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PubMed2005

Transitional transverse acetabular fractures: differences between fractures with a large posterio-superior fragment and the inverse T-fracture--a report of 10 unusual cases.

BACKGROUND: Classification of fractures is crucial in decision making and planning of acetabular surgery. Transverse fractures with secondary vertical fracture lines--which constitute either a large posterio-superior fragment (floating dome) or an inverse T with the posterior ileum attached to the axial skeleton--have not been described in detail in the literature. METHODS: All acetabular fractures at Ullevål University Hospital have been recorded prospectively since 1993 and classified according to Judet/Letournel. RESULTS: In 10/449 fractures (2%) there was a transverse fracture line through the acetabulum, with an additional vertical fracture line ascending either to the iliac crest or the SI-joint. In 6 of these fractures the vertical line started within the acetabulum, and the posterior part of the ileum with part of the articular surface was attached to the axial skeleton. In 4 fractures the vertical fracture line started posterior to the joint, constituting a very large posterio-superior fragment without any articular surface (a floating dome). INTERPRETATION: Open reduction and internal fixation of inverse T-fractures and transverse fractures with a floating dome require different surgical approaches. The latter can be treated through a single approach alone, while the inverse T-fracture may require extensile or combined approaches for adequate reduction and fixation.

Acetabulum↗
PubMed1975

Inverse relationship between net electric charge on the antigen and that on the sensitized cell in cellular immune response: demonstration with basic encephalitogen of the brain.

An inverse relationship exists between the net-electrical charge of immunogens and the antibodies elicited (1). The cellular basis of the net charge phenomenon has been established for both positively and negatively charged immunogens, by cell separation techniques over columns of opposite charge (7, 8). To establish whether this phenomenon can be extended to include cell-mediated immunity, the response to basic encephalitogenic protein (BE) which induces experimental allergic encephalomyelitis (EAE) was now investigated. Lymph node cells from sensitized strain 13 guinea pigs were fractionated over positively and negatively charged columns and compared to unfractionated cell populations in two assay systems: (a) in vitro response to BE in terms of lymphocyte transformation and (b) the passive transfer of EAE to unsensitized syngeneic recipients. The response was found to be confined to the fraction of cells eluted from glass bead columns, namely, the more negative cells. Cells eluted from poly-L-lysine-coated glass bead columns (i.e., positive cells) were devoid of the capacity to respond to this antigen either in vivo or in vitro. It was previously established that thymocytes rather than bone marrow cells account for the inverse charge phenomenon as assayed by T-helper-cell function in in vivo antibody production (8). We have now extended the inverse charge effect to include cell-mediated immune response of the delayed hypersensitivity type.

Animals↗
PubMed1987

Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem.

In this paper basic mathematical and physical concepts of the biomagnetic inverse problem are reviewed with some new approaches. The forward problem is discussed for both homogeneous and inhomogeneous media. Geselowitz' formulae and a surface integral equation are presented to handle a piecewise homogeneous conductor. The special cases of a spherically symmetric conductor and a horizontally layered medium are discussed in detail. The non-uniqueness of the solution of the magnetic inverse problem is discussed and the difficulty caused by the contribution of the electric potential to the magnetic field outside the conductor is studied. As practical methods of solving the inverse problem, a weighted least-squares search with confidence limits and the method of minimum norm estimate are discussed.

Animals↗
PubMed1988

An inverse filter for digital restoration of portal images.

Portal images obtained of patients during irradiation with high energy photon beams have a poor sharpness and contrast due to the physical limitations of the equipment forming these images. Consequently, improvement of the images is desirable. An inverse filter method was investigated for this purpose and values of the parameters of the filter have been determined for various clinical irradiation conditions. Data on the line spread function (LSF) were obtained from the image of a 0.2 mm wide slit between tungsten blocks that were positioned at the isocentre in front of a polystyrene phantom. Slit images were made in a 60Co beam and in a number of 8 and 16 MV x-ray beams with a copper screen-film detector. These images were made for various isocentre to detector distances, field sizes and phantom thicknesses. All slit images and a number of clinical images were digitised both with a TV camera system and a densitometer which were connected to a computer. The main factors that affect the LSF are the radiation source size and the isocentre to film distance. The photon energy had only a minor influence. The thickness of the phantom and the field size, however, did influence the contrast in the image and therefore they determined, together with the digitising system, the noise to signal ratio parameter of the inverse filter to a great extent. Application of the inverse filter improved significantly the visual appearance of anatomical details in the portal images. In addition to image restoration, the contrast was enhanced by the application of a low frequency cut-off filter.

