Ablative Heat Research Articles

Development of a rapid heat ablation (RHA) process using a hot tool

Rapid prototyping and manufacturing (RPM) technologies have played a crucial role in reducing the lead-time and development costs of new products since its birth in the late 1980s. As compared with laminating processes for RPM, the machining process has been more commonly used because it offers such practical advantages as precision and versatility. However, the traditional machining process requires a large amount of time for product cutting and the remaining material causes problem as inconvenience due to cleaning process. The objective of this paper is to propose a new rapid manufacturing process using a hot tool with tangential grooves, rapid heat ablation process (RHA), to overcome the limitations of traditional machining processes. In order to investigate the material removal zone according to process parameters, several experiments were carried out. From the results of experiments, the relationships between the radius of the material removal zone and the process parameters were obtained. Furthermore, the depth of cut was compared with the kerfwidth in order to verify the isotropy of the material removal zone. As a result, a method of toolpath generation for ball-end mill commercially used can be adopted into the RHA process because the geometry of material removal zone is equal to that of the ball-end mill. The practical applicability of the RHA process is then demonstrated by the results of these fabrications for a hemispherical shape and a standard test part for machining in terms of geometrical conformity, volume of remaining material, ablating time and dimensional accuracy.

Ablation and thermal degradation behaviour of a composite based on resol type phenolic resin: Process modeling and experimental

During atmospheric re-entry, ballistic or space vehicle is subjected to severe aerodynamic heating and its successful return through the Earth's atmosphere depends largely on the provision that is made for reducing aerodynamic heat transfer to its structure. For this purpose ablative heat shield is normally used which undergoes physical, chemical, and mostly endothermal transformations. These transformations produce new liquid or gas phases which are subsequently injected into the environment.Mass and energy balance equations have been solved in order to model the ablation and thermal degradation behaviour of an ablative composite. A method to determine and calculate some of the parameters in the ablative equation is proposed from the simultaneous thermal gravity and differential scanning calorimetry analysis techniques.The objective of this work is to model ablating, charring and thermal degradation behaviour of a heat shield resol-type phenolic resin/asbestos cloth composite in oxyacetylene flame test. This requires solving serious heat transfer equations with moving boundaries. Explicit forward finite difference method (FDM) is used for heat transfer calculation. Moving boundaries are fixed by the Landau transformation. The ablation equation has been solved numerically.Temperature distribution through the composite thickness, temperature of moving surface, and the rate of moving boundary changes are evaluated. The results are in a good agreement with the experimental data obtained from oxyacetylene flame tests. The model can successfully be used for both material selection and thickness calculation in the design of thermal protection shields.

Characterization of the RF ablation-induced ‘oven effect’: The importance of background tissue thermal conductivity on tissue heating

Purpose: To determine the effect of background tissue thermal conductivity on RF ablation heating using ex vivo agar phantoms and computer modelling.Method: Two-compartment cylindrical agar phantom models (5% agar, 5% NaCl, 3% sucrose) were constructed. These included a standardized inner compartment (2 cm diameter, 4 cm length, 0.25% agar) representing a tumour, surrounded by an outer compartment representing background tissue. The thermal conductivity of the outer compartment was varied from 0.48 W m−1°C (normal liver) to 0.23 W m−1°C (fat) by adding a fat-saturated oil-based solute (10–90%) to the agar. RF ablation was applied at 2000 mA current for 2 min. Temperatures were recorded up to 4 cm from the electrode tip at 1 cm intervals. Subsequently, a 2-D finite element computer model was used to simulate RF ablation of 2–24 min duration for tumours measuring 2–4 cm in diameter surrounded by tissues of different thermal conductivity with the presence or absence of perfusion (0–5 kg m−3 s−1) (n = 44). A comparison of results was performed.Results: In agar phantoms, the amount of fat in the background tissue correlated with thermal conductivity as a negative exponential function (r2 = 0.98). Significantly increased temperatures were observed at the edge of the inner compartment (1 cm from the electrode tip) as the fat content of the outer compartment increased (p < 0.01). Thus, temperatures at 2 min measured 31.5 ± 2.2°C vs 45.1 ± 3.1°C for thermal conductivities of 0.46 W m−1°C (10% fat) and 0.23 W m−1°C (90% fat), respectively. On the other hand, higher levels of fat led to lower temperature increases in the background compartment (0.2 ± 0.3°C for 90% fat vs. 1.1 ± 0.05°C for 10% fat, p < 0.05). Phantom thermal heating patterns correlated extremely well with computer modelling (r2 = 0.93), demonstrating that background tissues with low thermal conductivity increase heating within the central tumour, particularly for longer durations of RF ablation and in smaller tumours. Furthermore, computer modelling demonstrated that increases in temperature at the tumour margin for background tissues of lower thermal conductivity persisted in the presence of perfusion, with a clinically relevant 4.5°C difference between background thermal conductivities of fat and soft tissue for a 3 cm tumour with perfusion of 2 kg m−3 s−1, treated for 12 min.Conclusion: Lower thermal conductivity of background tissues significantly increases temperatures within a defined ablation target. These findings provide insight into the ‘oven effect’ (i.e. increased heating efficacy for tumours surrounded by cirrhotic liver or fat) and highlight the importance of both the tumour and the surrounding tissue characteristics when contemplating RF ablation efficacy.

