Empirical Mathematical Model Research Articles

Quantitative evaluation of simultaneous spatial and temporal regularization in dynamic contrast-enhanced MRI of the liver using Gd-EOB-DTPA

The purpose of this study was to quantitatively evaluate the usefulness of simultaneous spatial and temporal regularization using total variation (TV), total generalized variation (TGV), a combination of low-rank decomposition (LRD) and TV (LRD+TV), a combination of LRD and TGV (LRD+TGV), and nuclear norm (NN) when applied to dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) in rats with concanavalin A (ConA)-induced acute hepatic injury.The rats were divided into three groups: normal control (NC) (n = 10), ConA10 (n = 8), and ConA20 (n = 7). Rats in the ConA10 and ConA20 groups were intravenously injected with 10 and 20 mg/kg of ConA, respectively; those in the NC group were intravenously injected with the same volume of saline. DCE-MRI studies were performed using gadolinium ethoxybenzyl diethylenetriamine pentaacetic acid (Gd-EOB-DTPA; 0.025 mmol Gd/kg) as a contrast agent (CA), 24 h after the ConA or saline injection. After the DCE-MRI study, we generated zero-filled and undersampled k-space data from the original images using a pseudoradial sampling scheme with 4 to 64 spokes. We subsequently reconstructed images from these data using the above regularizers and calculated the signal-to-error ratio (SERimg) and structural similarity index measure (SSIM) using the original and reconstructed images. We also calculated the area under the curve (AUC), rate of CA washout (λw), maximum relative enhancement (REmax), and time to REmax (Tmax) from time-intensity curves using an empirical mathematical model (EMM) and the signal-to-error ratio for curve fitting (SERfit) from the original and fit curves. We also compared the parameters obtained using the pseudoradial and Cartesian sampling schemes in the NC group.When using LRD+TV and LRD+TGV, both SERimg and SSIM were greater than those for the other regularizers at all spoke numbers studied; the SERfit for TGV was the greatest. When using TGV and LRD+TGV, in the majority of cases the AUCs did not significantly differ from those obtained from the original images, whereas those for LRD+TV and NN were significantly less at several spoke numbers. The λw for NN was significantly greater at numerous spoke numbers in the NC group; the REmax values for LRD+TV and NN were significantly less at several spoke numbers in all groups. The Tmax values for TV, TGV, and LRD+TGV were significantly greater at numerous spoke numbers in the NC group. Although there were significant differences in SERimg and SSIM between the pseudoradial and Cartesian sampling schemes, the kinetic parameters obtained by the EMM did not significantly differ between the two sampling schemes, with certain exceptions.In conclusion, our results suggest that simultaneous spatial and temporal regularization using TGV or LRD+TGV is useful for accelerating DCE-MRI without significant reduction in the accuracy of the kinetic parameter estimation, even at extremely low sampling factors.

Tensile Strength of Threaded Rods Made by 3D Printing of Polymeric Material

The extension of 3D printing processes for parts made of polymeric materials highlighted the possibility of manufacturing threaded surfaces through such processes. In principle, the operation of a threaded joint involves tensile forces in the threaded rod. The dimensional characteristics of the threaded surface and some input factors in the 3D printing process can influence the tensile strength of threaded rods made of polymeric materials. An experimental research aimed at the tensile behavior of a threaded joint was designed, using a plastic screw and a special steel nut. A factorial experiment was designed and implemented to identify an empirical mathematical model capable of highlighting the influence of the dimensional characteristics of the threaded surface and some of the input factors in the 3D printing process on tensile strength. The test samples from polymeric materials were manufactured by 3D printing, then subjected to tensile tests. The mathematical processing of the experimental results allowed the determination of a mathematical model that allows the inclusion of the ordering of the factors taken into account in terms of the intensity of the influence that these factors exert on the tensile strength of the threaded rods. It was found that the diameter of the threaded rod exerts the strongest influence on the tensile strength of the threaded rod obtained by 3D printing, increasing the diameter of the threaded rod causing an increase in the maximum deformation of the rod. Increasing the thread pitch leads to a decrease in the maximum deformation of the threaded rod.

