High-resolution ultrasonography of subretinal structure and assessment of retina degeneration in rat.

The purpose of this work was to evaluate the ability of 80 MHz ultrasonography to differentiate intra-retinal layers and quantitatively assess photoreceptor dystrophy in small animal models. Four groups of 10 RCS rats each (five dystrophic and five controls) were explored at 25, 35, 45 and 55 days post-natal (PN). A series of retina cross-sections were obtained ex vivo from outside intact eyes using an 80 MHz three-dimensional ultrasound backscatter microscope (20-microm-axial resolution). Ultrasound features of normal retina were correlated to those of corresponding histology and thickness measurements of photoreceptor segment and nuclear layers were performed on all groups. To show the ability of 80 MHz ultrasonography to distinguish the retinal degeneration in vivo, one RCS rat was explored at 25 and 55 days post-natal. Ultrasound image of normal retina displayed four distinct layers marked by reflections at neurites/nuclei interfaces and permitted to differentiate the photoreceptor segment and nuclear layers. The backscatter level from the retina was shown to be related to the size, density and organization of the intra-layer structure. Ultrasound thickness measurements highly correlated with histologic measurements. A thinning (p<0.05) of outer nuclear layer (ONL) was detected over time for controls and was thought to be assigned to retina maturation. Retinal degeneration started at PN35 and resulted in a more pronounced ONL thinning (p<0.05) over time. ONL degeneration was accompanied by segment layer thickening (p<0.05) at PN35 and thinning thereafter. These changes may indicate accumulation of outer segment debris at PN35 then progressive destruction. In vivo images of rat intra-retinal structure showed the ability of the method to distinguish the photoreceptor layer changes. Our results indicate that 80 MHz ultrasonography reveals intra-retinal layers and is sensitive to age and degenerative changes of photoreceptors. This technique has great potential to follow-up retinal dystrophy and therapeutic effects in vivo.

Brain Connectivity Analysis in Children. Effects of Prematurity. and Prenatal Growth Restriction

