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PubMedDate not supplied

Interactive approximate rendering of reflections, refractions, and caustics.

Reflections, refractions, and caustics are very important for rendering global illumination images. Although many methods can be applied to generate these effects, the rendering performance is not satisfactory for interactive applications. In this paper, complex ray-object intersections are simplified so that the intersections can be computed on a GPU, and an iterative computing scheme based on the depth buffers is used for correcting the approximate results caused by the simplification. As a result, reflections and refractions of environment maps and nearby geometry can be rendered on a GPU interactively without preprocessing. We can even achieve interactive recursive reflections and refractions by using an object-impostor technique. Moreover, caustic effects caused by reflections and refractions can be rendered by placing the eye at the light. Rendered results prove that our method is sufficiently efficient to render plausible images interactively for many interactive applications.

Algorithms↗

PubMedDate not supplied

Interactive collision detection for deformable models using streaming AABBs.

We present an interactive and accurate collision detection algorithm for deformable, polygonal objects based on the streaming computational model. Our algorithm can detect all possible pairwise primitive-level intersections between two severely deforming models at highly interactive rates. In our streaming computational model, we consider a set of axis aligned bounding boxes (AABBs) that bound each of the given deformable objects as an input stream and perform massively-parallel pairwise, overlapping tests onto the incoming streams. As a result, we are able to prevent performance stalls in the streaming pipeline that can be caused by expensive indexing mechanism required by bounding volume hierarchy-based streaming algorithms. At runtime, as the underlying models deform over time, we employ a novel, streaming algorithm to update the geometric changes in the AABB streams. Moreover, in order to get only the computed result (i.e., collision results between AABBs) without reading back the entire output streams, we propose a streaming en/decoding strategy that can be performed in a hierarchical fashion. After determining overlapped AABBs, we perform a primitive-level (e.g., triangle) intersection checking on a serial computational model such as CPUs. We implemented the entire pipeline of our algorithm using off-the-shelf graphics processors (GPUs), such as nVIDIA GeForce 7800 GTX, for streaming computations, and Intel Dual Core 3.4G processors for serial computations. We benchmarked our algorithm with different models of varying complexities, ranging from 15K up to 50K triangles, under various deformation motions, and the timings were obtained as 30 approximately 100 FPS depending on the complexity of models and their relative configurations. Finally, we made comparisons with a well-known GPU-based collision detection algorithm, CULLIDE [4] and observed about three times performance improvement over the earlier approach. We also made comparisons with a SW-based AABB culling algorithm [2] and observed about two times improvement.

Algorithms↗

PubMed2004

Design-based estimation of surface area in thick tissue sections of arbitrary orientation using virtual cycloids.

Surface area is a first-order stereological parameter with important biological applications, particularly at the intersection of biological phases. To deal with the inherent anisotropy of biological surfaces, state-of-the-art design-based methods require tissue rotation around at least one axis prior to sectioning. This paper describes the use of virtual cycloids for surface area estimation of objects and regions in thick, transparent tissue sections cut at any arbitrary (convenient) orientation. Based on the vertical section approach of Baddeley et al., the present approach specifies the vertical axis as the direction of sectioning (i.e. the direction perpendicular to the tissue section), and applies computer-generated cycloids (virtual cycloids) with their minor axis parallel to the vertical axis. The number of surface-cycloid intersections counted on focal planes scanned through the z-axis is proportional to the surface area of interest in the tissue, with no further assumptions about size, shape or orientation. Optimal efficiency at each x-y location can be achieved by three virtual cycloids orientated with their major axes (which are parallel to the observation planes) mutually at an angle of 120 degrees. The major practical advantage of the present approach is that estimates of total surface area (S) and surface density (SV) can be obtained in tissue sections cut at any convenient orientation through the reference space.

Animals↗

PubMed1992

The clonal organization of the squamous epithelium of the tongue.

