial detection algorithm. Computed tomography scans of the cadaveric bones were used to validate the accuracy of the integrated system. The fiducial detection sensitivity was in the same range for both sizes of fiducials. While the detection sensitivity was 97.96% for the large fiducials, it was 97.62% for the small fiducials. The acetabulum and the proximal femur were reconstructed with a mean surface distance error of 1.06 and 1.01 mm, respectively. The results for fiducial detection sensitivity and 3D surface reconstruction demonstrated the capability of the integrated system for 3D hip joint reconstruction from 2D calibrated X-ray radiographs.

Clinical Significance of 3D Ultrasound Compared to MRI in Uterine Malformations

Purpose: Congenital uterine anomalies often remain asymptomatic until they cause problems, for example during pregnancy. We studied the diagnostic aspects of two- and three-dimensional ultrasound and MRI. Materials and Methods: 63 women referred for suspected uterine anomalies were studied: In the first group (until July 2008) with 2 D-US and MRI, in the second group (from August 2008) additionally with 3 D-US; these women also had diagnostic or therapeutic operative confirmation. In the third group, only 3D-US was used. Results: In all women 3D-US was possible and successful. The most common anomaly was a subseptate uterus, while a septate uterus was less frequent, and uterus bicornis (unicollis) and uterus didelphys (bicornis bicollis) were rare. The women in the first two groups all underwent at least diagnostic hysteroscopy, and some (subseptate or septate uterus) underwent operative hysteroscopy. After preoperative volume imaging, laparoscopies were required less often. 3D-US diagnoses as judged by intraoperative findings were correct in 100 % of cases, while the MRI diagnoses in the same group were correct in only 7/13 cases. Conclusion: Since the introduction of volume imaging (MRI, later 3 D-US), laparoscopy during hysteroscopic septum resection was not necessary in the majority of cases. 3D-US brings the diagnostics of uterine anomalies back into the hands of the gynecologist and can provide the gynecological surgeon with a higher subjective degree of certainty during operative hysteroscopy.

Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

3D Intervertebral Disc Localization and Segmentation from MR Images by Data-Driven Regression and Classification

In this paper we propose a new fully-automatic method for localizing and segmenting 3D intervertebral discs from MR images, where the two problems are solved in a unified data-driven regression and classification framework. We estimate the output (image displacements for localization, or fg/bg labels for segmentation) of image points by exploiting both training data and geometric constraints simultaneously. The problem is formulated in a unified objective function which is then solved globally and efficiently. We validate our method on MR images of 25 patients. Taking manually labeled data as the ground truth, our method achieves a mean localization error of 1.3 mm, a mean Dice metric of 87%, and a mean surface distance of 1.3 mm. Our method can be applied to other localization and segmentation tasks.