ADVANCED NUMERICAL METHODS FOR SIMULATING MICROBUBBLE IN AN AERATED MIXING TANK

Fluid mixing in mechanically agitated tanks is one of the major unit operations in many industries. Bubbly flows have been of interest among researchers in physics, medicine, chemistry and technology over the centuries. The aim of this thesis is to use advanced numerical methods for simulating microbubble in an aerated mixing tank. Main components of the mixing tank are a cylindrical vessel, a rotating Rushton turbine and the air nozzle. The objective of Computational Fluid Dynamics (CFD) is to predict fluid flow, heat transfer, mass transfer and chemical reactions. The CFD simulations of a turbulent bubbly flow are carried out in a cylindrical mixing tank using large eddy simulation (LES) and volume of fluid (VOF) method. The Rushton turbine induced flow is modeled by using a sliding mesh method. Numerical results are used to describe the bubbly flows in highly complex liquid flow. Some of the experimental works related to turbulent bubbly flow in a mixing tank are briefly reported. Numerical simulations are needed to complete and interpret the results of the experimental work. Information given by numerical simulations has a major role in designing and scaling-up mixing tanks. The results of this work have been reported in the following scientific articles: ·Honkanen M., Koohestany A., Hatunen T., Saarenrinne P., Zamankhan P., Large eddy simulations and PIV experiments of a two-phase air-water mixer, in Proceedings of ASME Fluids Engineering Summer Conference (2005). ·Honkanen M., Koohestany A., Hatunen T., Saarenrinne P., Zamankhan P., Dynamical States of Bubbling in an Aerated Stirring Tank, submitted to J. Computational Physics.

Combined T2 -preparation and two-dimensional pencil-beam inner volume selection.

PURPOSE: To improve coronary magnetic resonance angiography (MRA) by combining a two-dimensional (2D) spatially selective radiofrequency (RF) pulse with a T2 -preparation module ("2D-T2 -Prep"). METHODS: An adiabatic T2 -Prep was modified so that the first and last pulses were of differing spatial selectivity. The first RF pulse was replaced by a 2D pulse, such that a pencil-beam volume is excited. The last RF pulse remains nonselective, thus restoring the T2 -prepared pencil-beam, while tipping the (formerly longitudinal) magnetization outside of the pencil-beam into the transverse plane, where it is then spoiled. Thus, only a cylinder of T2 -prepared tissue remains for imaging. Numerical simulations were followed by phantom validation and in vivo coronary MRA, where the technique was quantitatively evaluated. Reduced field-of-view (rFoV) images were similarly studied. RESULTS: In vivo, full field-of-view 2D-T2 -Prep significantly improved vessel sharpness as compared to conventional T2 -Prep, without adversely affecting signal-to-noise (SNR) or contrast-to-noise ratios (CNR). It also reduced respiratory motion artifacts. In rFoV images, the SNR, CNR, and vessel sharpness decreased, although scan time reduction was 60%. CONCLUSION: When compared with conventional T2 -Prep, the 2D-T2 -Prep improves vessel sharpness and decreases respiratory ghosting while preserving both SNR and CNR. It may also acquire rFoV images for accelerated data acquisition.

Radiographic volume analysis as a novel tool to determine nasopalatine duct cyst dimensions and its association with presenting symptoms and postoperative complications.

OBJECTIVES: The aims of the study were to use cone beam computed tomography (CBCT) images of nasopalatine duct cysts (NPDC) and to calculate the diameter, surface area, and 3D-volume using a custom-made software program. Furthermore, any associations of dimensions of NPDC with age, gender, presence/absence of maxillary incisors/canines (MI/MC), endodontic treatment of MI/MC, presenting symptoms, and postoperative complications were evaluated. MATERIAL AND METHODS: The study comprised 40 patients with a histopathologically confirmed NPDC. On preoperative CBCT scans, curves delineating the cystic borders were drawn in all planes and the widest diameter (in millimeter), surface area (in square millimeter), and volume (in cubic millimeter) were calculated. RESULTS: The overall mean cyst diameter was 15 mm (range 7-47 mm), the mean cyst surface area 566 mm(2) (84-4,516 mm(2)), and the mean cyst volume 1,735 mm(3) (65-25,350 mm(3)). For 22 randomly allocated cases, a second measurement resulted in a mean absolute aberration of ±4.2 % for the volume, ±2.8 % for the surface, and ±4.9 % for the diameter. A statistically significant association was found for the CBCT determined cyst measurements and the need for preoperative endodontic treatment to MI/MC and for postoperative complications. CONCLUSION: In the hands of a single experienced operator, the novel software exhibited high repeatability for measurements of cyst dimensions. Further studies are needed to assess the application of this tool for dimensional analysis of different jaw cysts and lesions including treatment planning. CLINICAL RELEVANCE: Accurate radiographic information of the bone volume lost (osteolysis) due to expansion of a cystic lesion in three dimensions could help in personalized treatment planning.

