Solving inverse problems for biological models using the collage method for differential equations.

In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.

Surgical navigation for guidewire placement from intraoperative fluoroscopy in orthopaedic surgery.

Objective. Surgical guidewires are commonly used in placing fixation implants to stabilize fractures. Accurate positioning of these instruments is challenged by difficulties in 3D reckoning from 2D fluoroscopy. This work aims to enhance the accuracy and reduce exposure times by providing 3D navigation for guidewire placement from as little as two fluoroscopic images.Approach. Our approach combines machine learning-based segmentation with the geometric model of the imager to determine the 3D poses of guidewires. Instrument tips are encoded as individual keypoints, and the segmentation masks are processed to estimate the trajectory. Correspondence between detections in multiple views is established using the pre-calibrated system geometry, and the corresponding features are backprojected to obtain the 3D pose. Guidewire 3D directions were computed using both an analytical and an optimization-based method. The complete approach was evaluated in cadaveric specimens with respect to potential confounding effects from the imaging geometry and radiographic scene clutter due to other instruments.Main results. The detection network identified the guidewire tips within 2.2 mm and guidewire directions within 1.1°, in 2D detector coordinates. Feature correspondence rejected false detections, particularly in images with other instruments, to achieve 83% precision and 90% recall. Estimating the 3D direction via numerical optimization showed added robustness to guidewires aligned with the gantry rotation plane. Guidewire tips and directions were localized in 3D world coordinates with a median accuracy of 1.8 mm and 2.7°, respectively.Significance. The paper reports a new method for automatic 2D detection and 3D localization of guidewires from pairs of fluoroscopic images. Localized guidewires can be virtually overlaid on the patient's pre-operative 3D scan during the intervention. Accurate pose determination for multiple guidewires from two images offers to reduce radiation dose by minimizing the need for repeated imaging and provides quantitative feedback prior to implant placement.

[Compulsory treatment under legal uncertainty: part 1: the current legal situation on compulsory treatment of patients with psychiatric disorders incapable of consenting]. / Zwangsbehandlungen unter Rechtsunsicherheit : Teil 1: Die aktuelle Rechtslage zu Zwangsbehandlungen einwilligungsunfähiger Patienten mit psychischen Erkrankungen.

A series of recent court decisions have been concerned with the compulsory treatment of patients with mental disorders who are incapable of giving consent. This article describes the current legal situation on compulsory treatment for different cases to achieve the aim of internment, endangerment to third parties, self-endangerment, for intercurrent diseases and to achieve the aim of therapy. The verdicts contribute on the one hand to strengthen patient autonomy against governmental or medical paternalism. On the other hand the verdicts have effected a substantial legal uncertainty with the undesired indirect consequence that fixation will probably be used more often.

[Compulsory treatment under legal uncertainty: part 2: consequences of legal uncertainty in clinical practice - suggestions for improvement]. / Zwangsbehandlungen unter Rechtsunsicherheit : Teil 2: Folgen der Rechtsunsicherheit in der klinischen Praxis - Vorschläge zur Verbesserung.

The current legal uncertainty on compulsory treatment of mentally ill patient incapable of giving consent favors the practice of defensive treatment, such as the increased use of isolation and fixation instead of medication. Such a stance runs the risk of acute or chronic health damage for patients. The dissent between legal practitioners and psychiatrists on compulsory treatment is obviously based on a different understanding of autonomy and its prerequisites. We advocate an individual centered, preferably open form of treatment by medicinal and milieu therapeutic approaches in association with intensified relationships with the aim to restore or improve the ability for self-determination. We also call upon the legislative authorities to establish legal certainty. It is decisive that the characteristics of mental diseases and the possibilities of modern treatment are taken into consideration in order to suitably respect patient autonomy without neglecting the necessary help.

C-arm orbits for metal artifact avoidance (MAA) in cone-beam CT.