Investigation of Titan Aerogravity Assist for Capture into Orbit About Saturn

Introduction A EROCAPTURE has been studied extensively for application on manned Mars missions,1,2 and, more recently, for robotic probes to Neptune and Titan.3,4 However, use of traditional aerocapture at the gas giants has limited appeal because of very high atmospheric entry speeds, severe aerothermal heating, and heavy ablative heat shields.5 The present study considers the application of a related maneuver known as an aerogravity assist (AGA), in which the atmosphere and gravitational field of Titan would be used to decelerate a spacecraft and deflect its trajectory, resulting in capture into a closed orbit about Saturn. Because of its high atmospheric density, Titan is well suited for such a mission design. This approach is more appealing than capture using the atmosphere of Saturn itself, because of the much lower entry speed at Titan and the lower heating rate and heat load. The less severe aerothermal environment translates directly into weight savings in the vehicle’s thermal protection system. Titan has a near-circular, equatorial orbit about Saturn at a radius from the planetary center of 1.22 × 106 km and an orbital velocity (VT ) of approximately 5.57 km/s. This orbit is well outside the ring system, which extends in the equatorial plane to a radius of approximately 480,000 km. A wide range of potential target orbits about Saturn could be achieved by means of a successful AGA at Titan. The final Saturnian orbit will depend on both the orientation and magnitude of the probe’s outbound hyperbolic excess speed with respect to Titan (V T ∞) after the AGA. By lining up the outbound V T ∞ with VT , an orbit can be reached with a periapsis radius equal to that of Titan’s orbit and a higher apoapsis. If the outbound V T ∞ is in the opposite direction, the final orbit will have an apoapsis radius equal to that of Titan’s orbit and a lower periapsis radius (Fig. 1). The proposed strategy could be used on a Cassini-type mission with a Saturnian orbital periapsis of approximately 160,000 km, allowing the probe to pass through the gap between rings F and G. Achieving this periapsis radius will require an outbound V T ∞ of approximately 2.89 km/s, opposite in direction to Titan’s orbital

Steady ablation on the surface of a two-layer composite

Discovered is a quasi-steady ablation phenomenon on the surface of a two-layer composite which is formed by a layer of ablative material and another layer of non-ablative substrate. Theoretical exact solutions of quasi-steady ablation rate, the associated temperature distribution and end-of-ablation time of this two-layer composite are derived. A criterion for the occurrence of quasi-steady ablation is presented also. A one-dimensional transient numerical model is developed to perform a number of numerical experiments and hence to verify the correctness of the above theoretical solutions for the current quasi-steady ablation phenomenon. Based on the current results, a new method of measuring the ablation (or sublimation) heat is also proposed.

