A solution to the generalized birthday problem with application to allozyme screening for cell culture contamination

This paper gives the probability that no common allozyme signature is found among n randomly selected cell culture lines when the s mutually exclusive and exhaustive signatures have arbitrary known probabilities. This result is useful in detecting cell culture contamination by a single cell line. This problem is a generalization of the classic problem of finding the probability of no common birthday among n individuals when it is assumed that each individual has a chance 1/s = 1/365 of a birthday on a given day. Both an exact recursive solution and an approximate solution are given for the general problem.

Asymptotic form for random walk survival probabilities on three-dimensional lattices with traps

The problem of calculating statistics of time-to-trapping of a random walker on a trap-filled lattice is of interest in solid state physics. Several authors have suggested approximate methods for calculating the average survival probabilities. Here, an exact asymptotic form for the probability that an n step random walk visits S(n) distinct sites is used to ascertain the validity of a simple approximation suggested by Rosenstock. For trap concentrations below 0.05, the relative error in using Rosenstock's approximation is less than 10%.

Region visited by a spherical Brownian particle in the presence of an absorbing boundary

We calculate the time dependence of the average volume of a Wiener sausage in the presence of an absorbing boundary in one and three dimensions. In one dimension it is shown that the presence of an absorbing point reduces the time dependence of the average span from being proportional to sqrt[t] in an unbounded space, to being proportional to ln(t) at long times. In three dimensions the average volume increases as sqrt[t] at long times rather than being proportional to t as in free space.

Primary synovial sarcoma of the kidney: a case report with literature review

We describe a case of primary renal synovial sarcoma (SS) in a 48-year-old man. The patient presented with hematuria and was found to have a large tumor in his left kidney on computed tomography scan. Histology revealed a highly cellular spindle cell neoplasm with minimal pleomorphism. The major differential diagnoses included leiomyosarcoma, hemangiopericytoma, and SS. The presence of focal areas with a biphasic pattern, uniformly positive immunostain for bcl-2, focally positive immunostains for epithelial membrane antigen and cytokeratin, and negative immunostains for CD-34, smooth muscle actin and S-100 established the diagnosis. This was subsequently confirmed by molecular testing for t(X;18) translocation. Since the existence of primary SS in the kidney was first suggested in 1999, to the best of our knowledge a total of 19 cases including the present case have been reported to date. Although primary renal SS is rare, these findings indicate that it should be included in the differential diagnosis of spindle cell tumors of the kidney.

Occupancy of a single site by many random walkers

We consider an infinite number of noninteracting lattice random walkers with the goal of determining statistical properties of the time, out of a total time T, that a single site has been occupied by n random walkers. Initially the random walkers are assumed uniformly distributed on the lattice except for the target site at the origin, which is unoccupied. The random-walk model is taken to be a continuous-time random walk and the pausing-time density at the target site is allowed to differ from the pausing-time density at other sites. We calculate the dependence of the mean time of occupancy by n random walkers as a function of n and the observation time T. We also find the variance for the cumulative time during which the site is unoccupied. The large-T behavior of the variance differs according as the random walk is transient or recurrent. It is shown that the variance is proportional to T at large T in three or more dimensions, it is proportional to T(3/2) in one dimension and to T ln T in two dimensions.

Calcium kinetics in children with osteogenesis imperfecta type III and IV: pre- and post-growth hormone therapy

Children with osteogenesis imperfecta (OI) type III and type IV were studied using a (42)Ca stable isotope technique. Serum dilution kinetics of (42)Ca were studied pre- and post-growth hormone (GH) treatment in 9 OI III (age range 5-9 years) and 8 OI IV patients (age range 5-12 years). Each subject was studied twice: at baseline and following GH therapy (range 1-1.5 years). Isotopic enrichments of (42)Ca were followed over 7 days using thermal ionization mass spectrometry. A binding site model, which describes reversible and irreversible binding of calcium (Ca) ions to postulated short- and long-term binding sites in bone, was used to analyze the kinetic data. In type III patients, GH treatment (1) increased the fraction of short-term binding sites, theta (0.777 +/- 0.112 versus 0.877 +/- 0.05, respectively; P = 0.034); (2) increased the apparent half-life of a Ca ion attached to the long-term binding site by 76% (P = 0. 009); (3) although not statistically significant (P = 0.098), a trend toward an increased growth rate was observed with increasing change in theta (Deltatheta); (4) patients experienced a 75% increase in growth rate during the first 6 months of treatment. In type IV patients, GH treatment increased the apparent half-life of a Ca ion attached to the long-term binding site by 83% (P = 0.048), however, no trend toward an increased growth rate was observed with increasing Deltatheta in these patients. These significant changes in Ca binding to bone may influence growth in type III patients.