Knowledge of the kinetics and stem cell localization of the mouse lingual epithelium is largely based on studies using DNA labelling techniques. We have adopted a different approach, using histochemistry for the X-linked enzyme glucose-6-phosphate dehydrogenase (G6PD). We have deduced clone size and morphology from studies of patch size and distribution in mice heterozygous for G6PD deficiency and from the identification of clonal enzyme loss induced in normal mice by application of a mutagen. Lingual epithelium of female mice (CBA X GPDX) heterozygous for G6PD deficiency showed multiple clearly defined patches of strong or weak enzyme activity, corresponding in intensity to the strong staining uniformly present in the normal parental strain (CBA) or to the weak staining uniformly present in the G6PD deficient parental strain (GPDX). This pattern results from the random suppression of either the paternal or the maternal X chromosome in each cell early in embryonic development, and the subsequent inheritance of X inactivation in daughter cells, giving rise to phenotypic patches each composed of one or more clones. The patch borders intersected the base of the lingual epithelium at small indentations or at the apices of connective tissue papillae; the surface intersection in some cases bisected filiform papillae. Patch width measured in tissue sections at the mid rete ridge level, showed a clear mode close to 40 microns, corresponding very closely to the mode for rete ridge width (i.e. distance between connective tissue papillae). Further evidence for clonal organization was obtained by inducing mutations in the lingual epithelium of CBA mice by topical mutagen application. A few clearly defined patches of enzyme loss were found with a mean diameter of 36 microns. Their morphology was very similar to that of patches in the heterozygous animals. We interpret these patches as clones derived from stem cells with induced somatic G6PD mutations. We conclude that the mouse lingual epithelium is a stem cell epithelium composed of clonal units of about 40 microns diameter, based on the rete ridge structure and that both connective tissue papillae and filiform papillae occur at the junction of two or more epithelial clones.

Animals↗

PubMed2005

Algorithms to estimate the rose of directions of a spatial fibre system.

Summary The directional measure (which is up to normalization the rose of directions) is used to quantify anisotropy of stationary fibre processes in three-dimensional space. There exist a large number of approaches to estimate this measure from the rose of intersections (which is the mean number of intersections of fibres with lower dimensional test sets). Three recently suggested nonparametric algorithms to solve this problem are reviewed and compared. They were obtained from solutions of a least squares problem, a more general convex optimization problem and a linear program, respectively. Application to two different carbon fibre architectures and to simulated data allow an empirical comparison of these approaches. In addition, estimators for the associated zonoid (or Steiner compact) are suggested. This set turns out to be an intuitive tool for visualization.

Algorithms↗

PubMed1976

Phenylalanyl-tRNA synthetase from baker's yeast. Salt dependence of steady-state kinetics indicates two molecular forms of the enzyme.

Steady-state kinetic data of aminoacylation of tRNAPhe by phenylalanyl-tRNA synthetase depend on salt concentration. At 5 mM KCl and 20 mM MgSO4 a non-linear curve is found in the double-reciprocal plot for ATP and phenylalanine, while at 200 mM KCl and 50 mM MgSO4 a linear curve is observed. KCl and MgSO4 dependence of the reaction also show biphasic curves with intersection points of the two extrapolated linear parts at 50 mM and 10 mM, respectively. A biphasic curve is also found if the concentration of CTP is varied at constant low ATP concentration. Extrapolations of the linear parts of the curves for ATP as well as for CTP at 5 mM KCl and 20 mM MgSO4 intersected the 1/[NTP] axis at 1.2 +/- 0.1 mM. Hence the existence of a non-linear curve for ATP as well as phenylalanine does not necessarily indicate two non-equivalent binding sites for these substrates. A more likely explanation is the existence of two different molecular forms of phenylalanyl-tRNA synthetase which are interconvertible by salt. This explanation is substantiated by the observation that proteolytic digestion of phenylalanyl-tRNA synthetase is more easily achieved at low than at medium ionic strength. In addition mischarging of tRNAIle with phenylalanine by phenylalanyl-tRNA synthetase occurs at a moderate rate at 5 mM KCl and 20 mM MgSO4 whereas it is largely depressed by addition of either 5 mM CTP or 150 mM KCl.

Amino Acyl-tRNA Synthetases↗

PubMed1984

Primary structure of N-glycosidically linked asialoglycans of secretory immunoglobulins A from human milk.

The asialoglycopeptides obtained from secretory immunoglobulins A from human milk have been separated by gel filtration and affinity chromatography on Concanavalin A-Sepharose and Lens culinaris agglutinin-Sepharose columns. Their structures have been determined by sugar analysis, methylation studies including mass spectrometry and 500-MHz 1H-NMR spectroscopy. The glycans are of the biantennary N-acetyllactosamine type differing in their degree of extension by fucosyl-N-acetyllactosamine residues. The overall structures of the glycopeptides are as follows: (Formula: see text) Most of the asialoglycopeptide structures possess an intersecting GlcNAc residue; they are suggested to be located on the alpha chain of the secretory immunoglobulins A of human milk. The non-intersected structures probably occur on the secretory piece. The methodology applied to the structural analysis adequately coped with the extremely high degree of heterogeneity shown by the structures.