A new formula for calculating standard liver volume for living donor liver transplantation without using body weight.

BACKGROUND & AIMS: The standard liver volume (SLV) is widely used in liver surgery, especially for living donor liver transplantation (LDLT). All the reported formulas for SLV use body surface area or body weight, which can be influenced strongly by the general condition of the patient. METHODS: We analyzed the liver volumes of 180 Japanese donor candidates and 160 Swiss patients with normal livers to develop a new formula. The dataset was randomly divided into two subsets, the test and validation sample, stratified by race. The new formula was validated using 50 LDLT recipients. RESULTS: Without using body weight-related variables, age, thoracic width measured using computed tomography, and race independently predicted the total liver volume (TLV). A new formula: 203.3-(3.61×age)+(58.7×thoracic width)-(463.7×race [1=Asian, 0=Caucasian]), most accurately predicted the TLV in the validation dataset as compared with any other formulas. The graft volume for LDLT was correlated with the postoperative prothrombin time, and the graft volume/SLV ratio calculated using the new formula was significantly better correlated with the postoperative prothrombin time than the graft volume/SLV ratio calculated using the other formulas or the graft volume/body weight ratio. CONCLUSIONS: The new formula derived using the age, thoracic width and race predicted both the TLV in the healthy patient group and the SLV in LDLT recipients more accurately than any other previously reported formulas.

Effect of partial-thickness tear on loading capacities of the supraspinatus tendon: a finite element analysis.

Partial-thickness tears of the supraspinatus tendon frequently occur at its insertion on the greater tubercule of the humerus, causing pain and reduced strength and range of motion. The goal of this work was to quantify the loss of loading capacity due to tendon tears at the insertion area. A finite element model of the supraspinatus tendon was developed using in vivo magnetic resonance images data. The tendon was represented by an anisotropic hyperelastic constitutive law identified with experimental measurements. A failure criterion was proposed and calibrated with experimental data. A partial-thickness tear was gradually increased, starting from the deep articular-sided fibres. For different values of tendon tear thickness, the tendon was mechanically loaded up to failure. The numerical model predicted a loss in loading capacity of the tendon as the tear thickness progressed. Tendon failure was more likely when the tendon tear exceeded 20%. The predictions of the model were consistent with experimental studies. Partial-thickness tears below 40% tear are sufficiently stable to persist physiotherapeutic exercises. Above 60% tear surgery should be considered to restore shoulder strength.

Thoracic fat volume is independently associated with coronary vasomotion.