Descriptive parameter for photon trajectories in a turbid medium

In many applications of laser techniques for diagnostic or therapeutic purposes it is necessary to be able to characterize photon trajectories to know which parts of the tissue are being interrogated. In this paper, we consider the cw reflectance experiment on a semi-infinite medium with uniform optical parameters and having a planar interface. The analysis is carried out in terms of a continuous-time random walk and the relation between the occupancy of a plane parallel to the surface to the maximum depth reached by the random walker is studied. The first moment of the ratio of average depth to the average maximum depth yields information about the volume of tissue interrogated as well as giving some indication of the region of tissue that gets the most light. We have also calculated the standard deviation of this random variable. It is not large enough to qualitatively affect information contained in the first moment.

Radical prostatectomy versus brachytherapy for early-stage prostate cancer

BACKGROUND AND PURPOSE

The considerations in choosing a treatment for prostate cancer are potential for cure, acute toxicity, long-term morbidity, quality of life, and direct and indirect costs. The classic options are radical prostatectomy, external-beam radiation, and watchful waiting. During the last decade, technological advances have fostered another: brachytherapy.

METHODS

This article compares brachytherapy and radical prostatectomy in terms of cancer control, complications, and cost using series from medical centers that have pioneered and advocated particular procedures.

RESULTS

In the surgical series from Johns Hopkins, the 7-year success rate (no PSA >0.2 ng/mL) of anatomic radical prostatectomy was 97.8% in patients with stage T(2c) or lower disease and a Gleason score of < or =6. In the brachytherapy series from Seattle, the 7-year success rate (PSA < or =0.5 ng/mL) was 79%. Postoperatively, 68% of the patients who were potent preoperatively maintained erectile function, and 92% were fully continent. Urethral toxicity is slightly more common in patients treated by brachytherapy, but in the authors' series, no patient remained incontinent after 6 months. Some patients became impotent during follow-up. The cost of brachytherapy ($16,200) is less than that of ($27,000), although the difference may be reduced by the use of neoadjuvant hormonal therapy with the former.

CONCLUSION

Patients receiving brachytherapy appear to have a slightly higher rate of disease progression. The side effects generally are acceptable and may be less severe than those of surgery. Further follow-up data are needed to define the roles of these two treatments for early-stage prostate cancer.

Optimal time spacings for T2 measurements: monoexponential and biexponential systems

We have developed an optimal design strategy, i.e. a choice of times at which the magnetization should be measured, in spin-echo measurements, when the number of measurements is fixed in advance. Results are given for samples whose relaxation is described by either an exponential or biexponential decay curve. The analysis is based on having an initial estimate of the ranges in which the relaxation times are likely to lie. The optimal design consists of a set of easily parameterized non-uniformly spaced measurement times, as opposed to present implementation of spin-echo experiments. Analysis of the biexponential case shows that an order of magnitude greater signal-to-noise is required to achieve T2 estimates of comparable precision to monoexponential measurements with the same number of data points. The optimal designs lead to an improved ability to discriminate between two relatively similar relaxation times.

