EVALUATION OF INTENSITY MODULATED RADIATION THERAPY (IMRT) DELIVERY ERROR DUE TO IMRT TREATMENT PLAN COMPLEXITY AND IMPROPERLY MATCHED DOSIMETRY DATA

Intensity modulated radiation therapy (IMRT) is a technique that delivers a highly conformal dose distribution to a target volume while attempting to maximally spare the surrounding normal tissues. IMRT is a common treatment modality used for treating head and neck (H&N) cancers, and the presence of many critical structures in this region requires accurate treatment delivery. The Radiological Physics Center (RPC) acts as both a remote and on-site quality assurance agency that credentials institutions participating in clinical trials. To date, about 30% of all IMRT participants have failed the RPC’s remote audit using the IMRT H&N phantom. The purpose of this project is to evaluate possible causes of H&N IMRT delivery errors observed by the RPC, specifically IMRT treatment plan complexity and the use of improper dosimetry data from machines that were thought to be matched but in reality were not. Eight H&N IMRT plans with a range of complexity defined by total MU (1460-3466), number of segments (54-225), and modulation complexity scores (MCS) (0.181-0.609) were created in Pinnacle v.8m. These plans were delivered to the RPC’s H&N phantom on a single Varian Clinac. One of the IMRT plans (1851 MU, 88 segments, and MCS=0.469) was equivalent to the median H&N plan from 130 previous RPC H&N phantom irradiations. This average IMRT plan was also delivered on four matched Varian Clinac machines and the dose distribution calculated using a different 6MV beam model. Radiochromic film and TLD within the phantom were used to analyze the dose profiles and absolute doses, respectively. The measured and calculated were compared to evaluate the dosimetric accuracy. All deliveries met the RPC acceptance criteria of ±7% absolute dose difference and 4 mm distance-to-agreement (DTA). Additionally, gamma index analysis was performed for all deliveries using a ±7%/4mm and ±5%/3mm criteria. Increasing the treatment plan complexity by varying the MU, number of segments, or varying the MCS resulted in no clear trend toward an increase in dosimetric error determined by the absolute dose difference, DTA, or gamma index. Varying the delivery machines as well as the beam model (use of a Clinac 6EX 6MV beam model vs. Clinac 21EX 6MV model), also did not show any clear trend towards an increased dosimetric error using the same criteria indicated above.

Adolescent Sexual Behavior: Examining Data from Texas and the US

Background: The US has higher rates of teen births and sexually transmitted infections (STI) than other developed countries. Texas youth are disproportionately impacted. Purpose: To review local, state, and national data on teens’ engagement in sexual risk behaviors to inform policy and practice related to teen sexual health. Methods: 2009 middle school and high school Youth Risk Behavior Survey (YRBS) data, and data from All About Youth, a middle school study conducted in a large urban school district in Texas, were analyzed to assess the prevalence of sexual initiation, including the initiation of non-coital sex, and the prevalence of sexual risk behaviors among Texas and US youth. Results: A substantial proportion of middle and high school students are having sex. Sexual initiation begins as early as 6th grade and increases steadily through 12th grade with almost two-thirds of high school seniors being sexually experienced. Many teens are not protecting themselves from unintended pregnancy or STIs – nationally, 80% and 39% of high school students did not use birth control pills or a condom respectively the last time they had sex. Many middle and high school students are engaging in oral and anal sex, two behaviors which increase the risk of contracting an STI and HIV. In Texas, an estimated 689,512 out of 1,327,815 public high school students are sexually experienced – over half (52%) of the total high school population. Texas students surpass their US peers in several sexual risk behaviors including number of lifetime sexual partners, being currently sexually active, and not using effective methods of birth control or dual protection when having sex. They are also less likely to receive HIV/AIDS education in school. Conclusion: Changes in policy and practice, including implementation of evidence-based sex education programs in middle and high schools and increased access to integrated, teen-friendly sexual and reproductive health services, are urgently needed at the state and national levels to address these issues effectively.

