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Correctness of local probability in graphical models with loops.

Graphical models, such as Bayesian networks and Markov networks, represent joint distributions over a set of variables by means of a graph. When the graph is singly connected, local propagation rules of the sort proposed by Pearl (1988) are guaranteed to converge to the correct posterior probabilities. Recently a number of researchers have empirically demonstrated good performance of these same local propagation schemes on graphs with loops, but a theoretical understanding of this performance has yet to be achieved. For graphical models with a single loop, we derive an analytical relationship between the probabilities computed using local propagation and the correct marginals. Using this relationship we show a category of graphical models with loops for which local propagation gives rise to provably optimal maximum a posteriori assignments (although the computed marginals will be incorrect). We also show how nodes can use local information in the messages they receive in order to correct their computed marginals. We discuss how these results can be extended to graphical models with multiple loops and show simulation results suggesting that some properties of propagation on single-loop graphs may hold for a larger class of graphs. Specifically we discuss the implication of our results for understanding a class of recently proposed error-correcting codes known as turbo codes.

Bayes Theorem↗

A quantitative analysis of secondary RNA structure using domination based parameters on trees.

BACKGROUND: It has become increasingly apparent that a comprehensive database of RNA motifs is essential in order to achieve new goals in genomic and proteomic research. Secondary RNA structures have frequently been represented by various modeling methods as graph-theoretic trees. Using graph theory as a modeling tool allows the vast resources of graphical invariants to be utilized to numerically identify secondary RNA motifs. The domination number of a graph is a graphical invariant that is sensitive to even a slight change in the structure of a tree. The invariants selected in this study are variations of the domination number of a graph. These graphical invariants are partitioned into two classes, and we define two parameters based on each of these classes. These parameters are calculated for all small order trees and a statistical analysis of the resulting data is conducted to determine if the values of these parameters can be utilized to identify which trees of orders seven and eight are RNA-like in structure. RESULTS: The statistical analysis shows that the domination based parameters correctly distinguish between the trees that represent native structures and those that are not likely candidates to represent RNA. Some of the trees previously identified as candidate structures are found to be "very" RNA like, while others are not, thereby refining the space of structures likely to be found as representing secondary RNA structure. CONCLUSION: Search algorithms are available that mine nucleotide sequence databases. However, the number of motifs identified can be quite large, making a further search for similar motif computationally difficult. Much of the work in the bioinformatics arena is toward the development of better algorithms to address the computational problem. This work, on the other hand, uses mathematical descriptors to more clearly characterize the RNA motifs and thereby reduce the corresponding search space. These preliminary findings demonstrate that graph-theoretic quantifiers utilized in fields such as computer network design hold significant promise as an added tool for genomics and proteomics.

Algorithms↗

Divergent evolution of a structural proteome: phenomenological models.

We develop models of the divergent evolution of genomes; the elementary object of sequence dynamics is the protein structural domain. To identify patterns of organization that reflect mechanisms of evolution, we consider the individual genomes of many procaryote species, studying the arrangement of protein structural domains in the space of all polypeptide structures. We view the network of structural similarities as a graph, called the organismal Protein Domain Universe Graph (oPDUG); vertices represent types of structural domains and edges represent strong structural similarity. As observed before, each oPDUG is a highly nonrandom graph, as evidenced in the vertex degree distribution, which resembles a Pareto law (which has a power-law asymptotic). To explain this and other peculiar properties of the oPDUGs, we construct an evolving-graph model for the long-timescale evolutionary dynamics of oPDUGs, containing only divergent mechanisms of domain discovery. The model generates degree distributions (resembling Pareto laws) and clustering-coefficient distributions that are characteristic of the oPDUGs. In the infinite-graph limit, we analytically compute the exponent for specific biological parameters, as well as the complete phase diagram of the model, finding two distinct regimes of domain innovation dynamics. Thus, divergent evolutionary dynamics quantitatively explains the nonrandom organization of oPDUGs.