Metal artifacts present a challenge to cone-beam CT (CBCT) image-guided surgery, obscuring visualization of metal instruments and adjacent anatomy-often in the very region of interest pertinent to the imaging/surgical tasks. We present a method to reduce the influence of metal artifacts by prospectively defining an image acquisition protocol-viz., the C-arm source-detector orbit-that mitigates metal-induced biases in the projection data. The metal artifact avoidance (MAA) method is compatible with simple mobile C-arms, does not require exact prior information on the patient or metal implants, and is consistent with 3D filtered backprojection (FBP), more advanced (e.g. polyenergetic) model-based image reconstruction (MBIR), and metal artifact reduction (MAR) post-processing methods. The MAA method consists of: (i) coarse localization of metal objects in the field-of-view (FOV) via two or more low-dose scout projection views and segmentation (e.g. a simple U-Net) in coarse backprojection; (ii) model-based prediction of metal-induced x-ray spectral shift for all source-detector vertices accessible by the imaging system (e.g. gantry rotation and tilt angles); and (iii) identification of a circular or non-circular orbit that reduces the variation in spectral shift. The method was developed, tested, and evaluated in a series of studies presenting increasing levels of complexity and realism, including digital simulations, phantom experiment, and cadaver experiment in the context of image-guided spine surgery (pedicle screw implants). The MAA method accurately predicted tilted circular and non-circular orbits that reduced the magnitude of metal artifacts in CBCT reconstructions. Realistic distributions of metal instrumentation were successfully localized (0.71 median Dice coefficient) from 2-6 low-dose scout views even in complex anatomical scenes. The MAA-predicted tilted circular orbits reduced root-mean-square error (RMSE) in 3D image reconstructions by 46%-70% and 'blooming' artifacts (apparent width of the screw shaft) by 20-45%. Non-circular orbits defined by MAA achieved a further ∼46% reduction in RMSE compared to the best (tilted) circular orbit. The MAA method presents a practical means to predict C-arm orbits that minimize spectral bias from metal instrumentation. Resulting orbits-either simple tilted circular orbits or more complex non-circular orbits that can be executed with a motorized multi-axis C-arm-exhibited substantial reduction of metal artifacts in raw CBCT reconstructions by virtue of higher fidelity projection data, which are in turn compatible with subsequent MAR post-processing and/or polyenergetic MBIR to further reduce artifacts.

[Pay for performance in rehabilitation after stroke - results of a pilot project 2001-2008]. / Ergebnisorientierte Vergütung der Rehabilitation nach Schlaganfall - Entwicklungsschritte eines Modellprojekts 2001-2008.

The project aimed at developing and testing a new payment system which provides financial incentives for rehabilitation centers to achieve the best outcomes possible for their patients but does not create additional costs for the insurance funds. The system is conceived as a "quality competition" organized by the centers among themselves with a scientific institute acting as a "referee". Centers with outcomes above average receive a bonus financed by a corresponding malus from the centers below average. In a stepwise process which started in 2001 and was continually accompanied by a scientific institute, we developed the methodological and organizational prerequisites for the new payment system and tested them in two multicentric studies with large case numbers (n=1,058 and n=700, respectively). As a first step, a new assessment instrument (SINGER) was developed and validated in order to measure the outcomes in a reliable, valid, and change-sensitive way. In the second phase, we developed a regression analytic model which predicted the central outcome variable with >84% variance explained. With this model, the different case-mix in the participating centers can be controlled, so that comparisons of outcomes across centers can take place under fair conditions. In the recently completed third phase, we introduced an internet-based programme SINGER-online into which the centers can enter all relevant data. This programme ensures a high quality of all data and makes comparisons of outcomes across all centers possible at any chosen time. The programme contains a special module accessible to the medical services of the health insurance only, which allows sample checks of the data entered by the clinics and helps to ensure that all centers keep to the principles of a fair competition for better quality for their patients. After successful testing of these elements, a functioning model of pay-for-performance in rehabilitation after stroke is now available.

Combining Hopfield neural networks, with applications to grid-based mathematics puzzles.

Hopfield neural networks are useful for solving certain constrained set-selection problems. We establish that the vector fields associated with general networks of this type can be combined to produce a new network that solves the corresponding combination of set-selection/constraint problems, provided a relatively simple condition is satisfied. That is, we establish that just this one condition needs to be verified in order to be able to combine such networks. We introduce some generalizations of networks that exist in the literature, and, to demonstrate the usefulness of the work, we combine these networks to solve two well-known grid-based math puzzles (i.e. constraint problems): Kakuro and Akari (called Cross Sums and Light Up in North America). We present examples to illustrate the evolution of the solution process. We find that the difficulty rating of a Kakuro puzzle is strongly connected to the number of iterations used by the neural network solver.