PURPOSE: Thoracic fat has been associated with an increased risk of coronary artery disease (CAD). As endothelium-dependent vasoreactivity is a surrogate of cardiovascular events and is impaired early in atherosclerosis, we aimed at assessing the possible relationship between thoracic fat volume (TFV) and endothelium-dependent coronary vasomotion. METHODS: Fifty healthy volunteers without known CAD or major cardiovascular risk factors (CRFs) prospectively underwent a (82)Rb cardiac PET/CT to quantify myocardial blood flow (MBF) at rest, and MBF response to cold pressor testing (CPT-MBF) and adenosine (i.e., stress-MBF). TFV was measured by a 2D volumetric CT method and common laboratory blood tests (glucose and insulin levels, HOMA-IR, cholesterol, triglyceride, hsCRP) were performed. Relationships between CPT-MBF, TFV and other CRFs were assessed using non-parametric Spearman rank correlation testing and multivariate linear regression analysis. RESULTS: All of the 50 participants (58 ± 10y) had normal stress-MBF (2.7 ± 0.6 mL/min/g; 95 % CI: 2.6-2.9) and myocardial flow reserve (2.8 ± 0.8; 95 % CI: 2.6-3.0) excluding underlying CAD. Univariate analysis revealed a significant inverse relation between absolute CPT-MBF and sex (ρ = -0.47, p = 0.0006), triglyceride (ρ = -0.32, p = 0.024) and insulin levels (ρ = -0.43, p = 0.0024), HOMA-IR (ρ = -0.39, p = 0.007), BMI (ρ = -0.51, p = 0.0002) and TFV (ρ = -0.52, p = 0.0001). MBF response to adenosine was also correlated with TFV (ρ = -0.32, p = 0.026). On multivariate analysis, TFV emerged as the only significant predictor of MBF response to CPT (p = 0.014). CONCLUSIONS: TFV is significantly correlated with endothelium-dependent and -independent coronary vasomotion. High TF burden might negatively influence MBF response to CPT and to adenosine stress, even in persons without CAD, suggesting a link between thoracic fat and future cardiovascular events.

Independent and combined associations of risky single-occasion drinking and drinking volume with alcohol use disorder: Evidence from a sample of young Swiss men.

BACKGROUND: Risky single-occasion drinking (RSOD) is a prevalent and potentially harmful alcohol use pattern associated with increased alcohol use disorder (AUD). However, RSOD is commonly associated with a higher level of alcohol intake, and most studies have not controlled for drinking volume (DV). Thus, it is unclear whether the findings provide information about RSOD or DV. This study sought to investigate the independent and combined effects of RSOD and DV on AUD. METHODS: Data were collected in the longitudinal Cohort Study on Substance Use Risk Factors (C-SURF) among 5598 young Swiss male alcohol users in their early twenties. Assessment included DV, RSOD, and AUD at two time points. Generalized linear models for binomial distributions provided evidence regarding associations of DV, RSOD, and their interaction. RESULTS: DV, RSOD, and their interaction were significantly related to the number of AUD criteria. The slope of the interaction was steeper for non/rare RSOD than for frequent RSOD. CONCLUSIONS: RSOD appears to be a harmful pattern of drinking, associated with increased AUD and it moderated the relationship between DV and AUD. This study highlighted the importance of taking drinking patterns into account, for both research and public health planning, since RSO drinkers constitute a vulnerable subgroup for AUD.

Role of Doppler ultrasonography evaluation of superior mesenteric artery flow volume in the assessment of Crohn's disease activity

Objective To investigate superior mesenteric artery flow measurement by Doppler ultrasonography as a means of characterizing inflammatory activity in Crohn's disease. Materials and Methods Forty patients were examined and divided into two groups – disease activity and remission – according to their Crohn's disease activity index score. Mean superior mesenteric artery flow volume was calculated for each group and correlated with Crohn's disease activity index score. Results The mean superior mesenteric artery flow volume was significantly greater in the patients with active disease (626 ml/min ± 236 × 376 ml/min ± 190; p = 0.001). As a cut off corresponding to 500 ml/min was utilized, the superior mesenteric artery flow volume demonstrated sensitivity of 83% and specificity of 82% for the diagnosis of Crohn's disease activity. Conclusion The present results suggest that patients with active Crohn's disease have increased superior mesenteric artery flow volume as compared with patients in remission. Superior mesenteric artery flow measurement had a good performance in the assessment of disease activity in this study sample.

Multidetector-row computed tomography in the preoperative diagnosis of intestinal complications caused by clinically unsuspected ingested dietary foreign bodies: a case series emphasizing the use of volume rendering techniques

Objective The present study was aimed at describing a case series where a preoperative diagnosis of intestinal complications secondary to accidentally ingested dietary foreign bodies was made by multidetector-row computed tomography (MDCT), with emphasis on complementary findings yielded by volume rendering techniques (VRT) and curved multiplanar reconstructions (MPR). Materials and Methods The authors retrospectively assessed five patients with surgically confirmed intestinal complications (perforation and /or obstruction) secondary to unsuspected ingested dietary foreign bodies, consecutively assisted in their institution between 2010 and 2012. Demographic, clinical, laboratory and radiological data were analyzed. VRT and curved MPR were subsequently performed. Results Preoperative diagnosis of intestinal complications was originally performed in all cases. In one case the presence of a foreign body was not initially identified as the causal factor, and the use of complementary techniques facilitated its retrospective identification. In all cases these tools allowed a better depiction of the entire foreign bodies on a single image section, contributing to the assessment of their morphology. Conclusion Although the use of complementary techniques has not had a direct impact on diagnostic performance in most cases of this series, they may provide a better depiction of foreign bodies' morphology on a single image section.