Introduction: Survival of children born prematurely or with very low birth weight has increased dramatically, but the long term developmental outcome remains unknown. Many children have deficits in cognitive capacities, in particular involving executive domains and those disabilities are likely to involve a central nervous system deficit. To understand their neurostructural origin, we use DTI. Structurally segregated and functionally regions of the cerebral cortex are interconnected by a dense network of axonal pathways. We noninvasively map these pathways across cortical hemispheres and construct normalized structural connection matrices derived from DTI MR tractography. Group comparisons of brain connectivity reveal significant changes in fiber density in case of children with poor intrauterine grown and extremely premature children (gestational age<28 weeks at birth) compared to control subjects. This changes suggest a link between cortico-axonal pathways and the central nervous system deficit. Methods: Sixty premature born infants (5-6 years old) were scanned on clinical 3T scanner (Magnetom Trio, Siemens Medical Solutions, Erlangen, Germany) at two hospitals (HUG, Geneva and CHUV, Lausanne). For each subject, T1-weighted MPRAGE images (TR/TE=2500/2.91,TI=1100, resolution=1x1x1mm, matrix=256x154) and DTI images (30 directions, TR/TE=10200/107, in-plane resolution=1.8x1.8x2mm, 64 axial, matrix=112x112) were acquired. Parent(s) provided written consent on prior ethical board approval. The extraction of the Whole Brain Structural Connectivity Matrix was performed following (Cammoun, 2009 and Hagmann, 2008). The MPARGE images were registered using an affine registration to the non-weighted-DTI and WM-GM segmentation performed on it. In order to have equal anatomical localization among subjects, 66 cortical regions with anatomical landmarks were created using the curvature information, i.e. sulcus and gyrus (Cammoun et al, 2007; Fischl et al, 2004; Desikan et al, 2006) with freesurfer software (http://surfer.nmr.mgh.harvard.edu/). Tractography was performed in WM using an algorithm especially designed for DTI/DSI data (Hagmann et al., 2007) and both information were then combined in a matrix. Each row and column of the matrix corresponds to a particular ROI. Each cell of index (i,j) represents the fiber density of the bundle connecting the ROIs i and j. Subdividing each cortical region, we obtained 4 Connectivity Matrices of different resolution (33, 66, 125 and 250 ROI/hemisphere) for each subject . Subjects were sorted in 3 different groups, namely (1) control, (2) Intrauterine Growth Restriction (IUGR), (3) Extreme Prematurity (EP), depending on their gestational age, weight and percentile-weight score at birth. Group-to-group comparisons were performed between groups (1)-(2) and (1)-(3). The mean age at examination of the three groups were similar. Results: Quantitative analysis were performed between groups to determine fibers density differences. For each group, a mean connectivity matrix with 33ROI/hemisphere resolution was computed. On the other hand, for all matrix resolutions (33,66,125,250 ROI/hemisphere), the number of bundles were computed and averaged. As seen in figure 1, EP and IUGR subjects present an overall reduction of fibers density in both interhemispherical and intrahemispherical connections. This is given quantitatively in table 1. IUGR subjects presents a higher percentage of missing fiber bundles than EP when compared to control subjects (~16% against 11%). When comparing both groups to control subjects, for the EP subjects, the occipito-parietal regions seem less interhemispherically connected whilst the intrahemispherical networks present lack of fiber density in the lymbic system. Children born with IUGR, have similar reductions in interhemispherical connections than the EP. However, the cuneus and precuneus connections with the precentral and paracentral lobe are even lower than in the case of the EP. For the intrahemispherical connections the IUGR group preset a loss of fiber density between the deep gray matter structures (striatum) and the frontal and middlefrontal poles, connections typically involved in the control of executive functions. For the qualitative analysis, a t-test comparing number of bundles (p-value<0.05) gave some preliminary significant results (figure 2). Again, even if both IUGR and EP appear to have significantly less connections comparing to the control subjects, the IUGR cohort seems to present a higher lack of fiber density specially relying the cuneus, precuneus and parietal areas. In terms of fiber density, preliminary Wilcoxon tests seem to validate the hypothesis set by the previous analysis. Conclusions: The goal of this study was to determine the effect of extreme prematurity and poor intrauterine growth on neurostructural development at the age of 6 years-old. This data indicates that differences in connectivity may well be the basis for the neurostructural and neuropsychological deficit described in these populations in the absence of overt brain lesions (Inder TE, 2005; Borradori-Tolsa, 2004; Dubois, 2008). Indeed, we suggest that IUGR and prematurity leads to alteration of connectivity between brain structures, especially in occipito-parietal and frontal lobes for EP and frontal and middletemporal poles for IUGR. Overall, IUGR children have a higher loss of connectivity in the overall connectivity matrix than EP children. In both cases, the localized alteration of connectivity suggests a direct link between cortico-axonal pathways and the central nervous system deficit. Our next step is to link these connectivity alterations to the performance in executive function tests.

Disturbance, age and size structure in stands of Pinus uncinata Ram

Las estructuras de tamaño y edad de dos bosques monoespecificos subalpinos de Pinus uncinata en el Pirineo, fueron estudiadas e interpretadas introduciendo una clasificación sencilla de los árboles según la exposición de su copa a la radiación solar directa. Ambas poblaciones muestran distribuciones de diámetro de J invertida irregulares, cuya Interpretación es incierta. Por el contrario, la estructura de edad en ambos bosques muestra picos visibles, los cuales, si se tienen en cuenta la exposición de la copa, indican que la regeneración se produce en claros del bosque. Se analizaron las series de anillos de crecimiento de los árboles de cada sitio para reconstruir su historia reciente de perturbaciones Identificando los incrementos bruscos del crecimiento. El régimen de perturbaciones en los dos bosques es diferente, y en ambos casos muestra un efecto madelador análogo sobre la estructura de edad. Se concluye que P. uncinata se comporta como una especie heliófila que puede formar bosques maduros o multicohorte bajo determinados regímenes de perturbaciones suaves, gracias a su capacidad para iniciar la regeneración en claros pequeños. Este proceso tiene lugar en un lapso de tiempo corto después de la incidencia de las perturbaciones.

CT-guided cervical foraminal injection: Is a direct foraminal approach still necessary?

