Harvey E. Cline

Marching cubes: A high resolution 3D surface construction algorithm

We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.

Heat treating and melting material with a scanning laser or electron beam

A thermal analysis for laser heating and melting materials is derived for a Gaussian source moving at a constant velocity. The resulting temperature distribution, cooling rate distribution, and depth of melting are related to the laser spot size, velocity, and power level. As the power is increased to heat the liquid above the boiling point, a transition to deep penetration welding is described. Calculations are presented for 304‐stainless steel which are in agreement with experiment.

Three-dimensional segmentation of MR images of the head using probability and connectivity

We describe a three-dimensional (3D) segmentation method that comprises (a) user interactive identification of tissue classes; (b) calculation of a probability distribution for each tissue; (c) creation of a feature map of the most probable tissues; (d) 3D segmentation of the magnetic resonance (MR) data; (e) smoothing of the segmented data; (f) extraction of surfaces of interest with connectivity; (g) generation of surfaces; and (h) rendering of multiple surfaces to plan surgery. Patients with normal head anatomy and with abnormalities such as multiple sclerosis lesions and brain tumors were scanned with a 1.5 T MR system using a two echo contiguous (interleaved), multislice pulse sequence that provides both proton density and T2-weighted contrast. After the user identified the tissues, the 3D data were automatically segmented into background, facial tissue, brain matter, CSF, and lesions. Surfaces of the face, brain, lateral ventricles, tumors, and multiple sclerosis lesions are displayed using color coding and gradient shading. Color improves the visualization of segmented tissues, while gradient shading enhances the perception of depth. Manipulation of the 3D model on a workstation aids surgical planning. Sulci and gyri stand out, thus aiding functional mapping of the brain surface.

Two algorithms for the three‐dimensional reconstruction of tomograms

Three-dimensional (3-D) surface reconstructions provide a method to view complex anatomy contained in a set of computed tomography (CT), magnetic resonance imaging (MRI), or single photon emission computed tomography tomograms. Existing methods of 3-D display generate images based on the distance from an imaginary observation point to a patch on the surface and on the surface normal of the patch. We believe that the normalized gradient of the original values in the CT or MRI tomograms provides a better estimate for the surface normal and hence results in higher quality 3-D images. Then two algorithms that generate 3-D surface models are presented. The new methods use polygon and point primitives to interface with computer-aided design equipment. Finally, several 3-D images of both bony and soft tissue show the skull, spine, internal air cavities of the head and abdomen, and the abdominal aorta in detail.

Surface rippling induced by surface‐tension gradients during laser surface melting and alloying

During laser surface melting and alloying, temperature gradients on the melt surface between the laser‐beam impact point and the intersection line of the solid‐liquid interface with the surface generate surface‐tension gradients that sweep liquid away from beam impact point. The resulting flow of liquid creates a depression of the liquid surface beneath the beam and ridging of the liquid surface elsewhere. As the beam passes to other areas of the surface, this distortion of the liquid surface is frozen in, creating a roughened rippled surface. If the laser‐beam sweep velocity exceeds a critical velocity, the liquid does not have sufficient time to form ripples, and rippling from surface‐tension gradients can be avoided.

MR-Guided Focused Ultrasound Surgery

Magnetic resonance guided focused ultrasound surgery provides a minimally invasive controlled method for selectively destroying deep-lying tissue. A thermal analysis of focused ultrasound provides an estimate of the time-dependent temperature distribution and thermal dose required for ultrasound surgery. The temperature distribution is estimated by accumulating heat sources, considering the effects of thermal conductivity, heat content, and perfusion. In this study, both gel phantoms and excised in vitro bovine muscle specimens were imaged in a 1.5 T MR system while heated with a 5 cm diameter, 10 cm focal length, 1.1 MHz transducer. During sonication, the thermal effects were observed with T1-weighted pulse sequences. Below a critical temperature, the heat zone appeared as a dark spot that moved with the focal spot. Above a critical thermal dose, the in vitro tissue was irreversibly altered and the focal lesion was observed on both the MR image and the specimen slice.

Computer-assisted three-dimensional planning in craniofacial surgery

Three-dimensional surface reconstruction from computed tomographic (CT) data has been used to plan craniofacial operations. Cephalometric and anthropometric databases were integrated with three-dimensional CT reconstructions to quantitate the skeletal deformity and to assist in the design of the surgical procedure. Interactive techniques were developed to simulate osteotomies and skeletal movements in three dimensions on the computer-generated surface images. The ocular globes were referenced to position the orbital segments; i.e., the osteotomized segments were transposed into normal anatomic relationship with respect to the eyes. The measurements from the computer graphic simulation were used intraoperatively to establish the correct position of the skeletal segments. (Plast. Reconstr. Surg. 92: 576, 1993.)

System and method for the display of surface structures contained within the interior region of a solid body

A method and apparatus for displaying three dimensional surface images includes the utilization of a case table for rapid retrieval of surface approximation information. Eight cubically adjacent data points associated with a given voxel element are compared with a predetermined threshold value or range to generate an eight bit vector. This eight bit vector is employed to rapidly produce vector lists of approximating surfaces. An interpolation operation is performed so as to more closely approximate the desired surface and to provide more accurate representations of vectors normal to the desired surface. The accurate representation of these normal directions provides means for accurately representing shading information on a display screen. The method and apparatus of the present invention are particularly useful for the display of medical images both, from x-ray generated data and from data generated from various other sources including magnetic resonance imaging and positron emission tomography. The present invention provides a means for rapid generation of three dimensional images so as to enable interactive use by medical practitioners.

3D reconstruction of the brain from magnetic resonance images using a connectivity algorithm

We present high resolution three dimensional (3D) connectivity, surface construction and display algorithms that detect, extract, and display the surface of a brain from contiguous magnetic resonance (MR) images. The algorithms identify the external brain surface and create a 3D image, showing the fissures and surface convolutions of the cerebral hemispheres, cerebellum, and brain stem. Images produced by these algorithms also show the morphology of other soft tissue boundaries such as the cerebral ventricular system and the skin of the patient. For the purposes of 3D reconstruction, our experiments show that T1 weighted images give better contrast between the surface of the brain and the cerebral spinal fluid than T2 weighted images. 3D reconstruction of MR data provides a non-invasive procedure for examination of the brain surface and other anatomical features.

Computer-assisted Interactive Three-dimensional Planning for Neurosurgical Procedures

We have used three-dimensional reconstruction magnetic resonance imaging techniques to understand the anatomic complexity of operative brain lesions and to improve preoperative surgical planning. We report our experience with 14 cases, including intra- and extra-axial tumors and a vascular malformation. In each case, preoperative planning was performed using magnetic resonance imaging-based three-dimensional renderings of surgically critical structures, such as eloquent cortices, gray matter nuclei, white matter tracts, and blood vessels. Simulations, using the interactive manipulation of three-dimensional data, provided an efficient and comprehensive way to appreciate the anatomic relationships. Interactive three-dimensional computer-assisted preoperative simulations provided otherwise inaccessible information that was useful for the surgical removal of brain lesions.