Asymmetry of protein peaks in capillary zone electrophoresis: effect of starting zone length and presence of polymer

The asymmetry of R-phycoerythrin (M(r) = 240,000) peaks in capillary zone electrophoresis measured as In[(tm-t1)/(t2-tm)], where tm, t1 and t2 are migration times of the peak mode and at the intersection of the peak width at half-height with the ascending and descending limbs, respectively, was found to undergo a transition from negative to positive values with increasing starting zone length. The transition is compatible with a mathematical model of peak dispersion which assumes that an interaction of protein with the capillary walls governs the evolution of the peak during capillary zone electrophoresis. Models assuming a final peak shape defined solely by longitudinal diffusion, or by a heterogeneity with regard to mobility or by a conductivity difference between analyte zone and background electrolyte, have failed to give rise to a change in the sign of peak asymmetry when the starting zone length is varied. The presence of polyethylene glycol in the buffer within a concentration range up to 4% does not appreciably affect the peak asymmetry regardless of whether the concentration regime is dilute or semi-dilute. Above 4% of polyethylene glycol, the asymmetry becomes nearly independent of starting zone length, and progressively negative with increasing polymer concentration. The concentration range at which the transition from negative to positive asymmetry disappears coincides with that at which the average mesh size of the polymer network falls below the size of the protein.

Statistical properties of the penetration of photons into a semi-infinite turbid medium: a random-walk analysis

Statistical properties of the expected amount of time spent by a photon at different depths of a semi-infinite turbid medium are derived with formalism based on the continuous-time random walk. The formalism is applied to the study of both cw and time-gated experiments. Earlier analytical results relating to cw experiments are reproduced with a single approximation, rather than the more complicated approach used in earlier research based on the discrete-time random walk. The distribution of the occupancy of different depths in a time-gated experiment is found to have a convenient scaling form.

Lymphoceles after laparoscopic pelvic node dissection

OBJECTIVE

Lymphocele formation has been infrequently reported as a complication of laparoscopic pelvic lymph node dissection (LPLND). We determined the incidence of clinical and subclinical lymphocele formation in patients undergoing transperitoneal LPLND.

METHODS

Charts and radiological records of 111 patients undergoing transperitoneal LPLND at this institution between January 1991 and December 1995 were reviewed to determine the incidence of lymphocele formation.

RESULTS

Of 111 patients undergoing LPLND, 12.6% had positive lymph nodes and received hormonal therapy. Radical retropubic (12) or perineal (28) prostatectomy was performed either simultaneously or within 2 weeks in 41% of the node-negative patients. Radiation therapy was the treatment modality in the remaining node negative patients (N = 57). Twenty-three patients undergoing radiation therapy had preplanning pelvic computed tomography (CT) scans 2 to 16 weeks (mean 8.2 weeks) after LPLND. These were reviewed by a single radiologist to determine the presence of subclinical lymphoceles. Seven patients (30.4%) had lymphoceles of varying sizes (3 large and 4 small). Although most were identified on CT scans 4 weeks after the procedure, two were identified on scans 12 and 16 weeks after the procedure (mean 6.5 weeks). None of these patients developed symptoms referable to or had treatment for the lymphocele during a 2 to 37 month follow-up (mean 20 months). Only two patients (3.5%) undergoing LPLND as an isolated procedure had clinical evidence of lymphocele formation, both of which were subsequently confirmed with CT scans (1 large, 1 small). One was treated with CT-guided drainage and sclerosis and the other resolved spontaneously.

CONCLUSION

The clinical incidence of lymphocele formation following LPLND remains relatively low. Only a portion of these patients requires intervention. Subclinical lymphoceles, as detected on follow-up CT scans, occur with a much greater frequency. These seldom become symptomatic requiring treatment. Rather, they appear to resolve spontaneously. Nevertheless, clinical suspicion should remain high in order to detect and properly treat symptomatic lymphoceles when they occur.

Some properties of a measure of resolution in gel electrophoresis and capillary zone electrophoresis

The most commonly used measure of resolution for chromatographic and electrophoretic separations does not take into account the possibility of there being different amounts of each of the molecular species. A modification of a measure of resolution recently suggested by Aldroubi and Garner (BioTechniques 1992, 13, 620-624) can incorporate this effect explicitly. Their criterion for resolution is based on the time to observe a valley of specified magnitude separating two peaks. We examine how this measure depends on different physically relevant parameters that characterize the system.