A cladistic analysis of apolipoprotein B gene variation and plasma lipid and apolipoprotein B levels, using familial data

Any functionally important mutation is embedded in an evolutionary matrix of other mutations. Cladistic analysis, based on this, is a method of investigating gene effects using a haplotype phylogeny to define a set of tests which localize causal mutations to branches of the phylogeny. Previous implementations of cladistic analysis have not addressed the issue of analyzing data from related individuals, though in human studies, family data are usually needed to obtain unambiguous haplotypes. In this study, a method of cladistic analysis is described in which haplotype effects are parameterized in a linear model which accounts for familial correlations. The method was used to study the effect of apolipoprotein (Apo) B gene variation on total-, LDL-, and HDL-cholesterol, triglyceride, and Apo B levels in 121 French families. Five polymorphisms defined Apo B haplotypes: the signal peptide Insertion/deletion, Bsp 1286I, XbaI, MspI, and EcoRI. Eleven haplotypes were found, and a haplotype phylogeny was constructed and used to define a set of tests of haplotype effects on lipid and apo B levels.^ This new method of cladistic analysis, the parametric method, found significant effects for single haplotypes for all variables. For HDL-cholesterol, 3 clusters of evolutionarily-related haplotypes affecting levels were found. Haplotype effects accounted for about 10% of the genetic variance of triglyceride and HDL-cholesterol levels. The results of the parametric method were compared to those of a method of cladistic analysis based on permutational testing. The permutational method detected fewer haplotype effects, even when modified to account for correlations within families. Simulation studies exploring these differences found evidence of systematic errors in the permutational method due to the process by which haplotype groups were selected for testing.^ The applicability of cladistic analysis to human data was shown. The parametric method is suggested as an improvement over the permutational method. This study has identified candidate haplotypes for sequence comparisons in order to locate the functional mutations in the Apo B gene which may influence plasma lipid levels. ^

A study of patient satisfaction with medical care services in Yanbu al-Sinaiya, Saudi Arabia

This study attempts to provide reliable scientific data that will enable the health services department of the Royal Commission of Yanbu Al Sinaiyah, Saudi Arabia to improve the quality of health care services provided in their facilities. Patient satisfaction and dissatisfaction were investigated along seven dimensions: General satisfaction scale, Communication, Technical quality, Art of care, Continuity of care, Time spent with the doctor, and Access/Convenience/ and availability. Patient satisfaction parameters were compared for Saudi vs. non-Saudi, males vs. females, and for patients seen in the hospital vs. those seen in Al-nawa and Radwa primary care centers. The information was obtained by using a self-administered questionnaire. The results indicate that patients seen in Al-nawa primary care center were more satisfied with care than patients seen in the hospital who in turn were more satisfied than those seen in Radwa primary care center. The non-Saudi patients were more satisfied than the Saudi patients across all three facilities and satisfaction scales. The female patients were more satisfied than the male patients across all three facilities and satisfaction scales. ^

Survey of shift and work tolerance of City of Houston emergency medical service personnel

This study of ambulance workers for the emergency medical services of the City of Houston studied the factors related to shiftwork tolerance and intolerance. The EMS personnel work a 24-hour shift with rotating days of the week. Workers are assigned to A, B, C, D shift, each of which rotate 24-hours on, 24-hours off, 24-hours on and 4 days off. One-hundred and seventy-six male EMTs, paramedics and chauffeurs from stations of varying levels of activity were surveyed. The sample group ranged in age from 20 to 45. The average tenure on the job was 8.2 years. Over 68% of the workers held a second job, the majority of which worked over 20 hours a week at the second position.^ The survey instrument was a 20-page questionnaire modeled after the Folkard Standardized Shiftwork Index. In addition to demographic data, the survey tool provided measurements of general job satisfaction, sleep quality, general health complaints, morningness/eveningness, cognitive and somatic anxiety, depression, and circadian types. The survey questionnaire included an EMS-specific scaler of stress.^ A conceptual model of Shiftwork Tolerance was presented to identify the key factors examined in the study. An extensive list of 265 variables was reduced to 36 key variables that related to: (1) shift schedule and demographic/lifestyle factors, (2) individual differences related to traits and characteristics, and (3) tolerance/intolerance effects. Using the general job satisfaction scaler as the key measurement of shift tolerance/intolerance, it was shown that a significant relationship existed between this dependent variable and stress, number of years working a 24-hour shift, sleep quality, languidness/vigorousness. The usual amount of sleep received during the shift, general health complaints and flexibility/rigidity (R$\sp2$ =.5073).^ The sample consisted of a majority of morningness-types or extreme-morningness types, few evening-types and no extreme-evening types, duplicating the findings of Motohashi's previous study of ambulance workers. The level of activity by station was not significant on any of the dependent variables examined. However, the shift worked had a relationship with sleep quality, despite the fact that all shifts work the same hours and participate in the same rotation schedule. ^