Purpose: Cervical foraminal injection performed with a direct foraminal approach may induce serious neurologic complications. We describe a technique of CT-guided cervical facet joint (CFJ) injection as an indirect foraminal injection, including feasibility and diffusion pathways of the contrast agent. Methods and materials: Retrospective study included 84 punctures in 65 consecutive patients presenting neck pain and/or radiculopathy related to osteoarthritis or soft disc herniation. CT images were obtained from C2 to T1 in supine position, with a metallic landmark on the skin. CFJ punctures were performed by MSK senior radiologists with a lateral approach. CT control of the CFJ opacification was performed after injections of contrast agent (1 ml), followed by slow-acting corticosteroid (25 mg). CFJ opacification was considered as successful when joint space and/or capsular recess opacification occurred. The diffusion of contrast agent in foraminal and epidural spaces was recorded. We assessed the epidural diffusion both on axial and sagittal images, with a classification in two groups (small diffusion or large diffusion). Results: CFJ opacification was successful in 82% (69/84). An epidural and/or foraminal opacification was obtained in 74% (51/69). A foraminal opacification occurred in 92% (47/51) and an epidural opacification in 63% (32/51), with small diffusion in 47% (15/32) and large diffusion in 53% (17/32). No complication occurred. Conclusion: CT- guided CFJ injection is easy to perform and safe. It is most often successful, with a frequent epidural and/or foraminal diffusion of the contrast agent. This technique could be an interesting and safe alternative to foraminal cervical injection.

Una nova subespàcie de Pedicularis pyrenaica J. Gay (Scrophulariaceae) als Pirineus Centrals

A new subspecies of Pedicularis pyrenaica J. Gay (Scrophulariaceae) in Central Pyrenees. We describe a new subspecies of Pedicularis pyrenaica (P. pyrenaica subsp. praetermissa) from the Central Pyrenees, which differs from the typical in the shape of the upper lip of the corolla (fusiform, attenuated in a conical beak), as for the larger size of the corolla and the whole plant. We add several comments on the morphological characterization and the habitat of the plant in relation to close taxa

Magnetic resonance imaging correlates of first-episode psychosis in young adult male patients: combined analysis of grey and white matter.

Background: Several patterns of grey and white matter changes have been separately described in young adults with first-episode psychosis. Concomitant investigation of grey and white matter densities in patients with first-episode psychosis without other psychiatric comorbidities that include all relevant imaging markers could provide clues to the neurodevelopmental hypothesis in schizophrenia. Methods: We recruited patients with first-episode psychosis diagnosed according to the DSM-IV-TR and matched controls. All participants underwent magnetic resonance imaging (MRI). Voxel-based morphometry (VBM) analysis and mean diffusivity voxel-based analysis (VBA) were used for grey matter data. Fractional anisotropy and axial, radial and mean diffusivity were analyzed using tract-based spatial statistics (TBSS) for white matter data. Results: We included 15 patients and 16 controls. The mean diffusivity VBA showed significantly greater mean diffusivity in the first-episode psychosis than in the control group in the lingual gyrus bilaterally, the occipital fusiform gyrus bilaterally, the right lateral occipital gyrus and the right inferior temporal gyrus. Moreover, the TBSS analysis revealed a lower fractional anisotropy in the first-episode psychosis than in the control group in the genu of the corpus callosum, minor forceps, corticospinal tract, right superior longitudinal fasciculus, left middle cerebellar peduncle, left inferior longitudinal fasciculus and the posterior part of the fronto-occipital fasciculus. This analysis also revealed greater radial diffusivity in the first-episode psychosis than in the control group in the right corticospinal tract, right superior longitudinal fasciculus and left middle cerebellar peduncle. Limitations: The modest sample size and the absence of women in our series could limit the impact of our results. Conclusion: Our results highlight the structural vulnerability of grey matter in posterior areas of the brain among young adult male patients with first-episode psychosis. Moreover, the concomitant greater radial diffusivity within several regions already revealed by the fractional anisotropy analysis supports the idea of a late myelination in patients with first-episode psychosis.

Speciation of naturally-accumulated uranium in an organic-rich soil of an alpine region (Switzerland)