Protein band spreading in capillary zone electrophoresis effects of sample zone length and presence of polymer

It is commonly accepted that intra-column zone dispersion in CZE rests on multiple mechanisms, viz. diffusion, interaction of analyte with the capillary walls, Joule heat and conductivity differences between sample zone and the surrounding buffer. The most important extra-column contributor to bandwidth is thought to be the starting zone width. The present study shows that the length of the starting zone above 10 mm is linearly related to the bandwidth of R-phycoerythrin (M(r) 290.10(3)). Below that length, bandwidth demonstrates a plateau preceded by a slight rise. Within the 'plateau range', the ratio of bandwidth to effective capillary length is close to constant while it is independent of electric field strength in the range of 37 to 370 V cm-1 and of protein concentration in the range of 0.1 to 1000 micrograms ml-1. The experimental observations support the notion that the analyte-wall interaction is the determining source of intra-column zone dispersion. A slight rise observed at initial zone lengths of less than 2 mm was accounted for by a diffusion model taking into account a non-local initial concentration of analyte. The presence of polyethyleneglycol in the buffer within a concentration range up to 6% does not affect bandwidth. Above that concentration, the level of constant bandwidth is raised.

Effects of multiple-passage probabilities on fluorescent signals from biological media

By applying a random-walk model for photon migration, we find an exact expression for fluorescent signals emitted from a homogeneous, optically turbid medium containing a single fluorescent mass. In contrast to diffusion-theory-based models, our analysis accounts for multiple photon passages through the fluorophore sites and allows for a variable degree of fluorescent absorptivity. We particularly discuss effects on the amplitudes and phase shifts of frequency-domain fluorescent signals.

Effects of time delay in cardiac blood flow measurements by bolus H2(15)O

Myocardial blood flow (rMBF) can be measured using dynamic positron emission tomography (PET) and bolus injection of H2(15)O. Recent studies indicate that large errors in the estimates of flow (f) can be produced by time shifts between the true arterial input function and the measured input function [A(t)]. We have investigated this phenomenon further using A(t) derived from patient data, and using simulated myocardial time activity curves [M(t)]. We found that with judicious choice of scan parameters and region of interest (ROI) placement, these errors can be greatly reduced. In particular, when A(t) is measured from the left ventricular (LV) cavity, the bias in f is negligible over a wide range of circumstances. However, when A(t) is not measured from the LV cavity, the bias in flow can be large for short scans (< 2 min) or low flow values (f < 0.4 ml/g/min). We show that the bias is primarily due to the spill-over term in the model that is most commonly used to compute rMBF and suggest some correction methods. We conclude that it is possible to avoid errors in estimates of flow due to time delay.

Prostate cancer screening and management

Several other newer therapeutic modalities are being investigated to determine their potential role in the treatment of prostate cancer. Cryotherapy, microwave hyperthermia, laser therapy, and high-intensity focused ultrasound have all been introduced in recent years. Each of these techniques is based on a different principle, yet they all attempt to kill prostate cancer cells in a minimally invasive manner. Insufficient follow-up data are available to allow strong recommendations regarding these treatments.

Urinary and tissue levels of scatter factor in transitional cell carcinoma of bladder

PURPOSE

We previously reported increased titers of scatter factor in urine of 20 patients with transitional cell carcinoma of the bladder compared to noncancer and cancer control groups. Scatter factor was also found in bladder tumor extracts but the number of samples examined was too small for detailed analysis. We report a followup study of larger numbers of patients with transitional cell carcinoma and controls.

MATERIALS AND METHODS

The scatter factor content of urine samples and bladder tissue extracts was measured by enzyme-linked immunosorbent assay. Values were normalized per milligram creatinine or tissue protein. Statistical analysis was performed using the Mann-Whitney U test or, for multiple comparisons, the Kruskal-Wallis H test.