Bacterial Proteins↗

Symmetry properties of tetraammine platinum(II) with C2v and C4v point groups.

Let G be a weighted graph with adjacency matrix A=[a(ij)]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[d(ij)], where for i not = j, d(ij) is the Euclidean distance between the nuclei i and j. In this matrix d(ii) can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C2v and C4v point groups.

Algorithms↗

[Craniospinal radiotherapy in combined therapy of medulloblastoma in children and adolescents].

PURPOSE: The aim of this study was: 1. to evaluate treatment results of combined therapy (surgery, postoperative craniospinal radiotherapy with or without chemotherapy) and 2. to assess factors affecting prognosis (extend of tumor removal, involvement of the brain stem, extent of disease, postoperative meningitis, shunt placement, age, sex and time interval from surgery to start of postoperative radiotherapy). PATIENTS AND METHODS: During the period 1986-1996, 78 patients with medulloblastoma, aged 1-22 years (median 8.6 years), were treated with combined modality therapy and 72 of them were evaluable for the study endpoints. Entry criteria were histologically proven diagnosis, age under 22 years, and no history of previous malignant disease. The main characteristics of the group are shown in Table 1. Twenty-nine patients (37.2%) have total, 8 (10.3%) near total and 41 (52.5%) partial removal. Seventy-two of 78 patients were treated with curative intent and received postoperative craniospinal irradiation. Radiotherapy started 13-285 days after surgery (median 36 days). Only 13 patients started radiotherapy after 60 days following surgery. Adjuvant chemotherapy was applied in 63 (80.7%) patients. The majority of them (46; 73%) received chemotherapy with CCNU and Vincristine. The survival rates were calculated with the Kaplan-Meier method and the differences in survival were analyzed using the Wilcoxon test and log-rank test. RESULTS: The follow-up period ranged from 1-12 years (median 3 years). Five-year overall survival (OS) was 51% and disease-free survival (DFS) 47% (Graph 1). During follow-up 32 relapses occurred. Patients having no brain stem infiltration had significantly better survival (p = 0.0023) (Graph 2). Patients with positive myelographic findings had significantly poorer survival compared to dose with negative myelographic findings (p = 0.0116). Significantly poorer survival was found in patients with meningitis developing in the postoperative period, with no patient living longer than two years (p = 0.0134) (Graph 3). By analysis of OS and DFS in relation to presence of the malignant cells in liquor, statistically significant difference, i.e. positive CSF cytology was not obtained, which was of statistical importance for survival (p = 0.8207). Neither shunt placement nor shunt type showed any impact on survival (p = 0.5307 and 0.7119, respectively). Children younger than three years had significantly poorer survival compared to those older than 16 years (p = 0.0473). Although there was a better survival rate in females than in males this was not statistically significant (p = 0.2386). The analysis results of treatment showed that significantly better survival occurred in patients in whom total or subtotal tumor removal was possible (p = 0.0022) (Graph 4). Patients who started radiotherapy within two months after surgery have better survival, but again this was not statistically significant, probably due to the small number of patients receiving delayed radiotherapy (p = 0.2231) (Graph 5). CONCLUSION: Based on this factors standard and high risk group could be defined. Combined chemotherapy should to be investigated particularly for high risk subgroup. Future research should be done to define new therapeutic modalities (gene therapy, compounds active in tumor antiangiogenesis etc).

Adolescent↗

DNA computing the Hamiltonian path problem.

The directed Hamiltonian path (DHP) problem is one of the hard computational problems for which there is no practical algorithm on a conventional computer available. Many problems, including the traveling sales person problem and the longest path problem, can be translated into the DHP problem, which implies that an algorithm for DHP can also solve all the translated problems. To study the robustness of the laboratory protocol of the pioneering DNA computing for the DHP problem performed by Leonard Adleman (1994), we investigated how the graph size, multiplicity of the Hamiltonian paths, and the size of oligonucleotides that encode the vertices would affect the laboratory procedures. We applied Adleman's protocol with 18-mer oligonucleotide per node to a graph with 8 vertices and 14 edges containing two Hamiltonian paths (Adleman used 20-mer oligonucleotides for a graph with 7 nodes, 14 edges and one Hamiltonian path). We found that depending on the graph characteristics such as the number of short cycles, the oligonucleotide size, and the hybridization conditions that used to encode the graph, the protocol should be executed with different parameters from Adleman's.