Expression and hormonal regulation of Muc-1 at the apical surface of mouse uterine epithelial cells and its role in modulating embryo implantation

Previous studies from our lab have established that large molecular weight mucin glycoproteins are major apically-disposed components of mouse uterine epithelial cells in vitro (Valdizan et al., (1992) J. Cell. Physiol. 151:451-465). The present studies demonstrate that Muc-1 represents one of the apically-disposed mucin glycoproteins of mouse uterine epithelia, and that Muc-1 protein and mRNA expression are regulated in the peri-implantation stage mouse uterus by ovarian steroids. Muc-1 expression is high in the proestrous and estrous stages, and decreases during diestrous. Both Muc-1 protein and mRNA levels decline to barely detectable levels by day 4 of pregnancy, i.e., prior to the time of blastocyst attachment. In contrast, Muc-1 expression in the cervix and vagina is maintained during this same period. Delayed implantation was established in pregnant mice by ovariectomy and maintained by administration of exogenous progesterone. Initiation of implantation was triggered by coinjection of progesterone maintained mice with a nidatory dose of 17$\beta$-estradiol. Muc-1 levels in the uterine epithelia of progesterone maintained mice declined to similar low levels as observed on day 4 of normal pregnancy. Coinjection of estradiol did not alter Muc-1 expression suggesting that down-regulation of Muc-1 is a progesterone dominated event. This was confirmed in ovariectomized, non-pregnant mice which displayed stimulation of Muc-1 expression following 6 hr of estradiol injection. Estradiol stimulated Muc-1 expression was inhibited by the pure antiestrogen, ICI 164,384. While progesterone alone had no effect on Muc-1 expression, it antagonized estradiol action in this regard. Injection of pregnant mice with the antiprogestin, RU 486, a known implantation inhibitor, on day 3 of pregnancy restored high level expression of Muc-1 mRNA on day 4, indicating that down-regulation of Muc-1 is progesterone receptor-mediated. Muc-1 appears to function as an anti-adhesive molecule at the apical cell surface of mouse uterine epithelial cells. Treatment of polarized cultures of mouse uterine epithelial cells with O-sialoglycoprotein endopeptidase reduced mucin expression in vitro, by about 50%, and converted polarized uterine epithelia to a functionally receptive state. Similarly, ablation of Muc-1 in Muc-1 null mice resulted in polarized uterine epithelia that were functionally receptive as compared to their wild-type counterparts in vitro. Collectively, these data indicate that Muc-1 and other mucins function as anti-adhesive molecules and that reduction or removal of these molecules is a prerequisite for the generation of a receptive uterine state. ^

Structural equation modeling of the medical outcome study: Short Form 36 (SF-36)

The factorial validity of the SF-36 was evaluated using confirmatory factor analysis (CFA) methods, structural equation modeling (SEM), and multigroup structural equation modeling (MSEM). First, the measurement and structural model of the hypothesized SF-36 was explicated. Second, the model was tested for the validity of a second-order factorial structure, upon evidence of model misfit, determined the best-fitting model, and tested the validity of the best-fitting model on a second random sample from the same population. Third, the best-fitting model was tested for invariance of the factorial structure across race, age, and educational subgroups using MSEM.^ The findings support the second-order factorial structure of the SF-36 as proposed by Ware and Sherbourne (1992). However, the results suggest that: (a) Mental Health and Physical Health covary; (b) general mental health cross-loads onto Physical Health; (c) general health perception loads onto Mental Health instead of Physical Health; (d) many of the error terms are correlated; and (e) the physical function scale is not reliable across these two samples. This hierarchical factor pattern was replicated across both samples of health care workers, suggesting that the post hoc model fitting was not data specific. Subgroup analysis suggests that the physical function scale is not reliable across the "age" or "education" subgroups and that the general mental health scale path from Mental Health is not reliable across the "white/nonwhite" or "education" subgroups.^ The importance of this study is in the use of SEM and MSEM in evaluating sample data from the use of the SF-36. These methods are uniquely suited to the analysis of latent variable structures and are widely used in other fields. The use of latent variable models for self reported outcome measures has become widespread, and should now be applied to medical outcomes research. Invariance testing is superior to mean scores or summary scores when evaluating differences between groups. From a practical, as well as, psychometric perspective, it seems imperative that construct validity research related to the SF-36 establish whether this same hierarchical structure and invariance holds for other populations.^ This project is presented as three articles to be submitted for publication. ^