RESULTS

Patients with transitional cell carcinoma of the bladder (52) had higher urinary scatter factor titers than did 24 normal subjects (p < 0.001) or 14 with benign prostatic hypertrophy (p < 0.001), 49 with prostate cancer (p < 0.001) and 13 with other genitourinary tract cancers (p < 0.01). Transitional cell carcinoma cases with clinicopathological evidence of disease had greater urinary scatter factor levels than those with no evidence of disease at urine sampling (p < 0.01). However, patients with transitional cell carcinomas in remission still had much greater urinary scatter factors than did normal subjects (p < 0.001). In contrast, patients with active prostate cancer had urinary scatter factor levels similar to those in remission. Patients with muscle invasive or high grade transitional cell carcinomas tended to have higher urinary scatter factor levels than patients with nonmuscle invasive or low grade tumors, respectively, but the differences were not significant. Greater levels of scatter factor were present in tissue extracts of muscle invasive transitional cell carcinomas than in nonmuscle invasive tumors (p < 0.001) or nontumor tissue (p < 0.02). Invasion was more closely related to tissue scatter factor content than tumor grade, since high grade noninvasive transitional cell carcinomas had a scatter factor content similar to that of low grade noninvasive transitional cell carcinomas.

CONCLUSIONS

These studies suggest that scatter factor may be a marker of bladder cancer, urinary scatter factor titers tend to reflect disease activity and particularly high tissue titers of scatter factor are found in muscle invasive cancers. A larger prospective study will be necessary to determine the clinical significance of elevated scatter factor titers in transitional cell carcinoma of the bladder.

Calcium kinetics in glycogen storage disease type 1a

Glycogen storage disease type 1a (Von Gierke's disease) is one of the more common glycogen storage diseases (GSD). GSD 1a patients can have severe idiopathic osteopenia, often beginning at a young age. Since calcium tracer studies offer a sensitive probe of the bone microenvironment and of calcium deposition, kinetics might be disturbed in patients with GSD 1a. Plasma dilution kinetics obtained using the stable isotope 42Ca are shown in this paper to be quite different between GSD 1a patients and age-matched controls. Comparison of kinetic parameters in these two populations is made using a new binding site model for describing calcium dynamics at the plasma-bone interface. This model describes reversible binding of calcium ions to postulated short-term and long-term sites by a retention probability density function psi (t). Using this analysis, adult GSD subjects exhibited a significant decrease (P = 0.023) in the apparent half-life of a calcium ion on the longer-term site compared with controls. The general theory of calcium tracer dilution kinetics is then discussed in terms of a new model of short-term calcium homeostasis recently proposed by Bronner and Stein [5].

Interpretation of electrophoretic band shapes by a partition chromatographic model

Measurements of the shape of electrophoretic bands of phycoerythrin and conalbumin have been made at regular intervals during migration in agarose gels. Analysis of the peak shapes suggests the existence of a significant degree of asymmetry. This is to be contrasted with the symmetry around the peak associated with the generally assumed Gaussian band. The degree of asymmetry of the bands decreased as a function of time and increased with agarose concentration. A similar experiment on DNA indicated constancy of the degree of asymmetry as a function of time. These results can be interpreted as, but do not prove the validity of, a nonlocal diffusion equation which generalizes a theory originally put forth by Giddings and Eyring (J. Am. Chem. Soc. 1955, 59, 416-420). The results may be significant in framing a measure of the resolvability of electrophoretic peaks.

Fever following intracavitary bacillus Calmette-Guerin therapy for upper tract transitional cell carcinoma

PURPOSE

We attempted to identify the source of fever during intracavitary upper tract instillation of bacillus Calmette-Guerin (BCG).

MATERIALS AND METHODS

Of 34 patients who had previously undergone percutaneous resection of upper tract transitional cell carcinoma 18 received weekly intracavitary BCG through the nephrostomy tubes for 6 consecutive weeks. After treatment 6 all patients underwent nephroscopy and biopsy, and all cases were retrospectively reviewed. Parameters analyzed were BCG related symptoms, maximum temperature during treatment, maximum renal pelvic pressure during treatment, culture results, chest x-ray findings, pretreatment serum creatinine concentration, serum liver enzyme values, untoward events and treatments performed for BCG related complications.

RESULTS

No obvious pattern in appearance of fever occurred. During 88 treatment episodes evaluated there were 14 temperature elevations to more than 100F in 7 patients (39%). Positive urine cultures were associated with fever in only 4 cases and none was positive for Mycobacterium. There was no correlation between greater renal pelvic pressures and fever. All chest radiographs and serum creatinine levels were unchanged, and liver enzymes were normal in all but 1 patient. Two patients had prolonged fever with elevations to greater than 104F following treatment: 1 died in a motor vehicle accident and 1 died after the third BCG infusion led to overwhelming sepsis. No source of fever was identified in either patient.