Property enhancements via matrix microstructure modification of carbon–carbon composites prepared by CVI processing

Carbon-carbon (CC) composites have received considerable interest for aerospace applications due to their superior strength retention at high temperatures and high heats of ablation etc. [1]. In the manufacturing of CC composites, carbon fiber preforms can be categorized dependent upon their final applications, e.g. UD, 2-D, 3-D and n-D etc. [2, 3]. Among them, even though they are high labor-dependent, carbon fiber rodnetwork n-D preforms have been used for thick (larger than 100 mm thickness) and high performance CC composites, especially for aerospace applications. In general, rod-network n-D CC composites are employing three routes for densification (1) chemical vapor infiltration (CVI) of hydrocarbon gases (2) liquid process with impregnation and pyrolysis of high carbon yield polymers or pitches (liquid process) (3) combination of CVI and liquid process [4]. In CVI process, under suitable conditions, pyrolytic carbon (PC) matrix has a preferred crystalline orientation which results in considerable anisotropy. In pyrolytic graphite (PG) which is more anisotropic than PC, for instance, the thermal expansion in the thickness direction (c direction in graphite structure) is approximately 20 times that in the plane of deposition (ab plane) [5]. Similarly, mechanical properties measured parallel to the ab plane are considerably higher than those measured perpendicular to it. Even though the degree of anisotropy is lower than that of PG, PC anisotropy creates considerable thermal stresses during CC processing, which lead to delaminations between PC matrix and the carbon fiber rods and micro-cracks in PC matrix itself. These delamination defects may be eliminated or at least greatly reduced by the modification of PC microstructure resulting in increase of CC composites performance [6, 7]. High-strength PAN-based carbon fiber (ACELAN TZ-307, Korea) with 12 K manufactured by Taekwang Industries Co., (Korea) was used in the present study. The fiber has tensile strength of 3800 MPa, tensile modulus 260 GPa, elongation 1.3%, and density of 1800 kg/m3 [8]. Polyvinyl alcohol (PVA 110, Kuraray, Japan) was used as a binder for carbon fiber rods preparation. Carbon fiber rods with 1.0 mm diameter were prepared using a typical pultrusion process. Three-D orthogonal rod-network preforms (W 150 × D150 × H200 mm) having 59% fiber volume percent

A multiscale analysis of the hotspot dynamics during the deceleration phase of inertial confinement capsules

This paper is devoted to the study of the deceleration phase of inertial confinement capsules. First the self-similar flow exhibited by Betti et al. [Phys. Plasmas 8, 5257 (2001)] is proved to be an attractor in the sense that arbitrary initial conditions converge towards this solution. The convergence rate depends on the ablation process and heat conductivity and it is shown to be a power law of the increase rate of the hotspot mass. Second the thin layer that separates the hotspot from the cold shell is described and it is shown that it also converges to a locally self-similar profile. By using and generalizing a shell model introduced by Betti et al. [Phys. Plasmas 9, 2277 (2002)] a closed system of ordinary differential equations for the main hydrodynamic variables is derived. Finally the linear growth rates of the deceleration phase Rayleigh–Taylor instabilities are computed taking into account ablation and spherical convergence. Significant differences are exhibited between directly and indirectly driven capsules.

Vertebroplasty and Kyphoplasty in the Treatment of Malignant Vertebral Fractures

SummaryThe purpose of this retrospective study was to assess the effectiveness and safety of Percutaneous Vertebroplasty and Kyphoplasty, in the treatment of pain deriving from neoplastic vertebral compression fractures (VCF).We treated 33 oncologic patients with these new techniques (2 pts with aggressive haemangiomas, 8 pts with myelomas and 23 pts with metastases) suffering from severe motion pain in the back, notwithstanding conservative treatment with medication and corset therapy, in the absence of neurological signs.In 3 selected patients we associated radiofrequency heat ablation with vertebroplasty in the treatment of metastases. The aim is to destroy tumor tissue and to thrombose the paravertebral and intravertebral venous plexus before stabilizing the vertebra.

One-dimensional model for a laser-ablated slab under acceleration

A one-dimensional model for a laser-ablated slab under acceleration g is developed. A characteristic value gc is found to separate two solutions: Lower g values allow sonic or subsonic flow at the critical surface; for higher g the sonic point approaches closer and closer to the slab surface. A significant reduction in the ablation pressure is found in comparison to the g = 0 case. A simple dependence law between the ablation pressure and the slab acceleration, from the initial value g0 to infinity, is identified. Results compared well with fully hydrodynamic computer simulations with Multi2D code. The model has also been found a key step to produce indefinitely steady numerical solutions to study Rayleigh–Taylor instabilities in heat ablation fronts, and validate other theoretical analysis of the problem.