Forty-eight new cases with infertility due to balanced chromosomal rearrangements: detailed molecular cytogenetic analysis of the 90 involved breakpoints.

A molecular cytogenetic study was performed on 48 infertile patients who were identified as carriers of balanced translocations (40 cases), inversions (6 cases) or insertions (2 cases) by means of banding cytogenetics. Cases with a Robertsonian translocation or pericentric inversion 2 or 9 were not included. In summary, 100 break-events occurred in these patients, and 90 different chromosomal regions were involved. Thus, this study confirmed the presence of abnormal karyotypes in a subgroup of patients seeking infertility treatment. Breaks were demonstrated to appear preferentially in GTG-light bands in these patients. Furthermore, the observed breakpoints were associated with genomic regions prone to instability due to the presence of segmental duplications. Nonetheless, further detailed molecular analysis will be necessary in the future to characterize the mechanisms and genetic basis for this phenomenon.

Intralysosomal glycerophospholipid catabolism in liver: hydrolysis of amino alcohol-containing phospholipids and their metabolites.

Liver lysosomes were isolated from untreated rats and rats pretreated with Triton WR-1339. Purified lysosomes were also separated into lysosomal matrix and membrane fractions. With freshly prepared and frozen biological material, the lysosomal catabolism of various stereospecifically radiolabeled amino alcohol-containing glycerophospholipids and their potential metabolites was studied. Basically there was no qualitative difference in the formation of phospholipid metabolites in both preparations: after long-term incubation, free fatty acids, lysophospholipids, acyl-free phosphodiesters were detected, and to a far lesser extent, amino alcohol-containing phosphomonoesters and only traces of free amino alcohols. These findings indicate the presence of lysosomal phospholipases A as well as C and lysophospholipase(s), with pH optima of about 4.5, and they clearly exclude phospholipase D activity. Unfractionated lysosomes and their soluble as well as particulate subfractions were not capable of hydrolysing the acyl-free amino alcohol-containing phosphodiesters. These compounds must therefore be considered one of the end products of the intralysosomal catabolism of amino alcohol-containing phosphoglycerides. They are presumably cleared from the lysosomal compartment by an as yet unknown transport system in the lysosomal membrane. In liver, the extralysosomal site of their (Mg(2+)-dependent) hydrolysis seems to be the plasma membrane. By contrast, hydrolysis of glycero-3-phosphate and the amino alcohol-containing phosphomonoesters was catalysed in the lysosomal compartment, with a pH optimum of about 5.0, although at considerably lower rates than that of glycero-2-phosphate, a model substrate for lysosomal acid phosphatase.

Purification and properties of phospholipase A2 from human seminal plasma.

The soluble Ca2+-dependent phospholipase A2 (EC 3.1.1.4) was purified 6500-fold with a yield of about 20% from human seminal plasma. The successive purification steps comprised gel filtration, affinity chromatographies and micropartition. The final preparation consisted of two proteins in about equal quantities with molecular weights of 12000 and 14000, according to SDS-polyacrylamide slab gel electrophoresis. As yet these two proteins can not be separated without complete loss of activity. Apparent kinetic parameters have been determined for the purified preparation with different substrates (Vmax = 494 U/mg, and Km = 1.25 X 10(-4) M long-chain phosphatidylethanolamine; Vmax = 7.4 U/mg, and Km = 2.5 X 10(-5) M long-chain phosphatidylcholine; Vmax = 7196 U/mg and Km = 8.32 X 10(-4) M dioctanoylphosphatidylcholine). The enzymatic activity was not affected by diisopropylfluorophosphate and thiol reagents but it was inhibited by higher concentrations of nonionic and ionic (except taurocholate) detergents and by the alkylating reagent p-bromophenacyl bromide. Although the seminal enzyme functionally strongly resembles the pancreatic phospholipase A2, no immunochemical relationship was observed; anti-pancreatic phospholipase A2 IgGs did not inhibit seminal phospholipase A2. Similarly, partially purified phospholipase A2 from horse seminal fluid was not affected by antibodies raised against horse pancreatic phospholipase A2.

