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PubMed1999

A dynamic programming algorithm for RNA structure prediction including pseudoknots.

We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of O(N6) in time and O(N4) in storage. The description of the algorithm is complex, which led us to adopt a useful graphical representation (Feynman diagrams) borrowed from quantum field theory. We present an implementation of the algorithm that generates the optimal minimum energy structure for a single RNA sequence, using standard RNA folding thermodynamic parameters augmented by a few parameters describing the thermodynamic stability of pseudoknots. We demonstrate the properties of the algorithm by using it to predict structures for several small pseudoknotted and non-pseudoknotted RNAs. Although the time and memory demands of the algorithm are steep, we believe this is the first algorithm to be able to fold optimal (minimum energy) pseudoknotted RNAs with the accepted RNA thermodynamic model.

Algorithms↗

PubMed2000

A time-domain algorithm for NMR spectral normalization.

Recently, a new method for quantitatively comparing NMR spectra of control and treated samples, in order to examine the possible occurring variations in cell metabolism and/or structure in response to numerous physical, chemical, and biological agents, was proposed. This method is based upon the utilization of the maximum superposition normalization algorithm (MaSNAl) operative in the frequency domain and based upon maximizing, by an opportune sign variable measure, the spectral region in which control and treated spectra are superimposed. Although the frequency-domain MaSNAl algorithm was very precise in normalizing spectra, it showed some limitations in relation to the signal-to-noise ratio and to the degree of diversity of the two spectra being analyzed. In particular, it can rarely be applied to spectra with a small number of visible signals not buried in the noise such as generally in vivo spectra. In this paper, a time-domain normalization algorithm is presented. Specifically, it consists in minimizing the rank of a Hankel matrix constructed with the difference of the two free induction decay signals. The algorithm, denoted MiRaNAl (minimum rank normalization algorithm), was tested by Monte Carlo simulations as well as experimentally by comparing two samples of known contents both with the new algorithms and with an older method using a standard. Finally, the algorithm was applied to real spectra of cell samples showing how it can be used to obtain qualitative and quantitative biological information.

Algorithms↗

PubMedDate not supplied

The contour-buildup algorithm to calculate the analytical molecular surface.

A new algorithm is presented to calculate the analytical molecular surface defined as a smooth envelope traced out by the surface of a probe sphere rolled over the molecule. The core of the algorithm is the sequential build up of multi-arc contours on the van der Waals spheres. This algorithm yields substantial reduction in both memory and time requirements of surface calculations. Further, the contour-buildup principle is intrinsically "local", which makes calculations of the partial molecular surfaces even more efficient. Additionally, the algorithm is equally applicable not only to convex patches, but also to concave triangular patches which may have complex multiple intersections. The algorithm permits the rigorous calculation of the full analytical molecular surface for a 100-residue protein in about 2 seconds on an SGI indigo with R4400++ processor at 150 Mhz, with the performance scaling almost linearly with the protein size. The contour-buildup algorithm is faster than the original Connolly algorithm an order of magnitude.

Algorithms↗

PubMed2001

Measurement of cortical thickness using an automated 3-D algorithm: a validation study.

A validation study was conducted to assess the accuracy of the algorithm developed by MacDonald et al. (1999) for measuring cortical thickness. This algorithm automatically determines the cortical thickness by 3-D extraction of the inner and outer surfaces of the cerebral cortex from an MRI scan. A manual method of tagging the grey-csf and grey-white interface was used on 20 regions (10 cortical areas found in each hemisphere) in 40 MRIs of the brain to validate the algorithm. The regions were chosen throughout the cortex to get broad assessment of the algorithm's performance. Accuracy was determined by an anatomist tagging the csf-grey and grey-white borders of selected gyri and by allowing the algorithm to determine the csf-grey and grey-white borders and the corresponding cortical thickness of the same region. Results from the manual and automatic methods were statistically compared using overall ANOVA and paired t tests for each region. The manual and automatic methods were in agreement for all but 4 of the 20 regions tested. The four regions where there were significant differences between the two methods were the insula left and right, the right cuneus, and the right parahippocampus. We conclude that the automatic algorithm is valid for most of the cortex and provides a viable alternative to manual methods of determining cortical thickness in vivo. However, caution should be taken when measuring the regions mentioned previously where the results of the algorithm can be biased by surrounding grey structures.

