William P. Fox

Oncologic and functional outcome following sacrectomy for sacral chordoma.

BACKGROUND Sacral chordoma is a rare, low to intermediate-grade tumor that poses substantial challenges in terms of timely diagnosis and adequate treatment. Few studies have examined the oncologic and functional outcomes of patients treated for sacral chordoma. METHODS The clinical records of sixteen patients who had undergone sacrectomy for chordoma between 1985 and 2001 were evaluated retrospectively. All patients underwent resection by means of a sequential combined anterior and posterior approach. Patients were followed clinically at six-month intervals following recovery from the index surgical procedure. The disease onset, treatment, hospital stay, recurrence rates, survival, adjuvant therapy, functional outcome measures, and complications were evaluated. RESULTS The average age at the time of diagnosis was sixty-one years. The mean tumor size was 15.2 cm in diameter, and all patients had a resection involving S1 or S2. The mean duration of follow-up was sixty-six months, and the tumor recurred in twelve of the sixteen patients. The mean time to metastasis was fifty months. Four patients were clinically disease-free at a mean follow-up of 94.5 months, while five patients died as a result of progressive local or metastatic disease at a mean follow-up of 31.4 months. Only one patient had normal bowel and bladder control postoperatively, and only three were able to walk without assistive devices. Eight patients had wound complications, and one patient had a deep-vein thrombosis. With the numbers available, neither negative margins at the time of initial tumor resection nor adjuvant radiation therapy had a significant impact on survival or local recurrence. More cephalad levels of resection were associated with significantly worse bowel (p = 0.01) and bladder (p = 0.01) control. Complications were frequent and were more common with a larger tumor size at the time of presentation (p = 0.034). CONCLUSIONS The treatment of sacral chordoma is an arduous clinical undertaking that requires a multidisciplinary approach and attention to detail from the outset. Despite aggressive well-planned surgical management and adherence to strict surveillance protocols, frequent recurrence and the late onset of metastatic disease are to be expected in a substantial proportion of patients, especially those with a very large chordoma or one at a more cephalad level. Adequate surgical treatment results in substantial functional impairment and numerous complications; however, it does offer the possibility of long-term disease-free survival. We advocate an attempt at complete resection, when there is still a possibility of cure, and aggressive treatment of local recurrences. LEVEL OF EVIDENCE Therapeutic Level IV. See Instructions to Authors for a complete description of levels of evidence.

Incidence of clostridial contamination in donors’ musculoskeletal tissue

Reports of infection by Clostridium sordellii associated with allograft transplantation have generated considerable interest. We report our experience in recognising clostridial contamination in cadaver donors of musculoskeletal tissue. Tissues obtained from 795 consecutive donors were excised using standard surgical techniques. Samples of blood and bone marrow were also obtained. Donors with clostridia recovered from any site were matched with the preceding donor without clostridia as a procedural and environmental control. The histories of the donors were analysed to determine which variables had a relationship to contamination by running a contingency table and chi-squared test on the variables against the event of a donor being contaminated. Sixty-four donors (8.1%) had clostridia, most commonly C. sordellii. Clostridia were grown from the blood, marrow and tissue samples of 52, 37 and 30 donors, respectively. In eight cases, they were cultured from the tissue samples alone. There was no significant difference in age or gender between the contaminated donors and the control group. Open wounds were more common in control than in contaminated subjects, but only death by drowning in the contaminated group was statistically significant (p = 0.02). The time between death and the excision of tissue which was contaminated (16 hrs 10 mins) compared with control (11 hrs 10 mins) donors was also significant (p < 10(-6)). We conclude that there is clostridial contamination in a significant number of tissue donors, particularly with increasing time between death and tissue excision. Among the most commonly encountered species is C. sordellii. Multiple microbiological cultures, including blood, are necessary in order to identify clostridial contamination.

Incidence of foot and ankle injuries in West Point cadets with pes planus compared to the general cadet population

Background: The relationship between pes planus and injuries of the lower extremity is controversial. However, few studies have used standardized means of evaluating and defining pes planus, and none have had a controlled patient population. The objective of this study was to evaluate an ideal population of physically active individuals to establish a potential correlation between pes planus, as defined by a standardized method, and injuries to the lower extremity. Methods: A standardized technique for evaluating arch height, based on a midfoot ratio established by Harris mat print calculations, was used to assess a consecutive series of 512 newly entered West Point cadets. Pes planus was defined as more than 2 standard deviations above the mean midfoot ratio of the population. After 46 months, a retrospective chart review was done to identify lower extremity injuries sustained in this group of young healthy patients. The results of the footprint analysis were correlated with the medical record findings. Results: Thirty-three cadets were found to have pes planus; 13 had only left foot involvement, 15 had right foot only involvement, and five had bilateral pes planus. There were no cavus feet. Statistically significant relationships were seen between the degree of pes planus and total number of injuries sustained (p = 0.007), the overall size of the foot and total number of injuries (p = 0.041), left flat feet and left midfoot injuries (p = 0.028), left pes planus and right midfoot injuries (p = 0.008), left pes planus and left knee injuries (p = 0.038), and right pes planus and right knee injuries (p = 0.027). Women had smaller feet (p = 0.000), smaller midfoot ratios (right, p = 0.013; left p = 0.003), yet they had an increased number of injuries (Pearsons coefficient −0.119; p = 0.007). Conclusions: The current study found significant relationships between pes planus and number of injuries sustained over a 4-year period at West Point. While women were found to have smaller feet and lesser degrees of pes planus, they sustained more injuries than men.