Biospecific dye-binding and hydrophobic interaction chromatography as tools for high yield preparation of purified phospholipase A1 from rat liver.

A basically new approach is presented for purifying lysosomal phospholipase A1 (EC 3.1.1.32) from rat liver. This procedure not only simplifies and speeds up the purification process, but also improves the yield in comparison to the most efficient methods reported so far. A high recovery of about 88% was achieved by (1) homogenisation of whole rat liver in a hypotonic medium, (2) acid precipitation, (3) combined dye binding chromatography on triacinyl dyes (Yellow H-A and Red HE-3B) immobilised to agaroses, and (4) combined concanavalin A-Sepharose and phenyl-Sepharose chromatography. Ethylene glycol was required for enzyme stabilisation as well as for enzyme elution in dye-binding and hydrophobic chromatography. In SDS-polyacrylamide slab gel electrophoresis, the purified material showed two major protein bands of 56 and 33 kDa, which amounted to about 85 and 12%, respectively, of the total protein visualised. Under reductive conditions, the 56 kDa protein decomposed completely into three subunits of 30, 21 and 20 kDa. The 33 kDa protein in the non-reduced material seems to be identical with the 30 kDa protein in the reduced material. Native polyacrylamide gel electrophoresis provided strong evidence that the 56 kDa protein is the active form of PLA1. The purified material displayed a specific activity of approximately 7.7 mumol fatty acid released per min per mg of protein using 200 microM phosphatidylethanolamine as a substrate.

On the mechanism of lysophospholipase activity of secretory phospholipase A2 (EC 3.1.1.4): deacylation of monoacylphosphoglycerides by intrinsic sn-1 specificity and pH-dependent acyl migration in combination with sn-2 specificity.

We show for the first time that secreted low-molecular weight phospholipase A2 (EC 3.1.1.4) catalyzes the deacylation of monoacylphosphoglycerides directly from the sn-1 position, although at a very low rate: purified phospholipase A2 enzymes from bee venom, crotalus atrox venom, and porcine pancreas hydrolyze the sn-1 ester bond in 1-palmitoyl-2-O-methyl-sn-glycero-3-phosphorylcholine. Hydrolytic rates with the corresponding isomer, 1-O-methyl-2-palmitoyl-sn-glycero-3-phosphorylcholine, are about 3-4 orders of magnitude higher. The similarities in Ca2+ requirement and inactivation profiles suggest that deacylation, albeit with different rates, from both sn-1 and sn-2 positions is catalyzed by the same catalytic site of phospholipase A2. Furthermore, evidence is provided that phospholipase A2-catalyzed 1-acyl lysophospholipid deacylation is mediated by sn-1-directed action, but above pH 7 acyl migration with subsequent enzyme-catalyzed hydrolytic cleavage from the sn-2 position contributes to the overall deacylation of monoacylphosphoglycerides, acyl migration becoming eventually the rate-limiting factor.

Effects of local anaesthetics on the lipase of Rhizopus arrhizus.

1. A number of local anaesthetics were shown to inhibit the hydrolytic activity of a partially purified lipase from the mold Rhizopus arrhizur towards both triacylglycerol and phospholipid substrates. 2. Irrespective of whether triacylglycerol or phospholipid substrates were used, the inhibition was uncompetitive with respect to the substrate, independent of Ca2+ concentration, but pH dependent. 3. The inhibitory activity of the local anaesthetics studied closely paralleled the anaesthetic potency of the compounds.

Inhibition of rat liver cholesterol esterase by local anaesthetics.