Adult↗

PubMed2003

Do segmented reconstruction algorithms for cardiac multi-slice computed tomography improve image quality?

PURPOSE: To evaluate segmented reconstruction algorithms for spiral multi-slice computed tomography (MSCT) that use data from two cardiac cycles to improve temporal resolution (tau) for imaging of the heart. MATERIALS AND METHODS: An initial group of 78 cardiac patients (heart rates [HR] = 63-167 beats per minute [bpm]) were imaged on a 4-slice, 500 ms gantry rotation time scanner (scanner 1). Images were reconstructed with a single-segment algorithm using data from one cardiac cycle with a reconstruction window of fixed length (tau = 250 ms). Images were also reconstructed with two variants of a multi-segment algorithm using data from two cardiac cycles where only one end of the reconstruction window was fixed and the other end was freely moveable to allow adjustment of tau according to HR: (1) "2-segment fixed start" with fixed start of reconstruction, (2) "2-segment fixed end" with fixed end of reconstruction (for both, tau = 125-250 ms). The resulting image sets were ranked from best to worst (1-3, respectively) in a side-by-side, blinded comparison by two independent readers. A second group of 26 patients (HR = 74-90 bpm) were imaged on a 12-slice, 420 ms gantry rotation time scanner (scanner 2). Data were reconstructed with a single-segment algorithm (tau = 210 ms) and a "2-segment fixed start" algorithm (tau = 105-210 ms) and image sets were ranked from best to worst (1-2, respectively). RESULTS: There was no clear evidence that any one technique is superior for imaging on scanner 1. Reader 1 ranked single-segment images the highest for all HRs, but statistically significant differences among the three algorithms were only found for the lowest HRs (< 80 bpm), where reader 1 preferred single-segment over "2-segment fixed end" techniques (p = 0.048). The highest rankings given by reader 2 varied according to HR: single-segment images were superior for lowest HRs, while "2-segment fixed start" images were superior for HRs > 80 bpm; none of these comparisons reached statistical significance. Improved performance of 2-segment reconstruction was found with scanner 2. Both readers ranked "2-segment fixed start" images the highest (p < 0.01). CONCLUSIONS: The added value of 2-segment cardiac reconstruction algorithms for spiral MSCT was not demonstrated for a 4-slice, 500 ms gantry rotation time scanner but shown to be beneficial for a 12-slice, 420 ms gantry rotation time scanner in the crucial HR range of 74-90 bpm.

Adolescent↗

PubMed2001

Implementation and evaluation of a 3D one-step late reconstruction algorithm for 3D positron emission tomography brain studies using median root prior.

A fully three-dimensional (3D) one-step late (OSL), maximum a posteriori (MAP) reconstruction algorithm based on the median root prior (MRP) was implemented and evaluated for the reconstruction of 3D positron emission tomography (PET) studies. The algorithm uses the ordered subsets (OS) scheme for convergence acceleration and data update during iterations. The algorithm was implemented using the software package developed within the EU project PARAPET (www.brunel.ac.uk/~masrppet). The MRP algorithm was evaluated using experimental phantom and real 3D PET brain studies. Various experimental set-ups in terms of activity distribution and counting statistics were considered. The performance of the algorithm was assessed by calculating figures of merit such as: contrast, coefficient of variation, activity ratio between two regions and full width at half of maximum for resolution measurements. The performance of MRP was compared with that of 3D ordered subsets-expectation maximisation (OSEM) and 3D re-projection (3DRP) algorithms. In all the experimental situations considered, MRP showed: (1) convergence to a stable solution, (2) effectiveness in noise reduction, particularly for low statistics data, (3) good preservation of spatial details. Compared with the OSEM and 3DRP algorithms, MRP provides comparable or better results depending on the parameters used for the reconstruction of the images.

Algorithms↗

PubMed2004

Laparoscopic radiofrequency ablation of hepatic tumors: prospective clinical evaluation of ablation size comparing two treatment algorithms.

