Zusammenfassung Hintergrund Ein möglicher Ansatz komplexe Muster im Tumorgewebe objektiv klassifizieren zu können, ist die mathematische Erfassung der Verteilung von Tumorzellkernen, die als geometrische Repräsentation der Krebszellen dienen, durch fraktale Dimensionen. Die Existenz, sowie die Veränderungen der fraktalen Struktur der Verteilung der Zellkerne haben wichtige Konsequenzen für eine objektive Klassifizierung der Tumoren. Weiterhin kann auch die Komplexität des Tumorwachstums in verschiedenen Karzinomen sowie die interzellulären Interaktionen im Gewebesystem dadurch verglichen werden. Ergebnisse In dieser Arbeit stellen wir eine theoretische Einführung in die fraktale Geometrie sowie in die Algorithmen, die auf der Rényi-Familie der fraktalen Dimensionen basieren, dar. Wir führen ein geometrisches Modell für die Bewertung von Prostatakarzinomgeweben ein und erklären den Zusammenhang zwischen dem geometrischen Tumormuster und den fraktalen Dimensionen der Rényi-Familie.

Tumorgrading beim Prostatakarzinom hat eine signifikante Intra- und Interobservervariabilität von ca. 40–80 %. Kombinierte geometrische und statistische Methoden könnten ein objektives Grading bieten.

Significant intra- and interobserver variability ranging between 40 and 80% is observed in tumor grading of prostate carcinoma. By combining geometric and statistical methods, an objective system of grading can be designed.The distributions of cell nuclei in two-dimensional patterns of prostate cancer classified subjectively as Gleason score 3+3, 3+4, 4+3, 4+4, 4+5, 5+4, and 5+5 were analyzed with algorithms measuring the global fractal dimensions of the R,nyi family and with the algorithm for the local connected fractal dimension (LCFD).The dimensions for global fractal capacity, information, and correlation (standard deviation) were 1.470 (045), 1.528 (046), and 1.582 (099) for homogenous Gleason grade 3 (n = 16), 1.642 (034), 1.678 (041), and 1.673 (084) for homogenous Gleason grade 4 (n=18), and 1.797 (042), 1.791 (026), and 1.854 (031) for homogenous Gleason grade 5 (n=12), respectively. The LCFD algorithm can be used to distinguish both qualitatively and quantitatively between mixed and heterogeneous patterns, such as Gleason score 3+4=7a (intermediate risk cancer) and Gleason score 4+3=7b (high-risk cancer). Sensitivity of the method is 89.3%, and specificity 84.3%.The method of fractal geometry enables both an objective and quantitative grading of prostate cancer.

BACKGROUND:A possible approach to objectively classify complex patterns in tumor tissue is a mathematical and statistical investigation of the distribution of cell nuclei as a geometric representation of cancer cells by fractal dimensions. Both the existence and changes in the fractal structure of tumor tissue have important consequences for the objective system of tumor grading. In addition, the complexity of growth in different carcinomas or their intercellular interactions can be compared to each other. RESULTS:We present a theoretical introduction into fractal geometry as well as in the computer algorithms based upon the Rényi family of fractal dimensions. Finally, a geometric model of prostate cancer is introduced and the relationship between geometric patterns of prostate tumor and the fractal dimensions of the Rényi family are explained.