Carbohydrates↗

PubMed1985

The major oligosaccharides in the large subunit of the hemagglutinin from fowl plague virus, strain Dutch. Structure elucidation by one-dimensional and two-dimensional 1H nuclear magnetic resonance and by methylation analysis.

The N-glycosidically linked glycans in the large subunit (HA1) of the hemagglutinin from fowl plague virus, strain Dutch (containing about 15%, w/w, of carbohydrates), were liberated by alkaline hydrolysis, and were filtrated through Bio-Gel as the re-N-acetylated oligosaccharide alditols. One major fraction (90%, mol/mol) was obtained. It was subfractionated by concanavalin A affinity chromatography and was analyzed by methylation/capillary gas chromatography/mass fragmentography and especially by one-dimensional and two-dimensional 1H nuclear magnetic resonance. The major HA1 glycans, which are not sialylated, were thus found to comprise about 40%, 30% and 20% (mol/mol), respectively, of biantennary intersected, biantennary, and triantennary N-acetyllactosaminic ('complex') oligosaccharides. About two thirds of the internal GlcNAc residues in these glycans are substituted by Fuc(alpha 1----6), all the triantennary species carry the third Gal(beta 1----4)GlcNAc(beta 1----unit at the Man(alpha 1----6)-branch, and roughly one fourth of the N-acetyllactosamine units in the non-intersected biantennary oligosaccharides are incomplete.

Amino Acids↗

PubMed1990

Oligosaccharides at individual glycosylation sites in glycoprotein 71 of Friend murine leukemia virus.

Glycoprotein 71 from Friend murine leukemia virus was digested with proteases and the glycopeptides obtained were isolated and assigned, by amino acid sequencing, to the eight N-glycosylated asparagines in the molecule; only Asn334 and Asn341 could not be separated. The oligosaccharides liberated from each glycopeptide by endo-beta-N-acetylglucosaminidase H, or by peptide-N4-(N-acetyl-beta-glucosaminyl)asparagine amidase F, were fractionated and subjected to structural analysis by one- and two-dimensional 1H NMR, as well as by methylation/gas-liquid-chromatography/mass-fragmentography. At each glycosylation site, the substituents were found to be heterogeneous including, at Asn334/341 and Asn410, substitution by different classes of N-glycans: oligomannosidic oligosaccharides, mainly Man alpha 1----6(Man alpha 1----3)Man alpha 1----6(Man alpha 1----3)Man beta 1----4GlcNAc beta 1----4GlcNAc beta 1----, were detected at Asn168, Asn334/341 and Asn410. Hybrid species, partially sialylated, intersected and (proximally) funcosylated Man alpha 1----6(Man alpha 1----3)Man alpha 1----6 and Man alpha 1----3Man alpha 1----6 and Man alpha 1----3Man alpha 1----6(Gal beta 1----4GlcNAc beta 1----2Man alpha 1----3)Man beta 1----4GlcNAc beta 1----4GlcNAc beta 1----, were found at Asn12, as previously published [Schlüter, M., Linder, D., Geyer, R., Hunsmann, H., Schneider, J. & Stirm, S. (1984) FEBS Lett. 169, 194-198] and at Asn334/341. N-Acetyllactosaminic glycans, mainly partially intersected and fucosylated NeuAc alpha 2----3 or Gal alpha 1----3Gal beta 1----4GlcNAc beta 1----2Man alpha 1----6(NeuAc alpha 2----6 or NeuAc alpha 2----3Gal-beta 1----4GlcNAc beta 1----2Man alpha 1----3)Man beta 1----4GlcNac beta 1----4GlcNAc beta 1---- with some bifurcation at ----6Man alpha 1----6, were obtained from Asn266, Asn302, Asn334/341, Asn374 and Asn410. In addition, Thr268, Thr277, Thr279, Thr304/309, as well as Ser273 and Ser275, were found to be O-glycosidically substituted by Gal beta 1----3GalNAc alpha 1----, monosialylated or desialylated at position 3 of Gal or/and position 6 of GalNAc.

Amino Acid Sequence↗

PubMed1990

Purification and properties of N5, N10-methylenetetrahydromethanopterin reductase from Methanobacterium thermoautotrophicum (strain Marburg).