Algorithms↗

Image analysis of oronasal fistulas in cleft palate patients acquired with an intraoral camera.

The aim of this study was to examine the clinical technique of using an intraoral camera to monitor the size of residual oronasal fistulas in cleft lip-cleft palate patients, to assess its repeatability on study casts and patients, and to compare its use with other methods. Seventeen plaster study casts of cleft palate patients with oronasal fistulas obtained from a 5-year series of 160 patients were used. For the clinical study, 13 patients presenting in a clinic prospectively over a 1-year period were imaged twice by the camera. The area of each fistula on each study cast was measured in the laboratory first using a previously described graph paper and caliper technique and second with the intraoral camera. Images were imported into a computer and subjected to image enhancement and area measurement. The camera was calibrated by imaging a standard periodontal probe within the fistula area. The measurements were repeated using a double-blind technique on randomly renumbered casts to assess the repeatability of measurement of the methods. The clinical images were randomly and blindly numbered and subjected to image enhancement and processing in the same way as for the study casts. Area measurements were computed. Statistical analysis of repeatability of measurement using a paired sample t test showed no significant difference between measurements, indicating a lack of systematic error. An intraclass correlation coefficient of 0.97 for the graph paper and 0.84 for the camera method showed acceptable random error between the repeated records for each of the two methods. The graph paper method remained slightly more repeatable. The mean fistula area of the study casts between each method was not statistically different when compared with a paired samples t test (p = 0.08). The methods were compared using the limits of agreement technique, which showed clinically acceptable repeatability. The clinical study of repeated measures showed no systematic differences when subjected to a t test (p = 0.109) and little random error with an intraclass correlation coefficient of 0.98. The fistula size seen in the clinical study ranged from 18.54 to 271.55 mm. Direct measurements subsequently taken on 13 patients in the clinic without study models showed a wide variation in the size of residual fistulas presenting in a multidisciplinary clinic. It was concluded that an intraoral camera method could be used in place of the previous graph paper method and could be developed for clinical and scientific purposes. This technique may offer advantages over the graph paper method, as it facilitates easy visualization of oronasal fistulas and objective fistulas size determination and permits easy storage of data in clinical records.

Adolescent↗

Linking experimental results, biological networks and sequence analysis methods using Ontologies and Generalised Data Structures.

The structure of a closely integrated data warehouse is described that is designed to link different types and varying numbers of biological networks, sequence analysis methods and experimental results such as those coming from microarrays. The data schema is inspired by a combination of graph based methods and generalised data structures and makes use of ontologies and meta-data. The core idea is to consider and store biological networks as graphs, and to use generalised data structures (GDS) for the storage of further relevant information. This is possible because many biological networks can be stored as graphs: protein interactions, signal transduction networks, metabolic pathways, gene regulatory networks etc. Nodes in biological graphs represent entities such as promoters, proteins, genes and transcripts whereas the edges of such graphs specify how the nodes are related. The semantics of the nodes and edges are defined using ontologies of node and relation types. Besides generic attributes that most biological entities possess (name, attribute description), further information is stored using generalised data structures. By directly linking to underlying sequences (exons, introns, promoters, amino acid sequences) in a systematic way, close interoperability to sequence analysis methods can be achieved. This approach allows us to store, query and update a wide variety of biological information in a way that is semantically compact without requiring changes at the database schema level when new kinds of biological information is added. We describe how this datawarehouse is being implemented by extending the text-mining framework ONDEX to link, support and complement different bioinformatics applications and research activities such as microarray analysis, sequence analysis and modelling/simulation of biological systems. The system is developed under the GPL license and can be downloaded from http://sourceforge.net/projects/ondex/

Algorithms↗

[The effect of synchronization on estrus and pregnancy in sheep and on levels of thyroxine, triiodothyronine, 17 beta-estradiol, progesterone and cholesterol].