Highly compacted sperm DNA in protamine toroids and a minor fraction of nucleohistones are prerequisites for the efficient transmission of the paternal genome into the oocyte at fertilization. The objective of this study was to evaluate whether protamines might serve as a prognostic factor for stallion fertility. In situ hybridization detected specific expression of P1 mRNA in the cytoplasm of stage I to VII spermatids, whereas comparable immunohistochemical stainings showed that protein expression was delayed till elongating spermatids in differentiation stages III to VIII. No staining was detectable in cryptorchid testis because of the lack of spermatids in the seminiferous tubules. Using quantitative real-time polymerase chain reaction, we identified mRNA transcripts of P1 and 2 variants of protamine- 2 (P2, P3) in ejaculated spermatozoa from 45 thoroughbred stallions. According to the mare fertility descriptor (i.e. the 'none-return-rate 28 percentage' or NRR28%), stallions were divided into three groups (i.e. high, reduced and low fertility). The P2/P1 mRNA ratio was found to be significantly reduced in the group with lower fertility (p = 0.016) and was slightly correlated with sperm concentration (correlation coefficient r = 0.263). Furthermore, morphologically abnormal sperm count negatively correlated with P2/P1 mRNA ratio, indicating that spermatozoa carrying head defects display a diminished protamine ratio (r = -0.348). Conversely, the P2/P1 ratio was positively correlated with mare fertility or NRR28% (r = 0.274). Interestingly, P3/P1 mRNA ratio remained unaltered in the investigated groups indicating that this variant plays a minor role in equine sperm chromatin compaction. Aberrant protamine transcripts content in equine spermatozoa was not associated with DNA defragmentation rate as measured by flow cytometric acridine orange test. On the basis of these results, we suggest that, similar to human, equine protamine expression constitutes a checkpoint of spermatogenesis and as a corollary the level of protamine mRNA may reflect the quality of spermatogenesis and spermatozoa's fertilizing capacity.

Prostate biopsy is currently the gold standard in the diagnosis of carcinoma of the prostate. An estimated one million prostate biopsies are performed every year in Europe. Worldwide the most frequent form is the transrectal prostate biopsy using preoperative fluoroquinolone prophylaxis. In recent years an increasing rate of infectious complications after prostate biopsy has been observed. The main causative factor is fecal fluoroquinolone-resistant bacteria. This review aims to present the current evidence regarding infectious complications after prostate biopsy and strategies to reduce symptomatic infections and urosepsis.

Die Prostatabiopsie stellt derzeit den Goldstandard der Diagnostik eines Prostatakarzinoms dar. Europaweit werden jährlich schätzungsweise 1 Mio. Prostatastanzbiopsien durchgeführt. Die weltweit am meisten angewandte Form der Prostatastanzbiopsie ist die transrektale Prostatastanzbiopsie unter Antibiotikaprophylaxe mit Fluorchinolonen. In den letzten Jahren fand sich jedoch eine zunehmende Rate an infektiösen Komplikationen nach transrektaler Prostatastanzbiopsie, deren Ursache hauptsächlich fluorchinolonresistente fäkale Bakterien sind. Die vorliegende Übersichtsarbeit soll den derzeitigen Stand der Prostatastanzbiopsie hinsichtlich infektiöser Komplikationen und Strategien zur Vermeidung symptomatischer Infektionen und der Urosepsis darstellen.

In order to analyze sympathetic nerve discharges as an entity, not as the decomposed parts, a non-linear mathematical analyzing technique including chaos and fractal theory was utilized in healthy normal subjects. Muscle sympathetic nerve activity (MSNA) was recorded using the microneurography technique during supine position and tilt up position. MSNA was integrated by the integrator and analyzed in the computer system using the non-linear mathematical analyzing technique. Time series data of the sympathetic nerve discharges were quantified in R-R interval time series data and analyzed with the Lorenz plot. Fractal dimension analysis of the MSNA was performed by the changing coarse graining level (box-counting method). Both during supine position and tilt up, MSNA showed the characteristics of fractals. After the tilt up of the bed, MSNA tone was increased and the fractal dimensions of both R-R interval and MSNA were increased. Our results suggest that MSNA tone contributed to the increases of the fractal dimension.