CONCLUSIONS

Patients with low grade fever coincident with upper tract BCG may be treated conservatively simply by withholding the infusion. Fever greater than 103F should be considered an emergency condition with high potential for mortality. Immediate and aggressive attempts at identifying a source along with institution of antituberculous therapy are priorities.

Optimization of magnetization transfer experiments to measure first-order rate constants and spin-lattice relaxation times

A recent analysis of the optimization of magnetization transfer experiments to estimate first-order rate constants is extended to the design of experiments for measuring these constants and T1 when both parameters are initially unknown. When the number of measurement times is fixed, an optimal design will consist of a set of measurement times which ensures that the precision of the estimates of the combination of k and T1 is as small as possible in a worst-case scenario. Simple expressions are given for the parameters that characterize the optimal design.

Absorptivity contrast in transillumination imaging of tissue abnormalities

We calculate the time-resolved flux of photons transmitted across an optically turbid slab containing a partially absorbing inclusion. An analytical expression is obtained for the flux at a detector positioned opposite a point source (at a distance equal to the thickness of the slab) when the center of the inclusion lies on the line connecting those points. The calculation employs a discrete-time lattice random-walk model of photon transport. The resulting expression is used to assess the affects of time resolution on the detectability of the inclusion.

A model of bladder tumor xenografts in the nude rat

PURPOSE

An in vivo tumor model for the study of human urothelial carcinoma is desirable. Orthotopic xenografts are useful in order to better approximate human tumor cell behavior in situ. A prior model has been described in the nude mouse. However, its small bladder size limits both histologic characterization and the application of intravesical therapeutics. In the absence of preirradiation, orthotopic xenografts of human transitional cell carcinoma in the nude rat has not been previously reported.

MATERIALS AND METHODS

Nude rats 2 to 4 weeks of age were inoculated with 1-5 x 10(6) cells of RT4 (well differentiated papillary human bladder tumor cell line). Inoculation was performed via open cystotomy. Techniques of mucosal injury including acid treatment and cautery were explored in an effort to optimize tumor implantation and growth. Animals were sacrificed at varying intervals and histologic assessment was performed.

RESULTS

The overall rate of tumor implantation and growth was 93.4% (57 of 61). Tumors reliably grew within the muscularis and mucosal growth was seen as well. Intramuscular tumor growth was less differentiated and had a higher fraction of mitotic cells than mucosal tumor. Tumor growth was consistently seen as early as 2 weeks after inoculation which facilitates experimental trials. Distant metastasis was not observed. Mucosal injury did not increase the rate of tumor implantation.

CONCLUSION

This model is highly reproducible and will prove useful in the further study of bladder cancer progression as well as in the development of therapeutic modalities for both superficial and muscle invasive bladder carcinoma.

Percutaneous management of transitional cell carcinoma of the renal collecting system: 9-year experience

PURPOSE

We establish the effectiveness of percutaneous resection of transitional cell carcinomas of the renal collecting system.

MATERIALS AND METHODS

A retrospective analysis was done of 36 kidneys treated during a 9-year period. Adjunctive therapy with bacillus Calmette-Guerin was given in 19 cases.

RESULTS

Of 36 kidneys 6 were treated by immediate nephroureterectomy for aggressive disease, leaving 30 units treated by a complete course. The recurrence rate was 33%, which varied with histology as specific recurrence rates for grades 1 to 3 tumors (18%, 33% and 50%, respectively). The only cancer related mortalities occurred with grade 3 tumors. These tumors also had a higher incidence of understanding and vascular complications. Bacillus Calmette-Guerin therapy showed no significant improvement in survival.

CONCLUSIONS

With vigilant followup, percutaneous management of transitional cell carcinoma of the renal collecting system is an acceptable alternative to nephroureterectomy in patients with grade 1 disease, grade 2 disease who are at risk for renal insufficiency and medical contraindications to a major open operation.