1. A number of local anaesthetics was shown to inhibit rat liver cholesterol esterase activity towards radioactively labelled cholesterol oleate. The anaesthetics inhibited in the order dibucaine greater than chlorpromazine greater than tetracaine greater than benzocaine greater than procaine greater than lidocaine greater than cocaine. 2. The mode of inhibition was seen to be non-competitive with respect to the substrate and is probably independent of any involvement of Ca2+. 3. The inhibition by tetracaine is partially reversed by sodium deoxycholate. However, all ionic and non-ionic detergents studied, sodium deoxycholate, sodium taurocholate, Triton X-100, and cetyltrimethylammonium bromide are capable of inhibiting the rat liver cholesterol esterase in a concentration dependent manner. Only sodium taurocholate stimulates enzymic activity.

Hydrolytic degradation of phosphatidylethanolamine and phosphatidylcholine by isolated rat-liver lysosomes.

Lysosomal catabolism of radioactively labelled phosphatidylethanolamine, phosphatidylcholine and several potential metabolites of these diacylphospholipids was studied using rat-liver lysosomes which had been isolated from Triton WR-1339-treated animals. Hydrolysis of these lipids seems to be restricted to the soluble lysosomal compartment. The initial intralysosomal degradation is predominantly catalysed by phospholipase A1 (EC 3.1.1.32) followed by lysophospholipase (EC 3.1.1.5). The end products of this pathway are free fatty acids and glycerophosphorylethanolamine or glycerophosphorylcholine. These phosphodiesters are not hydrolysed further in lysosomes, as has been shown previously (Fowler, S. and De Duve, C. (1969) J. Biol. Chem. 144, 471-481). The intermediary lysophospholipids, however, are also hydrolysed by an alternative pathway, i.e. by a lysophospholipase which catalyses the hydrolysis of the glycerophosphate ester bond, followed by a monoacylglycerol lipase and a phosphomonoesterase (EC 3.1.3.2), respectively. Besides these two catabolic routes of intralysosomal hydrolysis of phosphatidylethanolamine and phosphatidylcholine, additional pathways are possible, which seem, however, to be of minor importance, at least in the substrate concentration ranges employed in these studies. These additional reactions include attack by a phospholipase A2 (EC 3.1.1.4) and--as discovered recently (Matsuzawa, Y. and Hostetler, K.Y. (1980) J. Biol. Chem. 255, 646-652)--by a phospholipase C (EC 3.1.4.3). Cations such as Mg2+, Ca2+, K+ and Na+ inhibit preferentially deacylation reactions.

Effects of antimalarial drugs on several rat-liver lysosomal enzymes involved in phosphatidylethanolamine catabolism.

The effects of three cationic amphiphilic antimalarial drugs (chloroquine, mepacrine and primaquine) on the intralysosomal catabolism of phosphatidylethanolamine and several of its metabolites were studied with rat-liver lysosomes which had been isolated from animals previously treated with Triton WR-1339. The activities of each of the various enzymes involved in the main pathways of intralysosomal phosphatidylethanolamine degradation (Kunze, H., Hesse, B. and Bohn, E. (1982) Biochim. Biophys. Acta 711, 10-18) exhibited almost identical inhibitory sensitivities towards mepacrine and primaquine. In contrast, chloroquine inhibited the activities of the various enzymes to different extents, lysophospholipid acylhydrolase (EC 3.1.1.5) being the most sensitive enzyme, followed by phospholipase A1 (EC 3.1.1.32) and monoacylglycerol lipase, and eventually lysophospholipid monoacylglycerol hydrolase as the least sensitive enzyme. The relative inhibitory potencies towards phospholipase A1 activity of chloroquine were increased with increasing pH, and the mode of inhibition was competitive. In contrast, the inhibitory potencies towards monoacylglycerol lipase activity of chloroquine increased only up to pH 5 but decreased above this value, and the mode of inhibition was noncompetitive.

Effects of antimalarial drugs on phospholipase A and lysophospholipase activities in plasma membrane, mitochondrial, microsomal and cytosolic subcellular fractions of rat liver.