Ablation Studies for a Super-Orbital Reentry Capsule Using a Three-Temperature Model

The aerodynamic heating to a super-orbital reentry capsule with ablation heat protection was studied numerically by using thermochemical nonequilibrium full-viscous-shock layer (VSL) equations. A species model composed of 11 air species and 6 carbonic species was used. In the case of the super-orbital reentry, radiative heat flux to the wall cannot be neglected. The intensity of emission spectrum is strongly dependent on rotational, vibrational, electron and electronic temperatures, so that a thermal nonequilibrium analysis is needed to predict these temperatures more accurately. Therefore, a 3-temperature model composed of translational-rotational, vibrational and electron-electronic temperatures was adopted. Stagnation heat fluxes to the wall with and without ablation were calculated at various wall temperatures. Results for the reentry flight conditions at an altitude of 64 km showed that the stagnation heat fluxes with and without ablation are almost equal below a wall temperature of 3,200 K, whereas at wall temperatures over 3,200 K, the stagnation heat flux is reduced owing to significant sublimation of ablation material.

Leonid meteor ablation, energy exchange, and trail morphology

This paper describes theoretical model studies of the interaction of Leonid meteoroids with the earth’s atmosphere. Subject to some modest-to-strenuous approximations we compute the rates of ablation and deceleration, energy deposition, and terminal altitudes of the meteors as functions of their initial mass and bulk density, velocity, trajectory entry angle, drag coefficient, heat of ablation, and an ablation energy transfer fraction. We find that the dominant energy deposition in the atmosphere is associated with the stopping of the ablated meteor particles and vapor by the surrounding air. Then having computed the energy deposition rates vs. altitude we compute the hydrodynamic and radiative expansion of the hot wake material in the radial direction, along with the associated air chemistry. From the computed results we can then plot two-dimensional temperature contours – as functions of the instantaneous distance behind the meteor and radial distance from the center of the wake, at various altitudes along the meteor’s path. We also compute the rates of emission of radiation and the radiative efficiency, and discuss comparisons with observations.

Percutaneous ultrasound-guided radiofrequency heat ablation for treatment of hyperthyroidism in cats.

To determine efficacy and safety of percutaneous radiofrequency heat ablation for treatment of hyperthyroidism in cats. Prospective study. 9 cats. Hyperthyroidism was diagnosed via clinical signs and high serum total (TT4) and free thyroxine (fT4) concentrations. One or 2 hyperfunctional cervical thyroid nodules were detected by use of scintigraphy and ultrasonography. If cats had 1 abnormal thyroid lobe, heat ablation was performed on that lobe; if cats had 2 abnormal lobes, heat ablation was applied to the larger lobe. Overall, heat ablation was performed 14 times in the 9 cats. Clinical signs and serum TT4, fT4, and calcium concentrations were monitored daily for 2 days after the procedure, weekly for the first month, and then monthly. Laryngeal function was evaluated and cervical ultrasonography and thyroid scintigraphy were also performed. Monitoring continued for as long as 9 months after heat ablation if a cat became euthyroid or until an owner chose an alternative treatment because of recurrence of hyperthyroidism. Serum TT4 and fT4 concentrations transiently decreased after all 14 heat ablation procedures (< or = reference range after 10 of 14 treatments) within 2 days after the procedure. Cats were euthyroid for 0 to 18 months (mean, 4 months). Hyperthyroidism recurred in all cats. Adverse effects included transient Horner's syndrome (2 cats) and laryngeal paralysis without clinical signs (1 cat). Percutaneous heat ablation as a treatment for hyperthyroidism in cats is effective transiently but not permanently.

Renal cell carcinoma: modern surgical approach.

In the past decade, minimally invasive therapy options for renal cell carcinoma have been devised in an attempt to minimize operative morbidity while achieving comparable oncologic and functional outcomes. Herein, we evaluate the new developments related to the modern surgical and energy ablative techniques for renal cell carcinoma. When compared with the open counterpart, laparoscopic radical and partial nephrectomies have equivalent operative time, decreased blood loss, superior recovery, and improved cosmesis. Nowadays, laparoscopic radical nephrectomy can be performed for pT2 tumors (up to 15 cm), and level I renal vein thrombus is not a formal contraindication for the laparoscopic procedure. Ongoing advances in laparoscopic techniques and operator skills have allowed the development of a reliable technique of laparoscopic partial nephrectomy, which includes the ability to achieve effective intracorporeal renal hypothermia. Cryoablation and radiofrequency ablation therapies have been performed through a laparoscopic or percutaneous approach, using a combination of fine probes and high-resolution imaging studies to precisely target the lesions and accurately monitor the freezing or heating ablation process. Noninvasive tumor ablation can now be achieved by extracorporeally induced high-intensity focused ultrasound. These minimally invasive techniques represent the modern surgical approach for renal cell carcinoma, aiming to decrease patient morbidity. Laparoscopic radical and partial nephrectomy techniques duplicate the open approach. Results obtained with energy ablative techniques are encouraging. Based on the known slow growth rates of small renal cell carcinoma, one should be cautious when interpreting the short-term results of energy ablative therapies monitored by imaging only.