HIV-related malignancies: A community-based study using a linkage of cancer registry and HIV registry data

Background. Increased incidence of cancer is documented in immunosuppressed transplant patients. Likewise, as survival increases for persons infected with the Human Immunodeficiency Virus (HIV), we expect their incidence of cancer to increase. The objective of this study was to examine the current gender specific spectrum of cancer in an HIV infected cohort (especially malignancies not currently associated with Acquired Immunodeficiency Syndrome (AIDS)) in relation to the general population.^ Methods. Cancer incidence data was collected for residents of Harris County, Texas who were diagnosed with a malignancy between 1975 and 1994. This data was linked to HIV/AIDS registry data to identify malignancies in an HIV infected cohort of 14,986 persons. A standardized incidence ratio (SIR) analysis was used to compare incidence of cancer in this cohort to that in the general population. Risk factors such as mode of HIV infection, age, race and gender, were evaluated for contribution to the development of cancer within the HIV cohort, using Cox regression techniques.^ Findings. Of those in the HIV infected cohort, 2289 persons (15%) were identified as having one or more malignancies. The linkage identified 29.5% of these malignancies (males 28.7% females 60.9%). HIV infected men and women had incidences of cancer that were 16.7 (16.1, 17.3) and 2.9 (2.3, 3.7) times that expected for the general population of Harris County, Texas, adjusting for age. Significant SIR's were observed for the AIDS-defining malignancies of Kaposi's sarcoma, non-Hodgkin's lymphoma, primary lymphoma of the brain and cancer of the cervix. Additionally, significant SIR's for non-melanotic skin cancer in males, 6.9 (4.8, 9.5) and colon cancer in females, 4.0 (1.1, 10.2) were detected. Among the HIV infected cohort, race/ethnicity of White (relative risk 2.4 with 95% confidence intervals 2.0, 2.8) or Spanish Surname, 2.2 (1.9, 2.7) and an infection route of male to male sex, with, 3.0 (1.9, 4.9) or without, 3.4 (2.1, 5.5) intravenous drug use, increased the risk of having a diagnosis of an incident cancer.^ Interpretation. There appears to be an increased risk of developing cancer if infected with the HIV. In addition to the malignancies routinely associated with HIV infection, there appears to be an increased risk of being diagnosed with non-melanotic skin cancer in males and colon cancer in females. ^

Statistical characterization and development of summary measures of non-normal distributions of nuclear morphometry data from prostate cancer cells for use as prognostic indicators

Nuclear morphometry (NM) uses image analysis to measure features of the cell nucleus which are classified as: bulk properties, shape or form, and DNA distribution. Studies have used these measurements as diagnostic and prognostic indicators of disease with inconclusive results. The distributional properties of these variables have not been systematically investigated although much of the medical data exhibit nonnormal distributions. Measurements are done on several hundred cells per patient so summary measurements reflecting the underlying distribution are needed.^ Distributional characteristics of 34 NM variables from prostate cancer cells were investigated using graphical and analytical techniques. Cells per sample ranged from 52 to 458. A small sample of patients with benign prostatic hyperplasia (BPH), representing non-cancer cells, was used for general comparison with the cancer cells.^ Data transformations such as log, square root and 1/x did not yield normality as measured by the Shapiro-Wilks test for normality. A modulus transformation, used for distributions having abnormal kurtosis values, also did not produce normality.^ Kernel density histograms of the 34 variables exhibited non-normality and 18 variables also exhibited bimodality. A bimodality coefficient was calculated and 3 variables: DNA concentration, shape and elongation, showed the strongest evidence of bimodality and were studied further.^ Two analytical approaches were used to obtain a summary measure for each variable for each patient: cluster analysis to determine significant clusters and a mixture model analysis using a two component model having a Gaussian distribution with equal variances. The mixture component parameters were used to bootstrap the log likelihood ratio to determine the significant number of components, 1 or 2. These summary measures were used as predictors of disease severity in several proportional odds logistic regression models. The disease severity scale had 5 levels and was constructed of 3 components: extracapsulary penetration (ECP), lymph node involvement (LN+) and seminal vesicle involvement (SV+) which represent surrogate measures of prognosis. The summary measures were not strong predictors of disease severity. There was some indication from the mixture model results that there were changes in mean levels and proportions of the components in the lower severity levels. ^