Activities of membrane-associated phospholipases A1 and A2, and membrane-associated as well as soluble lysophospholipases were measured in different subcellular fractions of rat liver, using suspensions of stereospecifically labelled radioactive phospholipids as substrates. Plasma membranes and endoplasmic reticulum were shown to contain phospholipase A1 and lysophospholipase activities, both of which could be stimulated by Ca2+, mitochondria Ca2+-dependent phospholipase A2 and cytosol Ca2+-independent lysophospholipase activities. Each of these lipolytic enzymes could be inhibited by antimalarial drugs (chloroquine, mepacrine, primaquine) at concentrations above 1 x 10(-4) M. Inhibition of the alkaline cytosolic lysophospholipase by these drugs was noncompetitive with respect to the substrate, and the inhibitory potency increased, when the pH was raised.

Effects of local anaesthetics on phospholipases.

1. The effects of six local anaesthetics have been studied on the activities of soluble phospholipases A2 (EC 3.1.1.4) and lysophospholipase (EC 3.1.1.5). 2. Phospholipase A2 activity in human seminal plasma towards sonicated radioactively-labelled phosphatidylethanolamine was slightly stimulated a low and inhibited at high concentrations of all anaesthetic compounds employed. The order of decreasing potency was chlorpromazine, dibucaine, tetracaine, lidocaine, cocaine and procaine. In line with previous findings, the mode of inhibition was seen to be competitive with respect to Ca2+. 3. Phospholipase A2 activity in crude venom of Crotalus adamanteus was not affected or slightly stimulated by local anaesthetics up to 10(-2) M concentrations, when egg yolk was used as substrate. However, with sonicated radioactively-labelled phosphatidylcholine or phosphatidylethanolamine as substrate, stimulation of phospholipase activity was seen with all local anaesthetics up to 10(-2) M, the order of decreasing potency again being chlorpromazine, dibucaine, tetracaine, lidocaine, cocaine and procaine. The mode of stimulation was seen to be un-competitive with respect to substrate and probably independent of any involvement of Ca2+. 4. As in seminal plasma phospholipase A2, the activity in crude Naja naja venom towards sonicated radioactively labelled phosphatidylcholine was stimulated at low and inhibited at high concentrations of dibucaine and chloropromazine, for example. The mode of inhibition was seen to be competitive with respect to Ca2+, whereas stimulation by the anaesthetic drugs was independent of Ca2+. Binding between drug and enzyme was demonstrated by equilibration filtration of purified phospholipase A2 of Naja naja venom through a Sephadex G 25-fine column, previously equilibrated with 0.5 mM radioactively labelled chlorpromazine. 5. Lysophospholipase activity in rat liver cytosol towards radioactively labelled lysophosphatidylcholine was inhibited by all local anaesthetics used; the order of decreasing potency was chlorpromazine, dibucaine, tetracaine, cocaine, lidocaine and procaine. The inhibition was un-competitive with respect to substrate. 6. The inhibitory and stimulatory potencies of the local anaesthetics employed closely parallel their lipid solubilities and anaesthetic potencies.

Set selection dynamical system neural networks with partial memories, with applications to Sudoku and KenKen puzzles.

After reviewing set selection and memory model dynamical system neural networks, we introduce a neural network model that combines set selection with partial memories (stored memories on subsets of states in the network). We establish that feasible equilibria with all states equal to ± 1 correspond to answers to a particular set theoretic problem. We show that KenKen puzzles can be formulated as a particular case of this set theoretic problem and use the neural network model to solve them; in addition, we use a similar approach to solve Sudoku. We illustrate the approach in examples. As a heuristic experiment, we use online or print resources to identify the difficulty of the puzzles and compare these difficulties to the number of iterations used by the appropriate neural network solver, finding a strong relationship.

Fractionation, biochemical characterization and lysosomal phospholipases of human liver.

Human liver was homogenised and fractionated by differential centrifugation, and the subcellular fractions were characterised biochemically. Absolute values and distribution patterns of protein and marker enzyme activities obtained from human liver have also been compared with those from rat liver. In addition, acid phospholipase activities have been studied in human liver. On the basis of product formation from stereo-specifically radiolabeled phosphatidylethanolamine substrates, lysosomal phospholipases A1 and A2 with optimal activities at pH 4.7 have been identified in human liver. Acid phospholipase C and lysophospholipase activities, however, were not found in human liver. Cationic amphiphilic drugs inhibited the activities of the acid phospholipases A in human and rat liver lysosomes to about the same extent.