The reduction of N5,N10-methylenetrahydromethanopterin (CH2 = H4MPT) to N5-methyltetrahydromethanopterin (CH3-H4MPT) is an intermediate step in methanogenesis from CO2 and H2. The reaction is catalyzed by CH2 = H4MPT reductase. The enzyme from Methanobacterium thermoautotrophicum (strain Marburg) was found to be specific for reduced coenzyme F420 as electron donor; neither NADH or NADPH nor reduced viologen dyes could substitute for the reduced 5-deazaflavin. The reductase was purified over 100-fold to apparent homogeneity. Sodium dodecyl sulfate/polyacrylamide gel electrophoresis revealed only one protein band at the 36-kDa position. The apparent molecular mass of the native enzyme was determined by gel filtration to be in the order of 150 kDa. The purified enzyme was colourless. It did not contain flavin or iron. The ultraviolet visible spectrum was almost identical to that of albumin, suggesting the absence of a chromophoric prosthetic group. Reciprocal plots of the enzyme activity versus the substrate concentration at different constant concentrations of the second substrate yielded straight lines intersecting at one point on the abscissa to the left of the vertical axis. This intersecting pattern is characteristic of a ternary complex catalytic mechanism. The Km for CH2 = H4MPT and for the reduced coenzyme F420 were determined to be 0.3 mM and 3 microM, respectively. Vmax was 6000 mumol.min-1.mg protein-1 (kcat = 3600 s-1). The CH2 = H4MPT reductase was stable in the presence of air; at 4 C less than 10% activity was lost within 24 h.

Electrophoresis, Polyacrylamide Gel↗

PubMed1994

Isovergence surfaces: the conjugacy of vertical eye movements in tertiary positions of gaze.

Conjugate gaze is often defined as the equal angle rotation of the two eyes. For fixation at far distances, the optical axes are parallel and conjugacy is defined irrespective of the coordinate system. For nearby or finite fixation distances, the evaluation of conjugacy for many gaze postures depends on the coordinate system used to measure it. For example, if the eye is elevated or depressed and the eye is rotated about a vertical axis, the intersections of lines of sight with a tangent screen will describe either straight lines or arcs depending on whether the vertical axis is fixed with respect to the head or to the eye. Because of the horizontal separation of the two eyes, the binocular fixation of near targets at tertiary positions of gaze will require a vertical vergence component for head-referenced but not eye-referenced measurements. The vertical gaze alignment of three human subjects was measured as they viewed targets placed at secondary and tertiary eye positions at two different distances. Vertical vergence was either held open or closed-loop. The lines of sight were found to intersect (i.e. vertical gaze was aligned) regardless of target position or viewing condition.

Convergence, Ocular↗

PubMed1988

Effects of cadmium on the slow inward current of frog heart muscle in relation to a lowering of pH in external solution.

1. The effect of cadmium (Cd) on the slow inward current (Isi) of frog atrial fibres was studied by the double sucrose gap technique. 2. Cd (5 microM) depressed Isi in a voltage-dependent manner without alteration of the apparent reversal potential for Isi. 3. Dose-response curves indicated an apparent dissociation constant for the Cd blocking effect of 4.5 microM at 0 mV, with a one to one relationship between Cd and the slow channel. 4. Increasing the external concentration of Ca ions ([Ca]0) in the tetrodotoxin (TTX)-containing Ringer solution antagonized the block of Isi by Cd. Double reciprocal plots for Isi versus [Ca]0 drawn in the presence or in the absence of Cd intersected at the ordinate, indicating that Cd competes with Ca for a common binding site. 5. Lowering the external pH from 7.3 to 6.3 depressed Isi. The block caused by H was voltage-dependent. Double reciprocal plots for Isi versus [Ca]0 drawn at pH 7.3 and 6.3 intersected at the abscissa, and indicated that H and Ca did not compete for a common site. 6. Lowering the external pH did not change the ability of Cd to inhibit Isi. 7. The data suggested the existence of two different sites within the slow channel in frog atrial fibres, one of them being H-sensitive and the other cadmium-sensitive.

Animals↗

PubMed2006

Influence of steroid drugs on orthodontically induced root resorption.