Prognostic value of baseline total metabolic tumor volume (TMTV0) measured on FDG-PET/CT in patients with peripheral T-cell lymphoma (PTCL).

BACKGROUND: Most peripheral T-cell lymphoma (PTCL) patients have a poor outcome and the identification of prognostic factors at diagnosis is needed. PATIENTS AND METHODS: The prognostic impact of total metabolic tumor volume (TMTV0), measured on baseline [(18)F]2-fluoro-2-deoxy-d-glucose positron emission tomography/computed tomography, was evaluated in a retrospective study including 108 PTCL patients (27 PTCL not otherwise specified, 43 angioimmunoblastic T-cell lymphomas and 38 anaplastic large-cell lymphomas). All received anthracycline-based chemotherapy. TMTV0 was computed with the 41% maximum standardized uptake value threshold method and an optimal cut-off point for binary outcomes was determined and compared with others prognostic factors. RESULTS: With a median follow-up of 23 months, 2-year progression-free survival (PFS) was 49% and 2-year overall survival (OS) was 67%. High TMTV0 was significantly associated with a worse prognosis. At 2 years, PFS was 26% in patients with a high TMTV0 (>230 cm(3), n = 53) versus 71% for those with a low TMTV0, [P < 0.0001, hazard ratio (HR) = 4], whereas OS was 50% versus 80%, respectively, (P = 0.0005, HR = 3.1). In multivariate analysis, TMTV0 was the only significant independent parameter for both PFS and OS. TMTV0, combined with PIT, discriminated even better than TMTV0 alone, patients with an adverse outcome (TMTV0 >230 cm(3) and PIT >1, n = 33,) from those with good prognosis (TMTV0 ≤230 cm(3) and PIT ≤1, n = 40): 19% versus 73% 2-year PFS (P < 0.0001) and 43% versus 81% 2-year OS, respectively (P = 0.0002). Thirty-one patients (other TMTV0-PIT combinations) had an intermediate outcome, 50% 2-year PFS and 68% 2-year OS. CONCLUSION: TMTV0 appears as an independent predictor of PTCL outcome. Combined with PIT, it could identify different risk categories at diagnosis and warrants further validation as a prognostic marker.

Impact of the Femoral Head Position on Moment Arms in Total Hip Arthroplasty: A Parametric Finite Element Study.

BACKGROUND: Although the importance of accurate femoral reconstruction to achieve a good functional outcome is well documented, quantitative data on the effects of a displacement of the femoral center of rotation on moment arms are scarce. The purpose of this study was to calculate moment arms after nonanatomical femoral reconstruction. METHODS: Finite element models of 15 patients including the pelvis, the femur, and the gluteal muscles were developed. Moment arms were calculated within the native anatomy and compared to distinct displacement of the femoral center of rotation (leg lengthening of 10 mm, loss of femoral offset of 20%, anteversion ±10°, and fixed anteversion at 15°). Calculations were performed within the range of motion observed during a normal gait cycle. RESULTS: Although with all evaluated displacements of the femoral center of rotation, the abductor moment arm remained positive, some fibers initially contributing to extension became antagonists (flexors) and vice versa. A loss of 20% of femoral offset led to an average decrease of 15% of abductor moment. Femoral lengthening and changes in femoral anteversion (±10°, fixed at 15°) led to minimal changes in abductor moment arms (maximum change of 5%). Native femoral anteversion correlated with the changes in moment arms induced by the 5 variations of reconstruction. CONCLUSION: Accurate reconstruction of offset is important to maintaining abductor moment arms, while changes of femoral rotation had minimal effects. Patients with larger native femoral anteversion appear to be more susceptible to femoral head displacements.