Soft and hard tissue ablation with short-pulse high peak power and continuous thulium-silica fibre lasers

Thulium lasers operating near approximately 2 microm are the subject of interest for various medical applications. The newly developed Tm3+ silica fibre laser in Q-switched and CW operation was investigated to determine its efficiency in the interaction with soft and hard tissues. The interaction was investigated using a free-running continuous (CW) Tm(3+)-doped fibre laser (wavelength 1.99 microm, with self-pulsation ranging over 1 to few tens of microseconds) and for novel Q-switched operation of the same fibre laser (pulse durations from 150 to 900 ns and pulse repetition rates from 100 Hz to 17 kHz). Residual damage and affected zones using the Q-switched laser were nearly six times smaller than using the CW fibre laser for about 50 s of exposure time, and increased with pulse repetition rate. The energy required to ablate tissue with the Q-switched fibre laser ranged from 0.2 to 0.6 kJ/cm3 and was significantly smaller than that for the CW fibre laser of 153 to 334 kJ/cm3. Under both high-resolution reflected optical microscopy and histological examination, tissue crater depths were observed as cleanly cut with smooth walls and minimal charring in the case of Q-switched operation of the fibre laser. This study is the first direct comparison of tissue interaction of short-pulse (Q-switched) and CW Tm(3+)-doped silica fibre lasers on crater depth, heat of ablation and collateral damage. The Q-switched Tm(3+)-doped silica fibre laser effectively ablates tissue with little secondary damage.

Diagnostic follow-up imaging: “Achilles heel” of performing radiofrequency heat ablation in lung malignancies

Purpose: To report on the successful radiofrequency heat ablation (RFA) in a patient with a bronchiogenic carcinoma verified by a combined imaging modality using computed tomography (CT) and 18-fluorodeoxyglucose ( 18FDG)-positron emission tomography (PET) in a follow-up period of 6 months. Methods: RFA was the favored treatment option for the 2.3×2.3 cm large brochiogenic carcinoma located in the right upper lobe. For this purpose a thermal lesion was created using a 15-gauge LeVeen™ Needle Electrode with an array diameter of 3.0 cm. Follow-up CT scans were performed at 3 and 6 months after RFA. In order to exclude metabolically active residual tumor 18FDG-PET was obtained 6 months after RFA. Results: Follow-up CT scan 3 months after RFA showed a slight increase in diameter of the treated tumor, presumably due to dystelectasis, surrounding hematoma or inflammation and granulation tissue. In line with the CT scan 6 months after RFA, which revealed shrinkage of the treated lesion according to scar formation; additionally the metabolic activity seen in whole body 18FDG-PET was not suspicious for viable tumor. Conclusion: Functional imaging like 18FDG-PET seems to be an important adjunct to CT in the early detection of local tumor recurrence after RFA of lung malignancies.

Combined Treatment of a Spinal Metastasis with Radiofrequency Heat Ablation and Vertebroplasty

Combined Treatment of a Spinal Metastasis with Radiofrequency Heat Ablation and VertebroplastyOliver Schaefer1, Christian Lohrmann1, Max Markmiller2, Peter Uhrmeister1 and Mathias Langer1Audio Available | Share

Numerical Study of Transient Thermal Ablation of High-Temperature Insulation Materials

A physical model has been developed to describe the transient ablation phenomena of high-temperature insulation materials for the cases with and without the formation of a melt layer on the material surface. The model takes account of the effects of transient melt-layer formation, variable ablation temperatures, and heat of ablation of the material. Validity of the model has been demonstrated numerically by comparison with available analytical solutions for the special case of a constant ablation temperature. For the general case of variable ablation temperatures, appreciable differences in the predicted ablation rates have been found between the cases with and without melt-layer formation for materials having low heats of ablation and for large imposed external heat fluxes. The present study clearly indicates that the melt-layer effect cannot be neglected at high external heat fluxes, especially for materials such as MXBE-350 that have low heats of ablation.