Filtration↗
PubMed1996

The inversion of the exponential Radon transform for quantitative brain SPECT.

The mathematical derivation for the inversion of the exponential Radon transform is presented and the implementation of the inversion is detailed. The inversion can be verified and implemented by the readers for practical applications, such as for quantitative reconstruction of brain SPECT (single-photon emission computed tomography).

Brain↗
PubMed1999

New adiabatic inversion pulses for magnetic resonance imaging.

We present a comparison between our strategy of computing new adiabatic pulses and the best results given so far in the literature by Rosenfeld and co-workers. Our technique has been described elsewhere and is based upon a simple physical idea (the adiabatic factor is offset independent) and an evolution strategy algorithm which stochastically searches for a 'solution' with optimal inversion profile and power characteristics. As expected for all adiabatic pulses, the inversion profiles are similar for our solutions and those of the literature. On the other hand, some of our pulses offer a substantial reduction of peak and average power relative to the solutions of Rosenfeld. We discuss the properties of the families of analytical functions, where, in our opinion, it is convenient to search for a pulse shape with optimal inversion profile and power characteristics.

Algorithms↗
PubMed2001

Reduction of computational dimensionality in inverse radiotherapy planning using sparse matrix operations.

For dynamic multileaf collimator-based intensity modulated radiotherapy in which small beam elements are used to generate continuous modulation, the sheer size of the dose calculation matrix could pose serious computational challenges. In order to circumvent this problem, the dose calculation matrix was reduced to a sparse matrix by truncating the weakly contributing entries below a certain cutoff to zero. Subsequently, the sparse matrix was compressed and matrix indexing vectors were generated to facilitate matrix-vector and matrix-matrix operations used in inverse planning. The application of sparsity permitted the reduction of overall memory requirement by an order of magnitude. In addition, the effect of disregarding the small scatter components on the quality of optimization was investigated by repeating the inverse planning using the dense dose calculation matrix. Comparison of dense and sparse matrix-based plans revealed an insignificant difference in optimization outcome, thus demonstrating the feasibility and usefulness of the sparse method in inverse planning. Furthermore, two additional methods of memory minimization are suggested, namely hexagonal dose sampling and limited normal tissue sampling.

Humans↗
PubMed2002

The use of mixed-integer programming for inverse treatment planning with pre-defined field segments.

Complex intensity patterns generated by traditional beamlet-based inverse treatment plans are often very difficult to deliver. In the approach presented in this work the intensity maps are controlled by pre-defining field segments to be used for dose optimization. A set of simple rules was used to define a pool of allowable delivery segments and the mixed-integer programming (MIP) method was used to optimize segment weights. The optimization problem was formulated by combining real variables describing segment, weights with a set of binary variables, used to enumerate voxels in targets and critical structures. The MIP method was compared to the previously used Cimmino projection algorithm. The field segmentation approach was compared to an inverse planning system with a traditional beamlet-based beam intensity optimization. In four complex cases of oropharyngeal cancer the segmental inverse planning produced treatment plans, which competed with traditional beamlet-based IMRT plans. The mixed-integer programming provided mechanism for imposition of dose-volume constraints and allowed for identification of the optimal solution for feasible problems. Additional advantages of the segmental technique presented here are: simplified dosimetry, quality assurance and treatment delivery.

Algorithms↗
PubMed2002

The syed temporary interstitial iridium gynaecological implant: an inverse planning system.

Patients with advanced gynaecological cancer are often treated with a temporary interstitial implant using the Syed template and Ir- 192 ribbons at the Memorial Sloan-Kettering Cancer Center. Urgency in planning is great. We created a computerized inverse planning system for the Syed temporary gynaecological implant, which optimized the ribbon strengths a few seconds after catheter digitization. Inverse planning was achieved with simulated annealing. We discovered that hand-drawn target volumes had drawbacks; hence instead of producing a grid of points based on target volume, the optimization points were generated directly from the catheter positions without requiring an explicit target volume. Since all seeds in the same ribbon had the same strength, the minimum doses were located at both ends of the implant. Optimization points generated at both ends ensured coverage of the whole implant. Inverse planning took only a few seconds, and generated plans that provide a good starting point for manual improvement.