BACKGROUND: Radiofrequency ablation (RFA) is gaining increased acceptance for the local control of liver tumors. Essential for achieving local tumor control are reproducible volumes of ablation that encompass the tumor and a margin of normal liver parenchyma. The technical algorithm for performing ablations was arrived at in an animal model using normal liver. Limited amounts of data exist as to whether this translates to the human tumor model. METHODS: We analyzed 531 ablated lesions in 154 patients undergoing laparoscopic RFA using RITA Medical Systems Starburst XL catheter deployed to a final diameter of 2-5 cm. The first 54 patients (algorithm 1) were treated with a larger initial deployment to 3 cm and incremental advancement of the catheter to the final diameter with a 20-min ablation time for a 5-cm lesion. The subsequent 100 patients (algorithm 2) were treated with a smaller initial deployment of 2 cm, incremental advancement to the final diameter, and 14-min total ablation time for a 5-cm lesion. Lesion size was measured on 1 week postablation CT scans. Analysis was performed using the two-tailed t-test. RESULTS: Ablation zones tended to be larger with the second method. On 1 week postablation CT scans, mean +/- SEM lesion sizes created using the first and second algorithms were 3.7 +/- 0.1 cm vs 4.0 +/- 0.1 cm at 3 cm deployment ( p < 0.05); 4.3 +/- 0.1 cm vs 4.8 +/- 0.1 cm at 4 cm deployment ( p < 0.05), and 5.5 +/- 0.1 cm vs 5.6 +/- 0.2 cm at 5 cm deployment ( p > 0.05), respectively. The mean +/- SEM total ablation times for the first and second algorithms were 7.9 +/- 0.3 min vs 7.0 +/- 0.2 min at 3 cm deployment ( p < 0.05); 13.3 +/- 0.3 min vs 11.1 +/- 0.02 min at 4 cm deployment ( p < 0.05); and 27.8 +/- 1.2 min vs 21.4 +/- 1.2 min at 5 cm deployment ( p < 0.05), respectively. The small SEM values indicate little variation in lesion size. CONCLUSIONS: These results show that both algorithms create dependable and reproducible zones of ablation, essential for reliable tumor destruction. Algorithm 2 demonstrates that creating an initial small core of ablation with rapid coagulation of the center of the lesion allows for equivalent, if not larger, final volumes to be performed in less time.

Adenocarcinoma↗

PubMed1991

Classification of postoperative cardiac patients: comparative evaluation of four algorithms.

Four classification algorithms based on Bayes' rule for minimum error are compared by evaluating their ability to recognize high- and normal-risk cardio-surgical patients. These algorithms differ in the modelling of the probability density function (pdf) for each class and include: (a) two parametric algorithms based on the assumption of normal pdf; (b) two non-parametric algorithms using Parzen multidimensional approximation of pdf with normal kernels. In each case, classes with both equal and different covariance matrices were considered. A set of 200 patients in the 6 h immediately following cardiac surgery has been used to test the performance of the algorithms. For each patient the three measured variables most effective in representing the difference between the two classes were considered. We found that the two algorithms which explicitly incorporate the information on the different sample covariance between the physiological variables existing in the two classes generally provide better recognition of high- and normal-risk patients. Of these two algorithms the parametric one appears extremely attractive for practical applications, since it exhibits slightly better performance in spite of its great simplicity.

Algorithms↗

PubMed1992

Fast ECG data compression algorithms suitable for microprocessor systems.

ECG data compression techniques have received extensive attention in ECG analysis. Numerous data compression algorithms for ECG signals have been proposed during the last three decades. We describe two algorithms based on the scan-along polygonal approximation algorithm (SAPA) that are suitable for multichannel ECG data reduction on a microprocessor-based system. One represents a modification of SAPA (MSAPA) which adopts the method of integer division table searching to speed up data reduction; the other (CSAPA) combines MSAPA and TP, a turning-point algorithm, to preserve ST segment signals. Results show that our algorithms achieve a compression ratio of more than 5:1 and a percent rms difference (PRD) to the original signal of less than 3.5%. In addition, the maximum execution time of MSAPA for processing one data point is about 50 microseconds. Moreover, the CSAPA algorithm retains all of the details of the ST segment, which are important in ischaemia diagnosis, by employing the TP algorithm.

Algorithms↗

PubMed1995

Comparison of simulated annealing algorithms for conformal therapy treatment planning.