Combined Radiofrequency Thermal Ablation and Percutaneous Cementoplasty Treatment of a Pathologic Fracture

Skeletal metastases commonly occur in patients with cancer and treatment is necessary to alleviate pain and prevent complications, such as mobility deficiencies and pathologic fractures. The authors present a patient with a stage IV malignant melanoma and a pathologic fracture of the left tibial plateau treated with radiofrequency heat ablation and percutaneous cementoplasty for defect filling and stabilization. The authors believe that this approach may be an alternative to the standard treatments in palliative-care situations.

Locoregional therapies for hepatocellular carcinoma: a critical review from the surgeon's perspective.

This article reviews the current results of various locoregional therapies for hepatocellular carcinoma (HCC), with special reference to the implications for surgeons. Resection or transplantation is the treatment of choice for HCC, but most patients are not suitable candidates. The past decade has witnessed the development of a variety of locoregional therapies for HCC. Surgeons are faced with the challenge of adopting these therapies in the management of patients with resectable or unresectable HCC. A review of relevant English-language articles was undertaken based on a Medline search from January 1990 to August 2001. Retrospective studies suggested that transarterial chemoembolization is an effective treatment for inoperable HCC, but its perceived benefit for survival has not been substantiated in randomized trials, presumably because its antitumor effect is offset by its adverse effect on liver function. Nonetheless, it remains a widely used palliative treatment for HCC not amenable to resection or ablative therapies, and it also plays an important role as a treatment of postresection recurrence and as a pretransplant therapy for transplantable HCC. Better patient selection, selective segmental chemoembolization, and treatment repetition tailored to tumor response and patient tolerance may improve its benefit-risk ratio. Transarterial radiotherapy is a less available alternative that produces results similar to those of chemoembolization. Percutaneous ethanol injection has gained wide acceptance as a safe and effective treatment for HCCs 3 cm or smaller. Uncertainty in tumor necrosis limits its potential as a curative treatment, but its repeatability allows treatment of recurrence after ablation or resection of HCC that is crucial to prolongation of survival. Cryotherapy affords a better chance of cure because of predictable necrosis even for HCCs larger than 3 cm, but its use is limited by a high complication rate. There has been recent enthusiasm for heat ablation by microwave, radiofrequency, or laser, which provides predictable necrosis with a low complication rate. Preliminary data indicated that radiofrequency ablation is superior to ethanol injection in the radicality of tumor ablation. The advent of more versatile radiofrequency probes has allowed ablation of HCCs larger than 5 cm. Recent studies have suggested that combined transarterial embolization and heat ablation is a promising strategy for large HCCs. Thus far, no randomized trials comparing various thermoablative therapies have been reported. It is also uncertain whether a percutaneous route, laparoscopy, or open surgery affords the best approach for these therapies. Thermoablative therapies have been combined with resection or used to treat postresection recurrence, and they have also been used as a pretransplant therapy. However, the value of such strategies requires further evaluation. Advances in locoregional therapies have led to a major breakthrough in the management of unresectable HCC, but the exact role of the various modalities needs to be defined by randomized studies. Novel thermoablative techniques provide the surgeon with an exciting opportunity to participate actively in the management of unresectable HCC. Locoregional therapies are also useful adjuncts in the management of patients with resectable or transplantable disease. Hence, surgeons must be equipped with the latest knowledge and techniques of ablative therapy to provide the most appropriate treatment for the wide spectrum of patients with HCC.

Energy transfer via a thermal capillary

Thermal radiation transfer in a cylindrical hohlraum is discussed. The mass and energy conservation equations for the ablated wall material, derived from the self-similar solution for ablative heat wave [R. Pakula and R. Sigel, Phys. Fluids 28, 232 (1985)], and coupled flux conservation equation, are solved to investigate energy redistribution inside the hohlraum. A similarity solution is obtained for a gold capillary heated by a uniform disc source, with which the re-emission flux from the wall and the energy transfer efficiency through the thermal capillary are calculated for different parametric conditions.