Algorithms↗
PubMed2002

The effect of dose calculation accuracy on inverse treatment planning.

The effect of dose calculation accuracy during inverse treatment planning for intensity modulated radiotherapy (IMRT) was studied in this work. Three dose calculation methods were compared: Monte Carlo, superposition and pencil beam. These algorithms were used to calculate beamlets. which were subsequently used by a simulated annealing algorithm to determine beamlet weights which comprised the optimal solution to the objective function. Three different cases (lung, prostate and head and neck) were investigated and several different objective functions were tested for their effect on inverse treatment planning. It is shown that the use of inaccurate dose calculation introduces two errors in a treatment plan, a systematic error and a convergence error. The systematic error is present because of the inaccuracy of the dose calculation algorithm. The convergence error appears because the optimal intensity distribution for inaccurate beamlets differs from the optimal solution for the accurate beamlets. While the systematic error for superposition was found to be approximately 1% of Dmax in the tumour and slightly larger outside, the error for the pencil beam method is typically approximately 5% of Dmax and is rather insensitive to the given objectives. On the other hand, the convergence error was found to be very sensitive to the objective function, is only slightly correlated to the systematic error and should be determined for each case individually. Our results suggest that because of the large systematic and convergence errors, inverse treatment planning systems based on pencil beam algorithms alone should be upgraded either to superposition or Monte Carlo based dose calculations.

Algorithms↗
PubMed2003

Statistical inversion for medical x-ray tomography with few radiographs: II. Application to dental radiology.

Diagnostic and operational tasks in dental radiology often require three-dimensional information that is difficult or impossible to see in a projection image. A CT-scan provides the dentist with comprehensive three-dimensional data. However, often CT-scan is impractical and, instead, only a few projection radiographs with sparsely distributed projection directions are available. Statistical (Bayesian) inversion is well-suited approach for reconstruction from such incomplete data. In statistical inversion, a priori information is used to compensate for the incomplete information of the data. The inverse problem is recast in the form of statistical inference from the posterior probability distribution that is based on statistical models of the projection data and the a priori information of the tissue. In this paper, a statistical model for three-dimensional imaging of dentomaxillofacial structures is proposed. Optimization and MCMC algorithms are implemented for the computation of posterior statistics. Results are given with in vitro projection data that were taken with a commercial intraoral x-ray sensor. Examples include limited-angle tomography and full-angle tomography with sparse projection data. Reconstructions with traditional tomographic reconstruction methods are given as reference for the assessment of the estimates that are based on the statistical model.

Algorithms↗
PubMed2005

Incorporating organ movements in inverse planning: assessing dose uncertainties by Bayesian inference.

We present a method to calculate dose uncertainties due to inter-fraction organ movements in fractionated radiotherapy, i.e. in addition to the expectation value of the dose distribution a variance distribution is calculated. To calculate the expectation value of the dose distribution in the presence of organ movements, one estimates a probability distribution of possible patient geometries. The respective variance of the expected dose distribution arises for two reasons: first, the patient is irradiated with a finite number of fractions only and second, the probability distribution of patient geometries has to be estimated from a small number of images and is therefore not exactly known. To quantify the total dose variance, we propose a method that is based on the principle of Bayesian inference. The method is of particular interest when organ motion is incorporated in inverse IMRT planning by means of inverse planning performed on a probability distribution of patient geometries. In order to make this a robust approach, it turns out that the dose variance should be considered (and minimized) in the optimization process. As an application of the presented concept of Bayesian inference, we compare three approaches to inverse planning based on probability distributions that account for an increasing degree of uncertainty. The Bayes theorem further provides a concept to interpolate between patient specific data and population-based knowledge on organ motion which is relevant since the number of CT images of a patient is typically small.

Algorithms↗
PubMed2006

A theoretical formulation of the electrophysiological inverse problem on the sphere.