Very high concentrations of uranium (up to 4000 ppm) were found in a natural soil in the Dischma valley, an alpine region in the Grisons canton in Switzerland. The goal of this study was to examine the redox state and the nature of uranium binding in the soil matrix in order to understand the accumulation mechanism. Pore water profiles collected from Dischma soil revealed the establishment of anoxic conditions with increasing soil depth. A combination of chemical extraction methods and spectroscopy was applied to characterize the redox state and binding environment of uranium in the soil. Bicarbonate extraction under anoxic conditions released most of the uranium indicating that uranium occurs predominantly in the hexavalent form. Surprisingly, the uranium redox state did not vary greatly as a function of depth. X-ray absorption near edge spectroscopy (XANES), confirmed that uranium was present as a mixture of U(VI) and U(IV) with U(VI) dominating. Sequential extractions of soil samples showed that the dissolution of solid organic matter resulted in the simultaneous release of the majority of the soil uranium content (>95%). Extended X-ray absorption fine structure (EXAFS) spectroscopy also revealed that soil-associated uranium in the soil matrix was mainly octahedrally coordinated, with an average of 1.7 axial (at about 1.76 Å) and 4.6 to 5.3 equatorial oxygen atoms (at about 2.36 Å) indicating the dominance of a uranyl-like (UO22+) structure presumably mixed with some U(IV). An additional EXAFS signal (at about 3.2 Å) identified in some spectra suggested that uranium was also bound (via an oxygen atom) to a light element such as carbon, phosphorus or silicon. Gamma spectrometric measurements of soil profiles failed to identify uranium long-life daughter products in the soil which is an indication that uranium originates elsewhere and was transported to its current location by water. Finally, it was found that the release of uranium from the soil was significantly promoted at very low pH values (pH 2) and increased with increasing pH values (between pH 5 and 9).

Characterisation of the PSI whole body counter by radiographic imaging.

A joint project between the Paul Scherrer Institut (PSI) and the Institute of Radiation Physics was initiated to characterise the PSI whole body counter in detail through measurements and Monte Carlo simulation. Accurate knowledge of the detector geometry is essential for reliable simulations of human body phantoms filled with known activity concentrations. Unfortunately, the technical drawings provided by the manufacturer are often not detailed enough and sometimes the specifications do not agree with the actual set-up. Therefore, the exact detector geometry and the position of the detector crystal inside the housing were determined through radiographic images. X-rays were used to analyse the structure of the detector, and (60)Co radiography was employed to measure the core of the germanium crystal. Moreover, the precise axial alignment of the detector within its housing was determined through a series of radiographic images with different incident angles. The hence obtained information enables us to optimise the Monte Carlo geometry model and to perform much more accurate and reliable simulations.

Non-Corrosive Tie Reinforcing and Dowel Bars for Highway Pavement Slabs, HR-343, 1993

The use of non-metallic load transfer and reinforcement devices for concrete highway pavements is a possible alternative to avoid corrosion problems related to the current practice of steel materials. Laboratory and field testing of highway pavement dowel bars, made of both steel and fiber composite materials, and fiber composite tie rods were carried out in this research investigation. Fatigue, static, and dynamic testing was performed on full-scale concrete pavement slabs which were supported by a simulated subgrade and which included a single transverse joint. The bahavior of the full-scale specimens with both steel and fiber composite dowels placed in the test joints was monitored during several million load cycles which simulated truck traffic at a transverse joint. Static bond tests were conducted on fiber composite tie rods to determine the required embedment length. These tests took the form of bending tests which included curvature and shear in the embedment zone and pullout tests which subjected the test specimen to axial tension only. Fiber composite dowel bars were placed at two transverse joints during construction of a new concrete highway pavement in order to evaluate their performance under actual field conditions. Fiber composite tie rods were also placed in the longitudinal joint between the two fiber composite doweled transverse joints.

Strengthening of Existing Single Span Steel Beam and Concrete Deck Bridges, HR-238, Part II, 1985