OBJECTIVES: To investigate the effect of acute and chronic corticosteroid treatment on orthodontically induced root resorption. DESIGN: 'Split mouth' design performing orthodontic tooth movement in 64, 6-month-old male rats divided into three groups: acute (n = 22), chronic (n = 23) and control group (n = 19). Acute and chronic group received corticosteroid treatment (8 mg/kg/day) for 3 and 7 weeks, respectively, while no pharmacological treatment was performed in the control group. Performed at the Department of Orthodontics, School of Dentistry, University of Aarhus, Aarhus, Denmark. EXPERIMENTAL VARIABLE: The upper left first molar was moved mesially for 21 days in all three groups with 25 g of force. Undecalcified histological sections were cut at the coronal and apical level. OUTCOME MEASURE: The number of intersections hitting resorption lacunae (ES), defined as a scalloped surface with or without cementoclasts, over the total number of intersections hitting the root surface (RS) were recorded and expressed as percentage. RESULTS: The acute group showed significantly more root resorption at the mesio-coronal level compared with the control and the chronic group. CONCLUSION: This could be ascribed to the lack of balance between blastic activities (inhibited by the drug) and the clastic activities (enhanced or unchanged by drug administration) occurring in the initial phase of drug administration. As a consequence, a careful monitoring of patients undergoing acute corticosteroid treatment is suggested.

Animals↗

PubMed2000

Effect of distance on the power density from two light guides.

PURPOSE: This study determined the effect of distance on the power density from standard and Turbo light guides (Demetron/Kerr, Danbury, Connecticut). MATERIALS AND METHODS: Power density was measured from 0 to 10 mm away from the tip of standard 8-mm curved light guides and 13/8-mm Turbo curved light guides. To determine the effect of distance on power density, a polynomial regression line was fitted. The Kolmogorov-Smirnov (K-S) statistic and the Wilcoxon rank sum (WR) tests were used to determine if there was a difference in the rate at which the power density decreased for the standard and Turbo light guides as the distance from the tip increased. Photographs of the light dispersion from each tip were also taken. RESULTS: At 0 mm, the mean (+/- SD) power density from the two standard light guides was 743 +/- 6.1 mW/cm2 and from the four Turbo light guides was 1128 +/- 22.1 mW/cm2. As the distance from the tip of the light-guide tip increased, the power density decreased, but the rate of decrease was greater from the Turbo light guides than from the standard light guides. At 6 mm the power density from the standard light guides fell to 372 mW/cm2 (50% of the original value) and the power density from the Turbo light guides fell to 263 mW/cm2 (23% of the original value). Both the K-S statistic and the WR sum test indicated that the distribution of light intensities was significantly different from the two light guides (WR p-value = .0246, K-S p-value < .0001). The two estimated polynomials intersected at 3.66 mm, and the 95% prediction intervals intersected at about 2.8 and 4.8 mm. Therefore, beyond 5 mm away from the tip of the light guide, the standard light guides gave higher power density readings than the Turbo light guides. Photographs showed that the light dispersed at a wider angle from the Turbo light guides than from the standard light guide. CLINICAL SIGNIFICANCE: The design of the light guide of a light curing unit affects light dispersion, power density, and ultimately the dentist's ability to properly cure composite. For these reasons, manufacturers should report the power density at the tip of the light guide and 6 mm from the tip of the light guide, since significant differences exist between light guide designs.

Dental Cavity Preparation↗

PubMedDate not supplied

Tracer mass recovery in fractured aquifers estimated from multiple well tests.

Forced-gradient tracer tests in fractured aquifers often report low mass recoveries. In fractured aquifers, fractures intersected by one borehole may not be intersected by another. As a result (1) injected tracer can follow pathways away from the withdrawal well causing low mass recovery and (2) recovered water can follow pathways not connected to the injection well causing significant tracer dilution. These two effects occur along with other forms of apparent mass loss. If the strength of the connection between wells and the amount of dilution can be predicted ahead of time, tracer tests can be designed to optimize mass recovery and dilution. A technique is developed to use hydraulic tests in fractured aquifers to calculate the conductance (strength of connection) between well pairs and to predict mass recovery and amount of dilution during forced gradient tracer tests. Flow is considered to take place through conduits, which connect the wells to each other and to distant sources or sinks. Mass recovery is related to the proportion of flow leaving the injection well and arriving at the withdrawal well, and dilution is related to the proportion of the flow from the withdrawal well that is derived from the injection well. The technique can be used to choose well pairs for tracer tests, what injection and withdrawal rates to use, and which direction to establish the hydraulic gradient to maximize mass recovery and/or minimize dilution. The method is applied to several tracer tests in fractured aquifers in the Clare Valley, South Australia.