Treatment and survival of osseous renal cell carcinoma metastases

Renal cell carcinoma is the seventh leading cause of cancer deaths. Studies have shown patients with solitary osseous metastases have a better prognosis; however, methods of resection are not well defined. The purpose of this study was to review factors associated with survival and assess the impact of wide versus intralesional management on function and disease‐specific outcomes in patients with renal cell carcinoma metastases.

A comparison of two microbial detection methods used in aseptic processing of musculoskeletal allograft tissues.

Tissues from 78 musculoskeletal donors were concurrently tested for microorganisms using both a swab and liquid culture method. An aggregate total of 20 organisms were detected by both methods. The swab detected 4/20 organisms while the liquid culture detected 18/20 organisms. The swab method yielded sensitivity and negative predictive values of 20 and 92.3%, respectively. Comparatively, the liquid culture displayed a sensitivity of 90% and a negative predictive value of 99%. These results clearly demonstrate that the liquid culture method is superior to swab cultures in microbial detection. Additional studies are necessary to determine the optimal culture conditions for different types of tissues when utilizing the liquid culture method.

Discrete combat models: investigating the solutions to discrete forms of Lanchester's combat models

Lanchester’s equations and their solutions, as continuous differential equations, have been studied for years. This article introduces a new approach with the use of the discrete form of Lanchester’s equations, using dynamical systems or difference equations. It begins with Lanchester’s square law and develops a generalized analytical solution for the discrete model that can be built by knowing only the kill rates and the initial force sizes of the combatants. It then forms the condition of parity (a draw) to develop a simple relationship of these variables to determine who wins the engagement. This article illustrates these models and their solutions using historic combat examples. It also illustrates that current counter-insurgency combat models can be built and solved using various forms of difference equations.

CORE MATHEMATICS AT THE UNITED STATES MILITARY ACADEMY: LEADING INTO THE 21st CENTURY

ABSTRACT The Department of Mathematical Sciences at the United States Military Academy is prepared to lead the young minds of America into the 21st century with a bold and innovative curriculum coupled with student and faculty growth models and interdisciplinary lively applications. In 1990, the mathematics department began its first iteration of their “7 into 4” core curriculum. Each year improvements have been incorporated into the core mathematics program. In 1992, interdisciplinary applications appeared in the core program as an opportunity to communicate and work with the academic disciplines. Our core curriculum is tied together both vertically and horizontally with threads. These threads tie together both the content within each course as well as among all the courses. Student attitudes are measured through course surveys as we attempt to develop “life long learners”. Student performance is measured or calibrated throughout their four years.

Teaching the applications of optimisation in game theory's zero sum and non-zero sum games

We apply linear and non-linear programming to find the solutions for Nash equilibriums and Nash arbitration in game theory problems. Linear programming was shown as a viable method for solving mixed strategy zero-sum games. We review this methodology and suggest a class of zero-sum game theory problems that are well suited for linear programming. We applied this theory of linear programming to non-zero sum games. We suggest and apply a separate formulation for a maximising linear programming problem for each player. We move on the Nash arbitration method and remodel this problem as a non-linear optimisation problem. We take the games payoff matrix and we form a convex polygon. Having found the status quo point (x*, y*), we maximise the product (x-x*)(y-y*) over the convex polygon using KTC non-linear optimisation techniques. The results give additional insights into game theory analysis.

Ranking terrorist targets using a hybrid AHP-TOPSIS methodology

We present a methodology and an example of preparing an order of merit list to rank terrorist targets based upon decision-maker weights. We used an old terrorist data set as our base data to keep the information unclassified. This data is used to demonstrate this methodology. We perform numerical iterative criteria weight sensitivity analysis to show the effects on the model’s outputs in changes in the weights. We identify the critical criterion.

Using data envelopment analysis and the analytical hierarchy process to find node influences in a social network

In a social network analysis the output provided includes many measures and metrics. For each of these measures and metrics, the output provides the ability to obtain a rank ordering of the nodes in terms of these measures. We might use this information in decision making concerning disrupting or deceiving a given network. All is fine when all the measures indicate the same node as the key or influential node. What happens when the measures indicate different key nodes? Our goal in this paper is to explore two methodologies to identify the key players or nodes in a given network. We apply two procedures to analyze these outputs to find the most influential nodes as a function of the decision makers’ inputs. We use data envelopment analysis as a method to optimize efficiency of the nodes over all criteria and use the analytical hierarchy process (AHP) as a process to consider both subjective and objectives inputs through pairwise comparison matrices. We illustrate our results using two common networks from the literature: the kite network and the information flow network. We discuss some basic sensitivity analysis that can be applied to the methods. We find the AHP method as the most flexible method to weight the criterion based upon the decision makers’ inputs or the topology of the network.