Knowledge of pathogenesis of sexual dysfunctions at altered thyroid activity is limited by the knowledge of multiple and ubiquitous action of its hormones throughout the organism. One of the possibilities of modulatory influence of thyroid hormones on sexual functions can be realized through the participation of thyroxine and triiodothyronine in the synthesis and metabolism of primary substrate of steroid synthesis--cholesterol. The presented work is aimed at the study of simultaneous dynamic changes of concentrations of thyroxine (T4), triiodothyronine (T3), 17 beta-estradiol (E2), progesterone (P4) and cholesterol (Chol) during synchronization of the rutting period and gravidity at parallel correlative evaluation of mutual relations of the followed parameters in ten Merino sheep in the seasonal period. Synchronization was achieved by chlorsuperlutin (Agelin--vaginal swabs, Spofa; 20 mg of chlorsuperlutin/swab) and PMSG (500 I. U./animal). Blood was sampled by means of a jugular vein puncture at the time of swab insertion (-13th day) and after three (-10th day) and seven (-7th day) following days, at the removal of swabs and application of PMSG (-3rd day), on the day of insemination (zero day), on the 7th, 14th and 17th day and in the middle of the 2nd, 3rd, 4th and 5th month of gravidity. In the phase of oestrus synchronization a significant increase of E2 concentrations on days -7 and -3 of the experiment (0.47 +/- 0.079 and 0.542 +/- 0.177 nmol.l-1 of serum, P less than 0.001; P less than 0.001) was observed compared to the E2 values on day -13 (0.084 +/- 0.036 nmol.l-1 of serum). Parallel to these observations, marked intermittent changes of T4 (Tab. I, Graph 1) were recorded with the lowest values of this parameter observed on days -10 (41.75 +/- 20.23, P less than 0.05) and -3 (50.22 +/- 18.77, P less than 0.05) and the highest on day -7 (96.77 +/- 17.51 nmol.l-1, P less than 0.01) and day zero (85.40 +/- 19.59 nmol.l-1 of serum, P less than 0.05) in comparison with the -13th day (67.22 +/- 18.29 nmol.l-1 of serum). Concentrations of P4 (Tab. I, Graph 4) declined to the lowest values on day zero observation (0.09 +/- 0.08 nmol.l-1 of serum, P less than 0.05 vs 3.40 +/- 3.61 nmol.l-1 on day -13). No significant changes of concentrations of T3 (Tab. I, Graph 2) and Chol (Tab. I, Graph 5) were observed during oestrus synchronization. During gravidity, concentrations of E2 (Tab. I Graph 3) showed an increasing trend compared to the -13th day.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

Prevention of hypovolemia-induced hypotension during hemodialysis by means of an optical reflection method.

In this study protocol we evaluate the clinical value of the continuous monitoring of blood volume (BV) during hemodialysis (HD) by means of an optical reflection method. In the course of a dialysis session the ratio between the ultrafiltration (UF) rate and the patient's refill capacity determines the extent of decrease of BV. A steep fall of BV and, moreover, a remaining absolute BV too low, cause the greater part of hemodialysis-induced complaints. During 23 standard HD sessions BV was monitored by means of the optical method. Nine of the sessions were complicated by hypotension (group H). Comparison of the mean BV graphs of group H with the graphs of non-complicated sessions (non-H) produces several differences. Most important is the fact that BV is better preserved in group non-H, a difference which is already significant during the first ninety minutes of dialysis. By making use of the shape of the monitored BV graph and HD patient, in that way, might be recognized as hypotension-prone during the first third of a dialysis session. To prevent the occurrence of hypovolemia-induced hypotension two strategies can be followed. First, the decrease of BV of a patient prone to hypotension can be triggered to the mean BV decrease according to the BV graph of the non-H group. This can be achieved by interventional methods, e.g. temporary lowering of the UF rate. However, for this intervention the development of a closed-loop circuit is required. Another possibility is to measure a patient's maximal refill capacity each hour of hemodialysis by taking advantage of the displayed BV graph.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

[Cognitive structuring by statistical graphics: effects on understanding and retention].