The construction of three-dimensional images of the primary current density (PCD) produced by neuronal activity is a problem of great current interest in the neuroimaging community, though being initially formulated in the 1970s. There exist even now enthusiastic debates about the authenticity of most of the inverse solutions proposed in the literature, in which low resolution electrical tomography (LORETA) is a focus of attention. However, in our opinion, the capabilities and limitations of the electro and magneto encephalographic techniques to determine PCD configurations have not been extensively explored from a theoretical framework, even for simple volume conductor models of the head. In this paper, the electrophysiological inverse problem for the spherical head model is cast in terms of reproducing kernel Hilbert spaces (RKHS) formalism, which allows us to identify the null spaces of the implicated linear integral operators and also to define their representers. The PCD are described in terms of a continuous basis for the RKHS, which explicitly separates the harmonic and non-harmonic components. The RKHS concept permits us to bring LORETA into the scope of the general smoothing splines theory. A particular way of calculating the general smoothing splines is illustrated, avoiding a brute force discretization prematurely. The Bayes information criterion is used to handle dissimilarities in the signal/noise ratios and physical dimensions of the measurement modalities, which could affect the estimation of the amount of smoothness required for that class of inverse solution to be well specified. In order to validate the proposed method, we have estimated the 3D spherical smoothing splines from two data sets: electric potentials obtained from a skull phantom and magnetic fields recorded from subjects performing an experiment of human faces recognition.

Algorithms↗
PubMed2000

The application of electrical impedance tomography to reduce systematic errors in the EEG inverse problem--a simulation study.

In this paper we propose a new method, using the principles of electrical impedance tomography (EIT), to correct for the systematic errors in the inverse problem (IP) of electroencephalography (EEG) that arise from the wrong specification of the electrical conductivities of the head compartments. By injecting known currents into pairs of electrodes and measuring the resulting potential differences recorded from the other electrodes, the equivalent conductivities of brain (sigma3), skull (sigma2) and scalp (sigma1) can be estimated. Since the geometry of the head is assumed to be known, the electrical conductivities remain as the only unknown parameters to be estimated. These conductivities can then be used in the inverse problem of EEG. The simulations performed in this study, using a three-layer sphere to model the head, prove the feasibility of the method, theoretically. Even in the presence of simulated noise with a value of signal-to-noise ratio (SNR) equal to 10, estimations of the electrical conductivities within 5% of the true values were obtained. Simulations showed the existence of a strong relation between errors in the skull thickness and the EIT estimated conductivities. If the skull thickness is wrongly specified, for example overestimated by a factor of two, the conductivity determined by EIT is also overestimated by a factor of two. Simulations showed that this compensation effect also works in the inverse problem of EEG. Application of the proposed method reduces systematic errors in the dipole localization, up to an amount of 1 cm. However it proved to be ineffective to decrease the dipole strength error.

Brain↗
PubMed2005

Solution of the inverse problem of magnetic induction tomography (MIT).

Magnetic induction tomography (MIT) of biological tissue is used to reconstruct the changes in the complex conductivity distribution inside an object under investigation. The measurement principle is based on determining the perturbation DeltaB of a primary alternating magnetic field B0, which is coupled from an array of excitation coils to the object under investigation. The corresponding voltages DeltaV and V0 induced in a receiver coil carry the information about the passive electrical properties (i.e. conductivity, permittivity and permeability). The reconstruction of the conductivity distribution requires the solution of a 3D inverse eddy current problem. As in EIT the inverse problem is ill-posed and on this account some regularization scheme has to be applied. We developed an inverse solver based on the Gauss-Newton-one-step method for differential imaging, and we implemented and tested four different regularization schemes: the first and second approaches employ a classical smoothness criterion using the unit matrix and a differential matrix of first order as the regularization matrix. The third method is based on variance uniformization, and the fourth method is based on the truncated singular value decomposition. Reconstructions were carried out with synthetic measurement data generated with a spherical perturbation at different locations within a conducting cylinder. Data were generated on a different mesh and 1% random noise was added. The model contained 16 excitation coils and 32 receiver coils which could be combined pairwise to give 16 planar gradiometers. With 32 receiver coils all regularization methods yield fairly good 3D-images of the modelled changes of the conductivity distribution, and prove the feasibility of difference imaging with MIT. The reconstructed perturbations appear at the right location, and their size is in the expected range. With 16 planar gradiometers an additional spurious feature appears mirrored with respect to the median plane with negative sign. This demonstrates that a symmetrical arrangement with one ring of planar gradiometers cannot distinguish between a positive conductivity change at the true location and a negative conductivity change at the mirrored location.