Strategies to evaluate the impact of rectal volume on prostate motion during three-dimensional conformal radiotherapy for prostate cancer

Abstract Objective: To evaluate the rectal volume influence on prostate motion during three-dimensional conformal radiotherapy (3D-CRT) for prostate cancer. Materials and Methods: Fifty-one patients with prostate cancer underwent a series of three computed tomography scans including an initial planning scan and two subsequent scans during 3D-CRT. The organs of interest were outlined. The prostate contour was compared with the initial CT images considering the anterior, posterior, superior, inferior and lateral edges of the organ. Variations in the anterior limits and volume of the rectum were assessed and correlated with prostate motion in the anteroposterior direction. Results: The maximum range of prostate motion was observed in the superoinferior direction, followed by the anteroposterior direction. A significant correlation was observed between prostate motion and rectal volume variation ( p = 0.037). A baseline rectal volume superior to 70 cm3 had a significant influence on the prostate motion in the anteroposterior direction ( p = 0.045). Conclusion: The present study showed a significant interfraction motion of the prostate during 3D-CRT with greatest variations in the superoinferior and anteroposterior directions, and that a large rectal volume influences the prostate motion with a cutoff value of 70 cm3. Therefore, the treatment of patients with a rectal volume > 70 cm3 should be re-planned with appropriate rectal preparation.

Methods for assessing the sustainability of integrated municipal waste management and

The general striving to bring down the number of municipal landfills and to increase the reuse and recycling of waste-derived materials across the EU supports the debates concerning the feasibility and rationality of waste management systems. Substantial decrease in the volume and mass of landfill-disposed waste flows can be achieved by directing suitable waste fractions to energy recovery. Global fossil energy supplies are becoming more and more valuable and expensive energy sources for the mankind, and efforts to save fossil fuels have been made. Waste-derived fuels offer one potential partial solution to two different problems. First, waste that cannot be feasibly re-used or recycled is utilized in the energy conversion process according to EU’s Waste Hierarchy. Second, fossil fuels can be saved for other purposes than energy, mainly as transport fuels. This thesis presents the principles of assessing the most sustainable system solution for an integrated municipal waste management and energy system. The assessment process includes: · formation of a SISMan (Simple Integrated System Management) model of an integrated system including mass, energy and financial flows, and · formation of a MEFLO (Mass, Energy, Financial, Legislational, Other decisionsupport data) decision matrix according to the selected decision criteria, including essential and optional decision criteria. The methods are described and theoretical examples of the utilization of the methods are presented in the thesis. The assessment process involves the selection of different system alternatives (process alternatives for treatment of different waste fractions) and comparison between the alternatives. The first of the two novelty values of the utilization of the presented methods is the perspective selected for the formation of the SISMan model. Normally waste management and energy systems are operated separately according to the targets and principles set for each system. In the thesis the waste management and energy supply systems are considered as one larger integrated system with one primary target of serving the customers, i.e. citizens, as efficiently as possible in the spirit of sustainable development, including the following requirements: · reasonable overall costs, including waste management costs and energy costs; · minimum environmental burdens caused by the integrated waste management and energy system, taking into account the requirement above; and · social acceptance of the selected waste treatment and energy production methods. The integrated waste management and energy system is described by forming a SISMan model including three different flows of the system: energy, mass and financial flows. By defining the three types of flows for an integrated system, the selected factor results needed in the decision-making process of the selection of waste management treatment processes for different waste fractions can be calculated. The model and its results form a transparent description of the integrated system under discussion. The MEFLO decision matrix has been formed from the results of the SISMan model, combined with additional data, including e.g. environmental restrictions and regional aspects. System alternatives which do not meet the requirements set by legislation can be deleted from the comparisons before any closer numerical considerations. The second novelty value of this thesis is the three-level ranking method for combining the factor results of the MEFLO decision matrix. As a result of the MEFLO decision matrix, a transparent ranking of different system alternatives, including selection of treatment processes for different waste fractions, is achieved. SISMan and MEFLO are methods meant to be utilized in municipal decision-making processes concerning waste management and energy supply as simple, transparent and easyto- understand tools. The methods can be utilized in the assessment of existing systems, and particularly in the planning processes of future regional integrated systems. The principles of SISMan and MEFLO can be utilized also in other environments, where synergies of integrating two (or more) systems can be obtained. The SISMan flow model and the MEFLO decision matrix can be formed with or without any applicable commercial or free-of-charge tool/software. SISMan and MEFLO are not bound to any libraries or data-bases including process information, such as different emission data libraries utilized in life cycle assessments.