Patterns of alcohol and illicit substance use in the United States and Mexico. Substantive and methodologic issues in the cross-national analysis of alcohol and drug use data

This research examines prevalence of alcohol and illicit substance use in the United States and Mexico and associated socio-demographic characteristics. The sources of data for this study are public domain data from the U.S. National Household Survey of Drug Abuse, 1988 (n = 8814), and the Mexican National Survey of Addictions, 1988 (n = 12,579). In addition, this study discusses methodologic issues in cross-cultural and cross-national comparison of behavioral and epidemiologic data from population-based samples. The extent to which patterns of substance abuse vary among subgroups of the U.S. and Mexican populations is assessed, as well as the comparability and equivalence of measures of alcohol and drug use in these national samples.^ The prevalence of alcohol use was somewhat similar in the two countries for all three measures of use: lifetime, past year and past year heavy use, (85.0%, 68.1%, 39.6% and 72.6%, 47.7% and 45.8% for the U.S. and Mexico respectively). The use of illegal substances varied widely between countries, with U.S. respondents reporting significantly higher levels of use than their Mexican counterparts. For example, reported use of any illicit substance in lifetime and past year was 34.2%, 11.6 for the U.S., and 3.3% and 0.6% for Mexico. Despite these differences in prevalence, two demographic characteristics, gender and age, were important correlates of use in both countries. Men in both countries were more likely to report use of alcohol and illicit substances than women. Generally speaking, a greater proportion of respondents in both countries 18 years of age or older reported use of alcohol for all three measures than younger respondents; and a greater proportion of respondents between the ages of 18 and 34 years reported use of illicit substances during lifetime and past year than any other age group.^ Additional substantive research investigating population-based samples and at-risk subgroups is needed to understand the underlying mechanisms of these associations. Further development of cross-culturally meaningful survey methods is warranted to validate comparisons of substance use across countries and societies. ^

Sequential updating via dynamic hierarchical models: A Bayesian approach to longitudinal data analysis

Most statistical analysis, theory and practice, is concerned with static models; models with a proposed set of parameters whose values are fixed across observational units. Static models implicitly assume that the quantified relationships remain the same across the design space of the data. While this is reasonable under many circumstances this can be a dangerous assumption when dealing with sequentially ordered data. The mere passage of time always brings fresh considerations and the interrelationships among parameters, or subsets of parameters, may need to be continually revised. ^ When data are gathered sequentially dynamic interim monitoring may be useful as new subject-specific parameters are introduced with each new observational unit. Sequential imputation via dynamic hierarchical models is an efficient strategy for handling missing data and analyzing longitudinal studies. Dynamic conditional independence models offers a flexible framework that exploits the Bayesian updating scheme for capturing the evolution of both the population and individual effects over time. While static models often describe aggregate information well they often do not reflect conflicts in the information at the individual level. Dynamic models prove advantageous over static models in capturing both individual and aggregate trends. Computations for such models can be carried out via the Gibbs sampler. An application using a small sample repeated measures normally distributed growth curve data is presented. ^

Evaluation of the accuracy of multilevel analysis parameter estimates for intra-cluster correlation in correlated binary data