PURPOSE: The efficiency of four fast simulated annealing algorithms for optimizing conformal radiation therapy treatment plans was studied and the resulting plans were compared with each other and to optimized conventional plans. METHODS AND MATERIALS: Four algorithms were selected on the basis of their reported successes in solving other minimization problems: fast simulated annealing with a Cauchy generating function, fast simulated annealing with a Lorentzian generating function, variable step size generalized simulated annealing (VSGSA), and very fast simulated reannealing (VFSR). They were tested on six clinical cases using a multiple beam coplanar conformal treatment technique. Relative beam weights were computed that maximized the minimum tumor dose subject to dose-volume constraints on normal organ doses. Following some initial tuning of the annealing parameters, each algorithm was applied identically to each test case. Optimization tests were run using different random number sequences and different numbers of iterations. RESULTS: The VSGSA algorithm consistently produced the best results. Using long run times, it generated plans with the highest minimum tumor dose in five of the six cases. For the short run times, the VSGSA solutions averaged larger minimum tumor doses than those of the other algorithms for all six patients, with increases ranging from 0.4 to 5.9 Gy. For three of the patients, the conformal plan gave a clinically significant increase in the minimum tumor dose over the conventional plan, ranging from 8.2 to 13.0 Gy. In two other cases, there was little difference between the two treatment approaches. For one case, the optimized conventional plan was much better than the conformal plan because the conventional beam arrangement included wedges, which offset the multiple beam advantage of the conformal plans. CONCLUSIONS: For equal computing times of both long and short duration, the VSGSA algorithm consistently produced conformal plans that were superior to those produced by the other algorithms. The simple conformal technique used in this study showed a significant potential advantage in the treatment of abdominal tumors. In three of the cases, the conformal plans showed clinically important increases in tumor dose over optimized conventional plans.

Abdominal Neoplasms↗

PubMed2005

Computer-assisted diagnosis of focal liver lesions on CT images evaluation of the Perceptron algorithm.

RATIONALE AND OBJECTIVE: The purpose of the study was to investigate a modified version of a so-called Perceptron algorithm in detecting focal liver lesions on CT scans. MATERIALS AND METHODS: The modified Perceptron algorithm is based on simulated annealing with a logarithmic cooling schedule and was implemented on a standard workstation. The algorithm was trained with 400 normal and 400 pathologic CT scans of the liver. An additional 100 normal and 100 pathologic scans were then used to test the detection of pathology by the algorithm. The total of 1000 scans used in the study were selected from the portal venous phase of upper abdominal CT examinations performed in patients with normal findings or hypovascularized liver lesions. The pathologic scans contained 1 to 4 focal liver lesions. For the preliminary version of the algorithm used in this study, it was necessary to define regions of interest that were converted to a matrix of 119 x 119. RESULTS: Training of the algorithm with 400 examples each of normal and abnormal findings took about 75 hours. Subsequently, the testing took several seconds for processing each scan. The diagnostic accuracy in discriminating scans with and without focal liver lesions achieved for the 200 test scans was approximately 99%. The error rate for pathologic and normal scans was comparable to results reported in the literature, which, however, were obtained for much smaller test sets. CONCLUSION: The modified Perceptron algorithm has an accuracy of close to 99% in detecting pathology on CT scans of the liver showing either normal findings or hypovascularized focal liver lesions.

Algorithms↗

PubMed2006

Comparison of retinal nerve fiber layer thickness and optic disk algorithms with optical coherence tomography to detect glaucoma.

PURPOSE: To compare the performance of the retinal nerve fiber layer (RNFL) thickness and optic disk algorithms as determined by optical coherence tomography to detect glaucoma. DESIGN: Observational cross-sectional study. METHODS: setting: Academic tertiary-care center. study population: One eye from 42 control subjects and 65 patients with open-angle glaucoma with visual acuity of > or =20/40, and no other ocular pathologic condition. observation procedures: Two optical coherence tomography algorithms were used: "fast RNFL thickness" and "fast optic disk." main outcome measures: Area under the receiver operating characteristic curves and sensitivities at fixed specificities were used. Discriminating ability of the average RNFL thickness and RNFL thickness in clock-hour sectors and quadrants was compared with the parameters that were derived from the fast optic disk algorithm. Classification and regression trees were used to determine the best combination of parameters for the detection of glaucoma. RESULTS: The average visual field mean deviation (+/-SD) was 0.0 +/- 1.3 and -5.3 +/- 5.0 dB in the control and glaucoma groups, respectively. The RNFL thickness at the 7 o'clock sector, inferior quadrant, and the vertical C/D ratio had the highest area under the receiver operating characteristic curves (0.93 +/- 0.02, 0.92 +/- 0.03, and 0.90 +/- 0.03, respectively). At 90% specificity, the best sensitivities (+/-SE) from each algorithm were 86% +/- 3% for RNFL thickness at the 7 o'clock sector and 79% +/- 4% for horizontal integrated rim width (estimated rim area). The combination of inferior quadrant RNFL thickness and vertical C/D ratio achieved the best classification (misclassification rate, 6.2%). CONCLUSION: The fast optic disk algorithm performs as well as the fast RNFL thickness algorithm for discrimination of glaucoma from normal eyes. A combination of the two algorithms may provide enhanced diagnostic performance.