Algorithms↗
PubMed2001

A linear-time algorithm for computing inversion distance between signed permutations with an experimental study.

Hannenhalli and Pevzner gave the first polynomial-time algorithm for computing the inversion distance between two signed permutations, as part of the larger task of determining the shortest sequence of inversions needed to transform one permutation into the other. Their algorithm (restricted to distance calculation) proceeds in two stages: in the first stage, the overlap graph induced by the permutation is decomposed into connected components; then, in the second stage, certain graph structures (hurdles and others) are identified. Berman and Hannenhalli avoided the explicit computation of the overlap graph and gave an O(nalpha(n)) algorithm, based on a Union-Find structure, to find its connected components, where alpha is the inverse Ackerman function. Since for all practical purposes alpha(n) is a constant no larger than four, this algorithm has been the fastest practical algorithm to date. In this paper, we present a new linear-time algorithm for computing the connected components, which is more efficient than that of Berman and Hannenhalli in both theory and practice. Our algorithm uses only a stack and is very easy to implement. We give the results of computational experiments over a large range of permutation pairs produced through simulated evolution; our experiments show a speed-up by a factor of 2 to 5 in the computation of the connected components and by a factor of 1.3 to 2 in the overall distance computation.

Algorithms↗
PubMed1995

Association of age with the threshold for detecting ankle inversion and eversion in upright stance.

A randomized quadruple staircase method and probit analysis were used to measure the thresholds for sensation of ankle inversion and eversion by 18 healthy young and 18 healthy old subjects while standing with a foot in a servo-driven cradle. The results of over 3600 trials show that the mean threshold for detecting inversion with a probability of 75% was 0.35 degrees in the older subjects, a value significantly greater than the 0.06 degrees threshold found in the younger group. The corresponding thresholds in eversion were significantly greater in both old (0.52 degrees) and young (0.35 degrees) subjects. Significant, but smaller, age differences were also found in unipedal stance. Few significant sex differences were found. When the velocity of a 0.1 degree inversion movement was increased from 2 to 200 degrees/s the probability of detecting it rose by only 22.6%. Although significantly increased with age, the threshold for sensing rotation in the weight-bearing ankle was measured in tenths of degrees, an order of magnitude better than previously reported (non-weight-bearing) values.

Adult↗
PubMed2001

Inverse association between trans isomeric and long-chain polyunsaturated fatty acids in cord blood lipids of full-term infants.

BACKGROUND: Previous studies showed significant inverse correlations between values of trans isomeric and long-chain polyunsaturated fatty acids in plasma lipids of preterm infants and healthy children aged 1-15 y. OBJECTIVE: We sought to evaluate the same correlations in full-term infants at birth. DESIGN: We studied healthy full-term infants (n = 42) born after normal pregnancies and deliveries. All infants had a family history of atopy (both parents or one of the parents and a sibling had atopic symptoms). The fatty acid composition of venous cord blood lipids was determined by high-resolution capillary gas-liquid chromatography. RESULTS: The mean (+/-SEM) sum of trans fatty acids was 0.49 +/- 0.02% by wt in phospholipids, 2.47 +/- 0.20% by wt in cholesterol esters, 1.73 +/- 0.09% by wt in triacylglycerols, and 1.59 +/- 0.07% by wt in nonesterified fatty acids. Linear correlation analysis showed significant inverse correlations between the sum of trans fatty acids and both arachidonic acid and docosahexaenoic acid in phospholipids (r = -0.56, P < 0.001, and r = -0.48, P = 0.01, respectively), cholesterol esters (r = -0.52, P < 0.001, and r = -0.39, P = 0.018, respectively), and nonesterified fatty acids (r = -0.41, P = 0.007, and r = -0.41, P = 0.006, respectively). CONCLUSION: Because trans fatty acids in the fetal circulation must originate from the maternal diet, our results indicate that maternal exposure to trans fatty acids may represent a previously neglected variable that inversely influences long-chain polyunsaturated fatty acid status in full-term infants at birth.

Cholesterol Esters↗