Many studies in biostatistics deal with binary data. Some of these studies involve correlated observations, which can complicate the analysis of the resulting data. Studies of this kind typically arise when a high degree of commonality exists between test subjects. If there exists a natural hierarchy in the data, multilevel analysis is an appropriate tool for the analysis. Two examples are the measurements on identical twins, or the study of symmetrical organs or appendages such as in the case of ophthalmic studies. Although this type of matching appears ideal for the purposes of comparison, analysis of the resulting data while ignoring the effect of intra-cluster correlation has been shown to produce biased results.^ This paper will explore the use of multilevel modeling of simulated binary data with predetermined levels of correlation. Data will be generated using the Beta-Binomial method with varying degrees of correlation between the lower level observations. The data will be analyzed using the multilevel software package MlwiN (Woodhouse, et al, 1995). Comparisons between the specified intra-cluster correlation of these data and the estimated correlations, using multilevel analysis, will be used to examine the accuracy of this technique in analyzing this type of data. ^

Managing the risks of medical technology: Do hazard surveillance systems provide an early warning of medical device problems?

The Food and Drug Administration (FDA) is responsible for risk assessment and risk management in the post-market surveillance of the U.S. medical device industry. One of the FDA regulatory mechanisms, the Medical Device Reporting System (MDR) is an adverse event reporting system intended to provide the FDA with advance warning of device problems. It includes voluntary reporting for individuals, and mandatory reporting for device manufacturers. ^ In a study of alleged breast implant safety problems, this research examines the organizational processes by which the FDA gathers data on adverse events and uses adverse event reporting systems to assess and manage risk. The research reviews the literature on problem recognition, risk perception, and organizational learning to understand the influence highly publicized events may have on adverse event reporting. Understanding the influence of an environmental factor, such as publicity, on adverse event reporting can provide insight into the question of whether the FDA's adverse event reporting system operates as an early warning system for medical device problems. ^ The research focuses on two main questions. The first question addresses the relationship between publicity and the voluntary and mandatory reporting of adverse events. The second question examines whether government agencies make use of these adverse event reports. ^ Using quantitative and qualitative methods, a longitudinal study was conducted of the number and content of adverse event reports regarding breast implants filed with the FDA's medical device reporting system during 1985–1991. To assess variation in publicity over time, the print media were analyzed to identify articles related to breast implant failures. ^ The exploratory findings suggest that an increase in media activity is related to an increase in voluntary reporting, especially following periods of intense media coverage of the FDA. However, a similar relationship was not found between media activity and manufacturers' mandatory adverse event reporting. A review of government committee and agency reports on the FDA published during 1976–1996 produced little evidence to suggest that publicity or MDR information contributed to problem recognition, agenda setting, or the formulation of policy recommendations. ^ The research findings suggest that the reporting of breast implant problems to FDA may reflect the perceptions and concerns of the reporting groups, a barometer of the volume and content of media attention. ^

THEORETICAL STUDIES ON THE METHODS OF RECONSTRUCTING PHYLOGENETIC TREES FROM DNA SEQUENCE DATA (MOLECULAR EVOLUTION, HOMINOID EVOLUTION, COMPUTER SIMULATION)

(1) A mathematical theory for computing the probabilities of various nucleotide configurations is developed, and the probability of obtaining the correct phylogenetic tree (model tree) from sequence data is evaluated for six phylogenetic tree-making methods (UPGMA, distance Wagner method, transformed distance method, Fitch-Margoliash's method, maximum parsimony method, and compatibility method). The number of nucleotides (m*) necessary to obtain the correct tree with a probability of 95% is estimated with special reference to the human, chimpanzee, and gorilla divergence. m* is at least 4,200, but the availability of outgroup species greatly reduces m* for all methods except UPGMA. m* increases if transitions occur more frequently than transversions as in the case of mitochondrial DNA. (2) A new tree-making method called the neighbor-joining method is proposed. This method is applicable either for distance data or character state data. Computer simulation has shown that the neighbor-joining method is generally better than UPGMA, Farris' method, Li's method, and modified Farris method on recovering the true topology when distance data are used. A related method, the simultaneous partitioning method, is also discussed. (3) The maximum likelihood (ML) method for phylogeny reconstruction under the assumption of both constant and varying evolutionary rates is studied, and a new algorithm for obtaining the ML tree is presented. This method gives a tree similar to that obtained by UPGMA when constant evolutionary rate is assumed, whereas it gives a tree similar to that obtained by the maximum parsimony tree and the neighbor-joining method when varying evolutionary rate is assumed. ^

A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^