We investigated how displaying the same set of data using different line graphs affects comprehension and retention of the data. In line graphs, the results of two-factor experiments can be displayed and structured in different ways by locating either one or the other independent variable on the abscissa. The experiment showed that the level of measurement as well as the number of levels of each independent variable affected comprehension and retention. Comprehension of graphs and retention of the information was better, if the graph showed an independent variable on the abscissa which was measured using an interval scale rather than a nominal scale, and when there were four rather than two levels. To account for the results, we propose a process model of graph comprehension.

Adult↗

[The rolandic line: a simple baseline for the identification of the central region. An MRI study and functional validation].

INTRODUCTION: The identification of the central region--i.e. the central sulcus, the pre- and post-central gyri, the paracentral lobule--on MRI and angiographic images may be necessary prior to stereotactic procedures such as biopsies or resection of centrally located tumors, depth electrode recordings for presurgical evaluation of drug-resistant epilepsies, or radiosurgery of arteriovenous malformations. Stereotactic methods, such as the Talairach's proportional grid based on the bicommissural system, demonstrated the statistical position of the central sulcus according to the Ac-Pc, Vac and Vpc baselines. However, the course and the spatial position of this sulcus have remarkable individual differences that sometimes make the sulcus difficult to identify on serial sagittal MRI or lateral angiographic images. In order to facilitate this identification, the authors propose a new oblique baseline, the rolandic (R) line. MATERIAL AND METHODS: The stereotactic MRI and angiography of 22 patients were reviewed for this study. Eleven of these patients had stereotactic biopsies for a low-grade tumor located in the central region, while eleven others had multiple intracerebral electrodes implantation and depth EEG recording (SEEG: stereoelectroencephalography) in the presurgical evaluation of drug-resistant partial epilepsy, prior to epileptogenic cortex resection. The Ac-Pc, Vac, Vpc baselines and segments of the central sulcus were drawn from the mid-sagittal and lateral T1-weighted MRI images and reported on an individual graph. Surface and deep margins as well as axis of the central sulcus were also reported along with corpus callosum baselines as defined by Olivier et al.: horizontal plane, anterior and posterior callosal planes. The rolandic line was then traced from the graph:it joined the intersection point between the anterior callosal plane and an orthogonal line passing through the floor of the temporal fossa, and the intersection point between posterior callosal plane and an orthogonal line passing through the top of the hemisphere. The rolandic line was then superimposed on any sagittal MRI image or lateral stereotactic angiographic film. Finally, the spatial position of electrode contracts through which electrical stimulations elicited motor and/or sensory responses, either from central electrode implanted for motor fibers identification prior to stereotactic biopsies or from SEEG electrodes implanted for epileptogenic zone identification and cortical mapping, was reported on the individual graph. Angular and linear measurements were taken from the graph, between the rolandic line, the central sulcus axis, the Ac-Pc and callosal baselines, and the central sulcus limits (top, bottom, anterior and posterior margins). RESULTS: Graph measurements indicated that the rolandic line was significantly closer to the inferior part of the central sulcus than to its superior part (average distance between the line and the inferior point of the sulcus: 1.86 +/- 1.87 mm; average distance between the line and the superior point of the sulcus: 4.5 +/- 2.3 mm; p < 0.001-t test); similarly, the rolandic line was closer to the deep margin of the sulcus rather than to its superficial border (average distance between the line and the most anterior point of the sulcus: 11.43 +/- 3.16 mm; average distance between the line and the most posterior point of the sulcus: 7.95 +/- 4.14 mm; p < 0.01-t test). In 90% of the cases, the rolandic line followed the deep or middle part of the sulcus, with an average angle of 4.18 degrees +/- 2.53 degrees between the line and the sulcus axis. The spatial position of the electrode contacts that elicited motor/or sensory responses to stimulations correlated topographically well in all cases with the position of the motor and sensory fibers defined according to the central sulcus, baselines and reference to stereotactic atlases. (ABSTRACT TRUNCATED)

Adolescent↗

The hydrogen perturbation in molecular connectivity computations.