Models, Theoretical↗

PubMed1988

Voltage dependence of sodium-calcium exchange current in guinea-pig atrial myocytes determined by means of an inhibitor.

1. Spontaneous transient inward currents (Iti) caused by cyclic release of Ca2+ ions from the sarcoplasmic reticulum were studied in cultured atrial myocytes from hearts of adult guinea-pigs. K+ channel currents were blocked by replacing K+ on both sides of the membrane by Cs+; the L-type Ca2+ current was inhibited by D600. 2. The voltage dependence of peak Iti and the background current displayed distinct outward-going rectification. The I-V curves for both currents approach each other at strongly positive membrane potentials but do not intersect. 3. 3'-4'Dichlorobenzamil (DCB) causes a concentration-dependent inhibition of peak Iti and a shift of the holding current (at -60 to -40 mV) in the inward direction. Inhibition of Iti is half-maximal at a concentration of 30 microM. 4. DCB reduces the outward-rectifying component of both peak Iti and the background current. The I-V curves of the control and DCB-inhibited currents intersect at ca. +10 mV (peak Iti) and negative to -75 mV (background current), suggesting the reversal potential of the DCB-inhibited current to be shifted by ca. 85 mV in the positive direction if Cai2+ rises following Ca2+ release. 5. The voltage dependence of the DCB-inhibited currents is highly compatible with the concept of Na+-Ca2+ exchange being the charge-carrying mechanism of the outward-rectifying background current. Ca2+ release from the SR alters the I-V curve of this current according to the shift of the thermodynamic driving force.

Action Potentials↗

PubMed2005

A method for measurement of joint kinematics in vivo by registration of 3-D geometric models with cine phase contrast magnetic resonance imaging data.

A new method is presented for measuring joint kinematics by optimally matching modeled trajectories of geometric surface models of bones with cine phase contrast (cine-PC) magnetic resonance imaging data. The incorporation of the geometric bone models (GBMs) allows computation of kinematics based on coordinate systems placed relative to full 3-D anatomy, as well as quantification of changes in articular contact locations and relative velocities during dynamic motion. These capabilities are additional to those of cine-PC based techniques that have been used previously to measure joint kinematics during activity. Cine-PC magnitude and velocity data are collected on a fixed image plane prescribed through a repetitively moved skeletal joint. The intersection of each GBM with a simulated image plane is calculated as the model moves along a computed trajectory, and cine-PC velocity data are sampled from the regions of the velocity images within the area of this intersection. From the sampled velocity data, the instantaneous linear and angular velocities of a coordinate system fixed to the GBM are estimated, and integration of the linear and angular velocities is used to predict updated trajectories. A moving validation phantom that produces motions and velocity data similar to those observed in an experiment on human knee kinematics was designed. This phantom was used to assess cine-PC rigid body tracking performance by comparing the kinematics of the phantom measured by this method to similar measurements made using a magnetic tracking system. Average differences between the two methods were measured as 2.82 mm rms for anterior/posterior tibial position, and 2.63 deg rms for axial rotation. An intertrial repeatability study of human knee kinematics using the new method produced rms differences in anterior/posterior tibial position and axial rotation of 1.44 mm and 2.35 deg. The performance of the method is concluded to be sufficient for the effective study of kinematic changes caused to knees by soft tissue injuries.

Biomechanical Phenomena↗

PubMed2001

A theoretical model for event statistics in microdosimetry. I: Uniform distribution of heavy ion tracks.

In this work we describe a novel approach to solving microdosimetry problems using conditional probabilities and geometric concepts. The intersection of a convex site with a field of randomly oriented straight track segments is formulated in terms of the relative overlap between the chord associated with the action line of the track and the track itself. This results in a general formulation that predicts the contribution of crossers, stoppers, starters, and insiders in terms of two separate functions: the chord length distribution (characteristic of the site geometry and the type of randomness) and an independent set of conditional probabilities. A Monte Carlo code was written in order to validate the proposed approach. The code can represent the intersection between an isotropic field of charged particle tracks and a general ellipsoid of unrestricted geometry. This code was used to calculate the event distribution for a sphere as well as the expected mean value and variance of the track length distribution and to compare these against the deterministic calculations. The observed agreement was shown to be very good, within the precision of the Monte Carlo approach. The formulation is used to calculate the event frequency, lineal energy, and frequency mean specific energy for several monoenergetic and isotropic proton fields in a spherical site, as a function of the site diameter, proton energy, and the event type.

Biophysical Phenomena↗