The objective of this pilot study was to find out whether urodynamic curves possess fractal structure, and how this structure changes along with changes of detrusor function in patients with longlasting outflow obstruction? We analyzed 25 multichannel urodynamic curves representing normal function of urinary bladder (n=10 curves) and dysfunction of detrusor muscle (n=15 curves). The curves were analyzed by Size-Frequency algorithm, R/S algorithm or Power-Spectral algorithm. All curves analyzed possess fractal structure. This structure is defined by Size-Frequency dimension, fractal dimension, and Hurst coefficient. The latter one was found to be much lower than 0.5 for all urodynamic curves representing normal filling and voiding function of the urinary bladder. The long-lasting outflow obstruction caused increment of the Hurst coefficient close up to 0.8. Long-lasting outflow obstruction changes the regular contractions of detrusor muscle into the deterministic chaotic contractions. We hypothesize that the Hurst coefficient equal to 0.5 is a limit value which allows to distinguish between cases of benign prostatic hyperplasia which can be treated pharmacologically and those which should be treated surgically.

The Gompertz function describes global dynamics of many natural processes including growth of normal and malignant tissues. On one hand, the Gompertz function defines a fractal. The fractal structure of time-space is a prerequisite condition for the coupling and Gompertzian growth. On the other hand, the Gompertz function is a probability function. Its derivative is a probability density function. Gompertzian dynamics emerges as a result of the co-existence of at least two antagonistic processes with the complex coupling of their probabilities. This dynamics implicates a coupling between time and space through a linear function of their logarithms. The spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium between regular states with predictable dynamics and chaotic states with unpredictable dynamics; a fact important for cancer chemoprevention. We conclude that the fractal-stochastic dualism is a universal natural law of biological complexity.

This paper describes a universal relationship between time and space for a nonlinear process with Gompertzian dynamics, such as growth. Gompertzian dynamics implicates a coupling between time and space. Those two categories are related to each other through a linear function of their logarithms. Moreover, we demonstrate that the spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium of regular states, that is, states with dynamics that are predictable for any time-point (e.g., sinusoidal glycolytic oscillations) and chaotic states, that is, states with dynamics that are unpredictable in time, but are characterized by certain regularities (e.g., the existence of strange attractor for any biochemical reaction). We conclude that both this equilibrium and volume of the available complementary Euclidean space determine temporal and spatial expansion of a process with Gompertzian dynamics.

The emergence of Gompertzian dynamics at the macroscopic, tissue level during growth and self-organization is determined by the existence of fractal-stochastic dualism at the microscopic level of supramolecular, cellular system. On one hand, Gompertzian dynamics results from the complex coupling of at least two antagonistic, stochastic processes at the molecular cellular level. It is shown that the Gompertz function is a probability function, its derivative is a probability density function, and the Gompertzian distribution of probability is of non-Gaussian type. On the other hand, the Gompertz function is a contraction mapping and defines fractal dynamics in time-space; a prerequisite condition for the coupling of processes. Furthermore, the Gompertz function is a solution of the operator differential equation with the Morse-like anharmonic potential. This relationship indicates that distribution of intrasystemic forces is both non-linear and asymmetric. The anharmonic potential is a measure of the intrasystemic interactions. It attains a point of the minimum (U(0), t(0)) along with a change of both complexity and connectivity during growth and self-organization. It can also be modified by certain factors, such as retinoids.

The normalized Gompertzian curve reflecting growth of experimental malignant tumors in time can be fitted by the power function y(t)=atb with the coefficient of nonlinear regression r⩾0.95, in which the exponent b is a temporal fractal dimension, (i.e., a real number), and time t is a scalar. This curve is a fractal, (i.e., fractal dimension b exists, it changes along the time scale, the Gompertzian function is a contractable mapping of the Banach space R of the real numbers, holds the Banach theorem about the fix point, and its derivative is ⩽1). This denotes that not only space occupied by the interacting cancer cells, but also local, intrasystemic time, in which tumor growth occurs, possesses fractal structure. The value of the mean temporal fractal dimension decreases along the curve approaching eventually integer values; a fact consistent with our hypothesis that the fractal structure is lost during tumor progression.