Ultrafast Dynamic Contrast-enhanced MRI of the Breast: How Is It Used?

Ultrafast dynamic contrast-enhanced (UF-DCE) MRI is a new approach to capture kinetic information in the very early post-contrast period with high temporal resolution while keeping reasonable spatial resolution. The detailed timing and shape of the upslope in the time–intensity curve are analyzed. New kinetic parameters obtained from UF-DCE MRI are useful in differentiating malignant from benign lesions and in evaluating prognostic markers of the breast cancers. Clinically, UF-DCE MRI contributes in identifying hypervascular lesions when the background parenchymal enhancement (BPE) is marked on conventional dynamic MRI. This review starts with the technical aspect of accelerated acquisition. Practical aspects of UF-DCE MRI include identification of target hypervascular lesions from marked BPE and diagnosis of malignant and benign lesions based on new kinetic parameters derived from UF-DCE MRI: maximum slope (MS), time to enhance (TTE), bolus arrival time (BAT), time interval between arterial and venous visualization (AVI), and empirical mathematical model (EMM). The parameters derived from UF-DCE MRI are compared in terms of their diagnostic performance and association with prognostic markers. Pitfalls of UF-DCE MRI in the clinical situation are also covered. Since UF-DCE MRI is an evolving technique, future prospects of UF-DCE MRI are discussed in detail by citing recent evidence. The topic covers prediction of treatment response, multiparametric approach using DWI-derived parameters, evaluation of tumor-related vessels, and application of artificial intelligence for UF-DCE MRI. Along with comprehensive literature review, illustrative clinical cases are used to understand the value of UF-DCE MRI.

Water uptake kinetics in soaking of grass pea

Grass pea (Lathyrus sativus) is a pulse of great importance for food and feed due its high resistance to poor environmental conditions. However, it contains anti-nutritional factors and a neurotoxin, which is partially lost during soaking. A first approach to mass transfer during the soaking of grass pea was carried out by modeling the water uptake during soaking time using empirical mathematical models. The water uptake behavior was successfully described by the Peleg and the Exponential models, with these models showing several advantages when compared to the Mitscherlich and Page models. Both models estimated an increase of the equilibrium moisture content at temperatures between 50 °C and 100 °C, and detected an increasing effect of the area per volume ratio of the seed on the water uptake rate, but only at 75 °C and 100 °C. Additionally, grass pea presented a high true porosity, 13.651%, showing that it contains a large empty volume into which water can enter by capillary flow. Solids loss was observed to be high, varying from 18% at 25 °C to 44% at 100 °C for long soaking times, confirming that its effect in soaking cannot be neglected.

Development of Empirical Models for the Estimation of CBR Value of Soil from Their Index Properties: A Case Study of the Ogbia-Nembe Road in Niger Delta Region of Nigeria

This study developed empirical-mathematical models to predict the California Bearing Ratio (CBR) using soil index properties in Ogbia-Nembe road in the Niger Delta region of Nigeria. The determination of CBR of soil is a laborious operation that requires a longer time and materials leading to increased cost and schedule; this can be reduced by adopting an empirical-mathematical model that can predict the CBR using other simpler soil index properties such as Plastic Limit (PL), the Liquid Limit (LL), the Plasticity Index (PI) and the Moisture Content (MC), which are less laborious and take lesser time to obtain. Thirteen models were developed to understand the relationship between these soil index properties: the independent variable and the California Bearing Ratio (CBR): the dependent variable; Six linear, Six quadratic and One multiple linear regression models were developed for this relationship. Analysis of variance (ANOVA) on the thirteen models showed that the Optimum Moisture Content (OMC) and the Maximum Dry Density (MDD) are better independent variables for the prediction of the CBR value of Ogbia-Nembe soil generating a quadratic model and a multiple linear regression model having a better coefficient of determination R2 = 0.96 and 0.94 respectively, mean square error (MSE) of 0.74 and 1.152 respectively with Root mean square errors of 0.861 and 1.073 accordingly. These models were used to predict the CBR of the soil. The CBR values predicted by the model were further compared with those of the actual experimental test and found to be relatively consistent with minimal variance. This establishes that CBR of any soil can be predicted from the Index Property of the soil and this is more economical and takes lesser time and can be universally adopted for soil investigation.

