Three-dimensional reconstruction of curves from pairs of projection views in the presence of error. II. Analysis of error

Quantitative analysis of the microvasculature growing in the fibrin interface between a skin graft and the recipient site

Current tissue engineering techniques have failed to provide an established microvasculature in skin substitutes, a requisite for the maintenance of graft viability and rapid revascularization subsequent to graft transplantation in vivo. To improve outcomes for both conventional skin grafts and skin substitutes, the existing knowledge gap concerning the spatio-temporal mechanisms of skin graft revascularization must be abrogated. The current knowledge gap is due, at least in part, to a lack of appropriate diagnostic methods to quantify skin graft revascularization. To enhance the understanding of skin graft revascularization, we quantitatively evaluated revascularization of autologous skin grafts in a rat model by quantifying 2- and 3-dimensional vascular metrics in the fibrin interface 3, 7, and 10 days after transplantation. In this study, the fibrin interface appeared to be completely replaced with fibrovascular tissue by postoperative day 10. Although the mean vessel diameter was about 10 mum for the time points sampled, the mean vessel number, area, and volume fraction increased about 2.5-fold from postoperative day 3 to 7 and then decreased about 1.27-fold at postoperative day 10. There was no significant difference between 2- and 3-dimensional vascular metrics based on Bland-Altman analysis. In conclusion, these data establish a standard for metrics of vessels growing in the fibrin interface of a rat autologous skin graft and its donor site and suggests that once the blood supply has been restored to a viable transplant, the number, area, and volume fractions of vessels decrease to levels found at postoperative day 3.

A method for correction of radiographic errors in serial three-dimensional cephalometry

OBJECTIVES

To improve the accuracy of location of anatomical structures in serial three-dimensional (3D) cephalometric radiography.

METHODS

A new method was developed to correct for geometrical errors in the calculation of the 3D coordinates of a point viewed on any two of three frontal, lateral and axial cephalometric radiographs. A computer-based method was used to reduce measurement errors. The methods were tested on a phantom containing metallic markers and on a dried skull.

RESULTS

The mean corrected geometric error was 0.43 mm (SD 0.25 mm) compared with a maximum of 8 mm (SD 0.2 mm) when calculated directly from the radiographs. The mean computer-based measurement error was 0.46 mm (SD 0.34 mm) compared with 1.38 mm (SD 0.74 mm) when made directly from the radiographs.

CONCLUSIONS

The new method for the correction of radiographic errors in 3D serial cephalometric radiography appears to be sufficiently accurate to justify clinical evaluation.

A technique for quantitative three-dimensional analysis of microvascular structure

Research into angiogenesis and vascular microarchitecture has contributed to progress in a wide variety of biomedical fields, but increased understanding is limited, in part, by the available assays and imaging modalities. Techniques that allow quantitation of vascular microarchitecture are needed. A comprehensive method is presented that uses 6-microm-thick serial sections of frozen tissue samples, immunostaining for CD31, brightfield microscopy, automated alignment of two-dimensional serial sections, and volume rendering to produce high-resolution, three-dimensional, quantifiable images of microvascular structure. Application of the technique is shown by characterizing vascularization into a fibrin gel implanted against the skeletal muscle of rats and explanted after 7 days. Comparing measurements from automated and manually aligned MRI and fibrin samples verified quantitation. Automation removes concerns of observer bias or variation inherent in manual alignment and increases the speed of analysis. Analysis of the fibrin gel reveals a dense (4.3 +/- 1.1% endothelial cell density) network of tortuous (1.37 +/- 0.05 tortuosity) capillaries that replaces the gel as it degrades. There is a high level of void space (22.8 +/- 3.6%) in the gel, and average capillary length in the fibrovascular tissue was 93.0 +/- 7.4 microm. Data obtained from these automatically aligned images agreed with those obtained using manual analysis (no statistical difference), and the results are consistent with data from traditional methods.

Symbolic description of intracerebral vessels segmented from magnetic resonance angiograms and evaluation by comparison with X-ray angiograms

We describe and evaluate methods that create detailed vessel trees by linking vessels that have been segmented from magnetic resonance angiograms (MRA). The tree-definition process can automatically exclude erroneous vessel segmentations. The parent-child connectivity information provided by our vessel trees is important to both surgical planning and to guidance of endovascular procedures. We evaluated the branch connection accuracy of our 3D vessel trees by asking two neuroradiologists to evaluate 140 parent-child connections comprising seven vascular trees against 17 digital subtraction angiography (DSA) views. Each reviewer rated each connection as (1) Correct, (2) Incorrect, (3) Partially correct (a minor error without clinical significance), or (4) Indeterminate. Analysis was summarized for each evaluator by calculating 95% confidence intervals for both the proportion completely correct and the proportion clinically acceptable (completely or partially correct). In order to protect the overall Type I error rate, alpha-splitting was done using a top down strategy. We additionally evaluated segmentation completeness by examining each slice in 11 MRA datasets in order to determine unlabeled vessels identifiable in cross-section following segmentation. Results indicate that only one vascular parent-child connection was judged incorrect by both reviewers. MRA segmentations appeared complete within MRA resolution limits. We conclude that our methods permit creation of detailed vascular trees from segmented 3D image data. We review the literature and compare other approaches to our own. We provide examples of clinically useful visualizations enabled by our methodology and taken from a visualization program now in clinical use.

A localization algorithm and error analysis for stereo x-ray image guidance

Stereo x-ray radiography attracts increasing attention in major clinical applications. The purpose of this paper is to analyze the 3D localization error for breast biopsy procedures and provide guidelines for improving its accuracy. Our prototype is a CCD based digital stereo x-ray imaging system. The mathematical model consists of two x-ray sources and one stationary detector plane. A closed form least-squares solution is derived for 3D localization of feature points, particularly a biopsy needle tip, from a pair of 2D digital radiographs. Based on the least-squares formula and its first order approximation, the 3D localization error is analyzed in terms of object location, measurement error, separation between the two x-ray sources, and distance from the source to the detector. The stereo imaging and error estimation formulas are numerically simulated and experimentally validated. The data are in agreement with theoretical prediction. These results can be used for the purpose of system design and protocol optimization.

Three-dimensional reconstruction of curves from pairs of projection views in the presence of error. I. Algorithms

We have previously described an approach to 3D intracerebral vascular reconstruction that uses an MRA as a reconstruction base. Additional vessels seen only by angiography are added by segmenting 2D curves from projection angiograms and reconstructing these curves into 3D, building upon the MRA. Intracerebral vascular reconstruction is difficult for at least two reasons. First, 2D curves must be associated on projection images even when the human eye cannot do so. Second, 3D curves must be reconstructed in the presence of errors such as misregistration, image distortion, and misdefinition of 2D curves. This paper is the first of two that address the specific issue of reconstruction of a 3D curve from a given pair of 2D curves in the presence of error. The method explicitly separates what can and cannot be determined from a pair of projection views. It is also capable of recognizing interruptions produced by viewplane errors, of continuing reconstruction beyond such interruptions, and of localizing and estimating the magnitude of the interruptions. These measurements can also be used to estimate the lengths of regional disparities between a pair of 2D curves, leading to a quantitative estimate of the capacity of a pair of 2D curves to combine to create a 3D object (match value). Match values can be used, in turn, as part of the strategy for automatically associating pairs of 2D curves. This paper provides methods for reconstructing a given pair of 2D curves into 3D in the presence of error and for calculating match values. Error analysis is given in the companion report.