Adult↗

PubMed2004

A novel kernelized fuzzy C-means algorithm with application in medical image segmentation.

Image segmentation plays a crucial role in many medical imaging applications. In this paper, we present a novel algorithm for fuzzy segmentation of magnetic resonance imaging (MRI) data. The algorithm is realized by modifying the objective function in the conventional fuzzy C-means (FCM) algorithm using a kernel-induced distance metric and a spatial penalty on the membership functions. Firstly, the original Euclidean distance in the FCM is replaced by a kernel-induced distance, and thus the corresponding algorithm is derived and called as the kernelized fuzzy C-means (KFCM) algorithm, which is shown to be more robust than FCM. Then a spatial penalty is added to the objective function in KFCM to compensate for the intensity inhomogeneities of MR image and to allow the labeling of a pixel to be influenced by its neighbors in the image. The penalty term acts as a regularizer and has a coefficient ranging from zero to one. Experimental results on both synthetic and real MR images show that the proposed algorithms have better performance when noise and other artifacts are present than the standard algorithms.

Algorithms↗

PubMed2006

Side chain placement using estimation of distribution algorithms.

OBJECTIVE: This paper presents an algorithm for the solution of the side chain placement problem. METHODS AND MATERIALS: The algorithm combines the application of the Goldstein elimination criterion with the univariate marginal distribution algorithm (UMDA), which stochastically searches the space of possible solutions. The suitability of the algorithm to address the problem is investigated using a set of 425 proteins. RESULTS: For a number of difficult instances where inference algorithms do not converge, it has been shown that UMDA is able to find better structures. CONCLUSIONS: The results obtained show that the algorithm can achieve better structures than those obtained with other state-of-the-art methods like inference-based techniques. Additionally, a theoretical and empirical analysis of the computational cost of the algorithm introduced has been presented.

Algorithms↗

PubMed2005

The use of a modified Fedorov exchange algorithm to optimise sampling times for population pharmacokinetic experiments.

We propose a new algorithm for optimising sampling times for population pharmacokinetic experiments using D-optimality. The algorithm was used in conjunction with the population Fisher information matrix as implemented in MATLAB (PFIM 1.1 and 1.2) to evaluate population pharmacokinetic designs. The new algorithm based on the classical Fedorov exchange algorithm optimises the determinant of the population Fisher information matrix. The performance of the new algorithm has been compared with other existing algorithms including simplex, simulated annealing and adaptive random search. The new algorithm performed better especially when dealing with complex designs at the expense of longer computing times.

Algorithms↗

PubMed2004

Performance of a dual-chamber implantable defibrillator algorithm for discrimination of ventricular from supraventricular tachycardia.