A new algorithm for the delta(v) number, the basic parameter of molecular connectivity indices, is proposed. The new algorithm, which is centered on graph concepts like complete graphs and general graphs, encodes the information of the bonded hydrogen on different atoms through a perturbation parameter that makes use of no new graph concepts. The model quality of the new algorithm is tested with 13 properties of seven different classes of compounds, as well as with composite classes of compounds with the same property and with composite properties of the same class of compounds. Chosen properties and classes of compounds display different percentage of bonded hydrogen atoms, which allow a checking of the importance of this parameter. A comparison is drawn with previous results with zero contribution for the hydrogen perturbation as well as among results obtained by changing the number of compounds of a property but keeping constant the percentage of hydrogen atoms. Results underline the importance of the property as well as the importance of the number of compounds in determining the level of the hydrogen perturbation. Molecular connectivity terms are in some cases more critical than the combination of indices in detecting the perturbation introduced by the hydrogen atoms.

Journal Article↗

Searching for pharmacophoric patterns in databases of three-dimensional chemical structures.

This paper provides an overview of the research that has been carried out in Sheffield over the last decade into searching techniques for databases of three-dimensional (3D) chemical structures. A 3D structure or query pattern is represented by a labelled graph, in which the nodes and the edges of the graph are used to represent atoms and the associated inter-atomic distances, respectively. The presence of a pharmacophore in each of the structures in a database can then be tested by means of a subgraph isomorphism algorithm, the computational requirements of which are minimized by the use of an initial screening procedure that eliminates the majority of the structures from the subgraph-isomorphism search. Analogous graph-based representation and searching methods can also be used with flexible 3D structures: in this case, the edges of the graphs represent inter-atomic distance ranges and a final conformational search needs to be carried out for those molecules that match the query pharmacophore in the subgraph-isomorphism search. The paper also reviews related work on the automatic identification of pharmacophoric patterns and on 3D similarity searching.

Algorithms↗

Combining functional and topological properties to identify core modules in protein interaction networks.

Advances in large-scale technologies in proteomics, such as yeast two-hybrid screening and mass spectrometry, have made it possible to generate large Protein Interaction Networks (PINs). Recent methods for identifying dense sub-graphs in such networks have been based solely on graph theoretic properties. Therefore, there is a need for an approach that will allow us to combine domain-specific knowledge with topological properties to generate functionally relevant sub-graphs from large networks. This article describes two alternative network measures for analysis of PINs, which combine functional information with topological properties of the networks. These measures, called weighted clustering coefficient and weighted average nearest-neighbors degree, use weights representing the strengths of interactions between the proteins, calculated according to their semantic similarity, which is based on the Gene Ontology terms of the proteins. We perform a global analysis of the yeast PIN by systematically comparing the weighted measures with their topological counterparts. To show the usefulness of the weighted measures, we develop an algorithm for identification of functional modules, called SWEMODE (Semantic WEights for MODule Elucidation), that identifies dense sub-graphs containing functionally similar proteins. The proposed method is based on the ranking of nodes, i.e., proteins, according to their weighted neighborhood cohesiveness. The highest ranked nodes are considered as seeds for candidate modules. The algorithm then iterates through the neighborhood of each seed protein, to identify densely connected proteins with high functional similarity, according to the chosen parameters. Using a yeast two-hybrid data set of experimentally determined protein-protein interactions, we demonstrate that SWEMODE is able to identify dense clusters containing proteins that are functionally similar. Many of the identified modules correspond to known complexes or subunits of these complexes.