The influence of a certain volume of fluid in the lower tear meniscus on intraocular pressure measurements using the non-contact tonometer

Background: Intraocular pressure (IOP) is the pressure inside the eye that helps to maintain the integrity and the suitable form of the ocular globe. Precise and accurate measures of IOP are needed for the diagnosis as well as follow-up of glaucoma. In daily clinical practice, Goldmann applanation tonometer (GAT) and Non-contact tonometer (NCT) are the most common devices for measuring IOP. A close agreement between these methods has been showed, particularly in normotensive patients and a poor agreement, especially when IOP levels are above the normal range. Ophthalmologists have noticed a poor agreement between NCT and GAT, observing that by using NCT and after comparing with GAT, there is an overestimation of IOP readings, and particularly it occurs when the eyes are tearful. Previous studies investigate the effect of tears in Non-contact tonometer readings by the instillation of artificial tears, concluding in one of the studies that the variation was less than 1mmHg and not clinically significant, in contrast with another study which the increases were sadistically significant. Tear menisci are a thin strip of tear fluid located between the bulbar conjunctiva and the eyelid margins. We think that the overestimation of IOP readings using NCT could be due to the presence of a higher volume of tear in the lower tear meniscus which might cause an optical interference in the optoelectronic applanation monitoring system of this deviceObjectives: To research the influence of a certain volume of fluid in the lower tear meniscus on IOP measurements using the NCT in healthy eyes. Moreover, to investigate the agreement between IOP readings obtained by NCT and GAT in the presence and absence of this volume of fluidMethods: The study design will be transversal for diagnostic tests of repeated measures. We will study patients with no ocular pathology and IOP<21mmHg. It will consist in the measurement of IOP using NCT before and after the instillation of COLIRCUSÍ FLUOTEST, used as a volume of fluid in the lower tear meniscus, to observe if there will be differences using the paired t-test. Moreover, we will take IOP measures by GAT in order to know the agreement between these methods after and before the application of these eyedrops, using the ICC (intraclass correlation coefficient) and the Bland-Altmann method

Methods and Models for Accelerating Dynamic Simulation of Fluid Power Circuits

The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, twomechanisms whichmake the systemstiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation are proposed. Generally, in hydraulic power transmission systems the orifice flow is clearly in the turbulent area. The flow becomes laminar as the pressure drop over the orifice approaches zero only in rare situations. These are e.g. when a valve is closed, or an actuator is driven against an end stopper, or external force makes actuator to switch its direction during operation. This means that in terms of accuracy, the description of laminar flow is not necessary. But, unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when the pressure drop comes close to zero since the first derivative of flow with respect to the pressure drop approaches infinity when the pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. A numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline function are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. In the dynamic simulation of fluid power circuits, a tradeoff exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. Especially inside of many types of valves, as well as between them, there exist very small volumes. The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. Particularly in realtime simulation, these numerical problems are a great weakness. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step explicit algorithms for solving ordinary differential equations (ODE) are used, the system stability would easily be lost when integrating pressures in small volumes. To solve the problem caused by small fluid volumes, a pseudo-dynamic solver is proposed. Instead of integration of the pressure in a small volume, the pressure is solved as a steady-state pressure created in a separate cascade loop by numerical integration. The hydraulic capacitance V/Be of the parts of the circuit whose pressures are solved by the pseudo-dynamic method should be orders of magnitude smaller than that of those partswhose pressures are integrated. The key advantage of this novel method is that the numerical problems caused by the small volumes are completely avoided. Also, the method is freely applicable regardless of the integration routine applied. The superiority of both above-mentioned methods is that they are suited for use together with the semi-empirical modelling method which necessarily does not require any geometrical data of the valves and actuators to be modelled. In this modelling method, most of the needed component information can be taken from the manufacturer’s nominal graphs. This thesis introduces the methods and shows several numerical examples to demonstrate how the proposed methods improve the dynamic simulation of various hydraulic circuits.