The unifying objective of Phases I and II of this study was to determine the feasibility of the post-tensioning strengthening method and to implement the technique on two composite bridges in Iowa. Following completion of these two phases, Phase III was undertaken and is documented in this report. The basic objectives of Phase III were further monitoring bridge behavior (both during and after post-tensioning) and developing a practical design methodology for designing the strengthening system under investigation. Specific objectives were: to develop strain and force transducers to facilitate the collection of field data; to investigate further the existence and effects of the end restraint on the post-tensioning process; to determine the amount of post-tensioning force loss that occurred during the time between the initial testing and the retesting of the existing bridges; to determine the significance of any temporary temperature-induced post-tensioning force change; and to develop a simplified design methodology that would incorporate various variables such as span length, angle-of-skew, beam spacing, and concrete strength. Experimental field results obtained during Phases II and III were compared to the theoretical results and to each other. Conclusions from this research are as follows: (1) Strengthening single-span composite bridges by post-tensioning is a viable, economical strengthening technique. (2) Behavior of both bridges was similar to the behavior observed from the bridges during field tests conducted under Phase II. (3) The strain transducers were very accurate at measuring mid-span strain. (4) The force transducers gave excellent results under laboratory conditions, but were found to be less effective when used in actual bridge tests. (5) Loss of post-tensioning force due to temperature effects in any particular steel beam post-tensioning tendon system were found to be small. (6) Loss of post-tensioning force over a two-year period was minimal. (7) Significant end restraint was measured in both bridges, caused primarily by reinforcing steel being continuous from the deck into the abutments. This end restraint reduced the effectiveness of the post-tensioning but also reduced midspan strains due to truck loadings. (8) The SAP IV finite element model is capable of accurately modeling the behavior of a post-tensioned bridge, if guardrails and end restraints are included in the model. (9) Post-tensioning distribution should be separated into distributions for the axial force and moment components of an eccentric post-tensioning force. (10) Skews of 45 deg or less have a minor influence on post-tensioning distribution. (11) For typical Iowa three-beam and four-beam composite bridges, simple regression-derived formulas for force and moment fractions can be used to estimate post-tensioning distribution at midspan. At other locations, a simple linear interpolation gives approximately correct results. (12) A simple analytical model can accurately estimate the flexural strength of an isolated post-tensioned composite beam.

Strengthening of an Existing Continuous-Span, Steel-Stringer, Concrete-Deck Bridge, HR-333, 1993

The need to upgrade understrength bridges in the United States has been well documented in the literature. The concept of strengthening steel stringer bridges in Iowa has been developed through several Iowa DOT projects. The objective of the project described in this report was to investigate the use of one such strengthening system on a three-span continuous steel stringer bridge in the field. In addition, a design methodology was developed to assist bridge engineers with designing a strengthening system to obtain the desired stress reductions. The bridge selected for strengthening was in Cerro Gordo County near Mason City, Iowa on County Road B65. The strengthening system was designed to remove overstresses that occurred when the bridge was subjected to Iowa legal loads. A two part strengthening system was used: post-tensioning the positive moment regions of all the stringers and superimposed trusses in the negative moment regions of the two exterior stringers at the two piers. The strengthening system was installed in the summers of 1992 and 1993. In the summer of 1993, the bridge was load tested before and after the strengthening system was activated. The load test results indicate that the strengthening system was effective in reducing the overstress in both the negative and positive regions of the stringers. The design methodology that was developed includes a procedure for determining the magnitude of post-tensioning and truss forces required to strengthen a given bridge. This method utilizes moment and force fractions to determine the distribution of strengthening axial forces and moments throughout the bridge. Finite element analysis and experimental results were used in the formulation and calibration of the methodology. A spreadsheet was developed to facilitate the calculation of these required strengthening forces.

Assessment of vascular invasion by bone and soft tissue tumours of the limbs: usefulness of MDCT angiography.

OBJECTIVE: To evaluate the accuracy of computed tomography angiography (CTA) in predicting arterial encasement by limb tumours, by comparing CTA with surgical findings (gold standard). METHODS: Preoperative CTA images of 55 arteries in 48 patients were assessed for arterial status: cross-sectional CTA images were scored as showing a fat plane between artery and tumour (score 0), slight contact between artery and tumour (score 1), partial arterial encasement (score 2) or total arterial encasement (score 3). Reformatted CTA images were assessed for arterial displacement, rigid wall, stenosis or occlusion. At surgery, arteries were classified as free or surgically encased; 45 arteries were free and 10 were surgically encased. RESULTS: Multivariate logistic regression identified the axial CTA score as a relevant predictor for arterial encasement and subsequent vascular intervention during surgery. All sites where CTA showed a fat plane between the tumour and the artery were classified as free at surgery (n = 28/28). The sensitivity of total arterial encasement on CTA (score 3) was 90%, specificity 93%, accuracy 93% and positive likelihood ratio 13.5. CONCLUSION: CTA evidence of total arterial encasement is a highly specific indication of arterial encasement. The presence of fat between the tumour and the artery on CTA rules out arterial involvement at surgery.

Inexperienced sonographers can successfully visualize and assess a three-dimensional image of the fetal face using a standardized ultrasound protocol.