Algorithms↗

Converting relative risks to absolute risks: a graphical approach.

This paper presents a graphical method for converting relative risks to absolute risks. These absolute risk estimates are a function of the patient's current age, the patient's risk of developing cancer relative to some baseline population, the age specific cancer hazard in the baseline population, and the patient's competing mortal risk from all other causes. Graphs for breast cancer morbidity in women, cardiovascular mortality in men, and lung cancer morbidity in men illustrate the method. These graphs provide the probability of developing cancer in the next twenty years given the patient's current age and relative risk. They are derived under the proportional hazards model. A graph for lung cancer in men that uses a plausible exponential hazards model is also provided. The paper illustrates the importance of competing mortal hazard from other causes on absolute cancer risk. The strengths and weaknesses of this method are discussed. The graphs presented in this paper may be used as an aid in clinical decision making and in patient counselling.

Adult↗

Cumulative sum (CUSUM) analysis in the assessment of trainee competence in fetal biometry measurement.

OBJECTIVE: To determine the value of cumulative sum (CUSUM) analysis in assessing trainee proficiency in fetal biometry measurement. METHODS: Three primary healthcare doctors with no prior ultrasound training were recruited. Each trainee measured the fetal biparietal diameter (BPD), head circumference (HC), abdominal circumference (AC) and femur length (FL) on 100 consecutive pregnant women. The supervisor repeated the measurements. The CUSUM for each set of trainee measurements was calculated at a set failure rate of 10%. The point at which the graph fell below two consecutive boundary lines indicated the number of examinations required to achieve competence. RESULTS: The CUSUM graphs showed that the rate of learning measurement skills varied among the three trainees. The graph for the CUSUM series for BPD and HC measurement for all trainees fell below two consecutive boundary lines and remained there, indicating competence. The CUSUM series for AC measurement for two of the trainees indicated that competence was achieved; however, for the third trainee, while the graph fell below two consecutive boundary lines, indicating competence, it rose again, crossing two consecutive boundary lines. This indicated a loss of competence and the need for further training. FL measurements for the same trainee never fell below two consecutive boundary lines, indicating failure to achieve competence; the other two achieved competence, but failed to maintain it. CONCLUSIONS: CUSUM is a useful tool for identifying points of competence and for quantifying the duration of ultrasound training required for each trainee. It provides an early indication of performance, and highlights difficulties in individual performance.

Abdomen↗

Interaction of heart and arterial system.

We have studied the interrelation of left ventricle and arterial system in the anesthetized open-thorax cat. The ventricle was characterized by its pump function graph, relating mean ventricular pressure (Plv) and mean aortic flow (F). The pump function graph was determined by means of an artificial periphery and on a beat-to-beat basis. The periphery was characterized by relating mean aortic pressure (Pao) and mean flow. Mean aortic and mean left ventricular pressure could be related over a wide range of values by a proportionality factor Pao = a . Plv. In a series of five separate experiments a value of a = 1.72 +/- 0.14 (mean +/- SD) was found. This simplified relation allows direct comparison of apparent source resistance (i.e., slope of pump function graph), (Rs), and peripheral resistance (Rp). It was also found experimentally that total external power (w) could be calculated from mean aortic pressure and mean flow as well as from mean left ventricular pressure and mean flow (thus from the pump function graph) by w = c . Pao . F = c . a . Plv . F. The value of c = 1.16 +/- 0.12 (mean +/- SD, n = 4). Maximum external power was predicted for Rp/Rs = Pao/Plv = a. In six different cats Rp/Rs ratio in the working point (i.e., mean left ventricular pressure and mean flow when the normal periphery loaded the heart) was found to be Rp/Rs = 2.63 +/- 0.92. This value could not be shown to differ from that in the point where maximal external power was found, i.e., Rp/Rs = 1.81 +/- 0.08 (n = 6).

Animals↗