BACKGROUND: Inappropriate therapies remain a major problem in patients with implantable cardioverter defibrillators (ICDs). Decreasing the proportion of inappropriate therapies is a major objective. With the addition of atrial detection and advanced algorithms, dual-chamber ICDs are designed to offer better discrimination of ventricular (VT) and supraventricular (SVT) arrhythmias. The present multicentre, open study aimed to evaluate the performance of a dual-chamber detection algorithm, the Atrial View algorithm, incorporated in a dual-chamber ICD, the Ventak AV (Guidant Inc., St. Paul, Minnesota, USA). METHODS AND RESULTS: Fifty-one patients (45 males, 62+/-11 years, ejection fraction 42+/-15%) with standard indications received a Ventak AV ICD which analyzes, within the VT zone RR stability, tachycardia onset, atrial rate and AV relationship. Predischarge enhanced-detection algorithms were prospectively programmed: stability 24 ms, onset 9%, atrial fibrillation threshold 200 beats/min, and Vrate>Arate. An additional sustained rate duration criterion was programmed at least at 30 s. ICDs were interrogated every 3 months or when patients received shocks. A blinded review of electrograms for arrhythmia diagnosis and appropriateness of therapy was performed by 2 experts. Over the follow-up period (12+/-3.6 months), a total of 400 tachycardia episodes was recorded within the VT zone. After the review of stored electrograms, 237 (59%) true positive, 143 (36%) true negative, 17 (4%) false positive and 3 (1%) false negative episodes were diagnosed. Considering the 3 VTs incorrectly detected by the detection algorithms, therapy was delivered in 2 cases after sustained rate duration and 1 VT reverted spontaneously. Inappropriate therapy occurred in 17 cases. All but 1 were related to SVT with 1:1 atrioventricular relationship. Finally, on a per episode basis, the detection algorithm sensitivity was 99% and specificity was 89%. CONCLUSIONS: Programming of detection criteria based on stability, onset, atrial fibrillation rate threshold and Vrate>Arate allows a 99% sensitivity and an 89% specificity in Guidant ICDs. Discrimination of SVT with 1:1 atrioventricular relationship, however, remains a challenge for which new algorithms have to be designed.

Aged↗

PubMed2006

Performance comparison of neural network training algorithms in modeling of bimodal drug delivery.

The major aim of this study was to model the effect of two causal factors, i.e. coating weight gain and amount of pectin-chitosan in the coating solution on the in vitro release profile of theophylline for bimodal drug delivery. Artificial neural network (ANN) as a multilayer perceptron feedforward network was incorporated for developing a predictive model of the formulations. Five different training algorithms belonging to three classes: gradient descent, quasi-Newton (Levenberg-Marquardt, LM) and genetic algorithm (GA) were used to train ANN containing a single hidden layer of four nodes. The next objective of the current study was to compare the performance of aforementioned algorithms with regard to predicting ability. The ANNs were trained with those algorithms using the available experimental data as the training set. The divergence of the RMSE between the output and target values of test set was monitored and used as a criterion to stop training. Two versions of gradient descent backpropagation algorithms, i.e. incremental backpropagation (IBP) and batch backpropagation (BBP) outperformed the others. No significant differences were found between the predictive abilities of IBP and BBP, although, the convergence speed of BBP is three- to four-fold higher than IBP. Although, both gradient descent backpropagation and LM methodologies gave comparable results for the data modeling, training of ANNs with genetic algorithm was erratic. The precision of predictive ability was measured for each training algorithm and their performances were in the order of: IBP, BBP>LM>QP (quick propagation)>GA. According to BBP-ANN implementation, an increase in coating levels and a decrease in the amount of pectin-chitosan generally retarded the drug release. Moreover, the latter causal factor namely the amount of pectin-chitosan played slightly more dominant role in determination of the dissolution profiles.

Acrylic Resins↗

PubMed2005

Automatic navigation path generation based on two-phase adaptive region-growing algorithm for virtual angioscopy.

In this paper, we propose a fast and automated navigation path generation algorithm to visualize inside of carotid artery using MR angiography images. The carotid artery is one of the body regions not accessible by real optical probe but can be visualized with virtual endoscopy. By applying two-phase adaptive region-growing algorithm, the carotid artery segmentation is started at the initial seed, which is located on the initially thresholded binary image. This segmentation algorithm automatically detects the branch position with stack feature. Combining with a priori knowledge of anatomic structure of carotid artery, the detected branch position is used to separate the carotid artery into internal carotid artery and external carotid artery. A fly-through path is determined to automatically move the virtual camera based on the intersecting coordinates of two bisectors on the circumscribed quadrangle of segmented carotid artery. In consideration of the interactive rendering speed and the usability of standard graphic hardware, endoscopic view of carotid artery is generated by using surface rendering algorithm with perspective projection method. In addition, the endoscopic view is provided with ray casting algorithm for off-line navigation of carotid artery. Experiments have been conducted on both mathematical phantom and clinical data sets. This algorithm is more effective than key-framing and topological thinning method in terms of automated features and computing time. This algorithm is also applicable to generate the centerline of renal artery, coronary artery, and airway tree which has tree-like cylinder shape of organ structures in the medical imagery.

Algorithms↗