Introduction: A standardized three-dimensional ultrasonographic (3DUS) protocol is described that allows fetal face reconstruction. Ability to identify cleft lip with 3DUS using this protocol was assessed by operators with minimal 3DUS experience. Material and Methods: 260 stored volumes of fetal face were analyzed using a standardized protocol by operators with different levels of competence in 3DUS. The outcomes studied were: (1) the performance of post-processing 3D face volumes for the detection of facial clefts; (2) the ability of a resident with minimal 3DUS experience to reconstruct the acquired facial volumes, and (3) the time needed to reconstruct each plane to allow proper diagnosis of a cleft. Results: The three orthogonal planes of the fetal face (axial, sagittal and coronal) were adequately reconstructed with similar performance when acquired by a maternal-fetal medicine specialist or by residents with minimal experience (72 vs. 76%, p = 0.629). The learning curve for manipulation of 3DUS volumes of the fetal face corresponds to 30 cases and is independent of the operator's level of experience. Discussion: The learning curve for the standardized protocol we describe is short, even for inexperienced sonographers. This technique might decrease the length of anatomy ultrasounds and improve the ability to visualize fetal face anomalies.

CT angiography helps to differentiate acute from chronic carotid occlusion: "carotid ring sign".

INTRODUCTION: Currently, there is no reliable method to differentiate acute from chronic carotid occlusion. We propose a novel CTA-based method to differentiate acute from chronic carotid occlusions that could potentially aid clinical management of patients. METHODS: We examined 72 patients with 89 spontaneously occluded extracranial internal carotids with CT angiography (CTA). All occlusions were confirmed by another imaging modality and classified as acute (imaging <1 week of presumed occlusion) orchronic (imaging >4 weeks), based on circumstantial clinical and radiological evidence. A neuroradiologist and a neurologist blinded to clinical information determined the site of occlusion on axial sections of CTA. They also looked for (a) hypodensity in the carotid artery (thrombus), (b) contrast within the carotid wall (vasa vasorum), (c) the site of the occluded carotid, and (d) the "carotid ring sign" (defined as presence of a and/or b). RESULTS: Of 89 occluded carotids, 24 were excluded because of insufficient circumstantial evidence to determine timing of occlusion, 4 because of insufficient image quality, and 3 because of subacute timing of occlusion. Among the remaining 45 acute and 13 chronic occlusions, inter-rater agreement (kappa) for the site of proximal occlusion was 0.88, 0.45 for distal occlusion, 0.78 for luminal hypodensity, 0.82 for wall contrast, and 0.90 for carotid ring sign. The carotid ring sign had 88.9% sensitivity, 69.2% specificity, and 84.5% accuracy to diagnose acute occlusion. CONCLUSION: The carotid ring sign helps to differentiate acute from chronic carotid occlusion. If further confirmed, this information may be helpful in studying ischemic symptoms and selecting treatment strategies in patients with carotid occlusions.

Design Manual for Strengthening of Continuous-Span Composite Bridges, HR-333, 1993

The need for upgrading a large number of understrength bridges in the United States has been well documented in the literature. This manual presents two methods for strengthening continuous-span composite bridges: post-tensioning of the positive moment regions of the bridge stringers and the addition of superimposed trusses at the piers. The use of these two systems is an efficient method of reducing flexural overstresses in undercapacity bridges. Before strengthening a given bridge however, other deficiencies (inadequate shear connection, fatigue problems, extensive corrosion) should be addressed. Since continuous-span composite bridges are indeterminant structures, there is longitudinal and transverse distribution of the strengthening axial forces and moments. This manual basically provides the engineer with a procedure for determining the distribution of strengthening forces and moments throughout the bridge. As a result of the longitudinal and transverse force distribution, the design methodology presented in this manual for continuous-span composite bridges is extremely complex. To simplify the procedure, a spreadsheet has been developed for use by practicing engineers. This design aid greatly simplifies the design of a strengthening system for a given bridge in that it eliminates numerous tedious hand calculations, computes the required force and moment fractions, and performs the necessary iterations for determining the required strengthening forces. The force and moment distribution fraction formulas developed in this manual are primarily for the Iowa DOT V12 and V14 three-span four-stringer bridges. These formulas may be used on other bridges if they are within the limits stated in this manual. Use of the distribution fraction formulas for bridges not within the stated limits is not recommended.