Mathematical modeling of solids-drilling fluid separation in shale shakers in oil fields: A state of art review

The solids control system originated from oil well drilling recovers the fluid for reuse and ensures compliance with environmental legislation that defines the conditions for solids disposal. The first step of this system is the separation of mud formed by gravels with different granulometry and aqueous or oily base drilling fluid in vibrating shale shakers. In this review three characteristic regions of the screening screen are identified, according to the content of solids and fluid present: drainage region, drying region and beach region. In order to evaluate the efficiency of the separation in the sieves, predict the influence of operational and geometric parameters on the separation, a broad review of empirical and phenomenological mathematical models is presented. The models are classified in: models based on screening kinetics, probabilistic models, models based on the coupling between the Discrete Element Model and the Smoothed Particle Hydrodynamics, cake formation models, Lattice Models and analogy with capillary tubes.

The Influence of Lubrication on the Roughness of the Vibroburnished Surface

One of the processes by which hardening of the surface layer and diminishing the heights of the surface roughness occur in the case of steel parts is vibroburnishing. The analysis of the conditions of using the vibroburnishing process of the cylindrical surfaces showed that the use of lubrication could influence the heights of the asperities resulting from the processing. The problem of conducting experimental research was formulated to highlight the intensity of the influence exerted by some input factors in the vibroburnishing process on the roughness of the processed surfaces, evaluated by using the roughness parameter Ra. An experimental program was designed aiming to use different values of ball diameter, ball pressing force, and initial roughness, in conditions of dry vibro-burnishing and using lubricating oil, respectively. The experimental results were processed using a software based on the least-squares method. The determined empirical mathematical models showed that, under the conditions in which the experimental tests were performed, the strongest influence on the value of the roughness parameter Ra is exerted by the initial surface roughness, followed by the size of the ball pressing force on the surface and by the ball diameter, the latter exerting very little influence. It was confirmed that the presence of a lubricant in the processing area results in a decrease in the size of the roughness parameter Ra, compared to the situation where such a lubricant is not used.

3D Pore Structure Characterization of Stored Grain Bed

Highlights An image analysis for reconstruction of 3D pore structure within bulk grain was presented. Mathematical models for porosity and tortuosity were developed from the 3D reconstructed images. The mathematical models can be incorporated in computational model of flow through bulk grains. Abstract. An image analysis technique for reconstruction of the complex 3D pore structure within bulk grain from 2D section images was presented. The technique relies on aligning successive 2D images of cut-sections obtained from colored-wax solidified soybean grain beds, which were then subjected to image processing using ImageJ software developed by the National Institute of Health (NIH, Bethesda, Md.) for the reconstruction and visualization of different airflow paths within the bulk grain. Porosity and tortuosity values were quantified from the 3D image volume and 3D reconstructed inter-connected airflow paths to develop empirical mathematical models for predicting porosity and tortuosity as a function of compaction due to the pressure exerted by the grain depth. Results indicated that the rate of decrease in porosity was higher at the lower compaction grain depth and then gradually approached a minimum value as the compaction grain depth increased. At the top of the compacted grain, the porosity of the tested soybean bed was determined to be 0.42 and reduced to 0.34 at a compaction pressure of 14.2 kPa (equivalent to a compaction grain depth of 25 m). Tortuosity increased with the compaction pressure from 1.15 to 1.58 at a compaction pressure of 14.2 kPa (equivalent to 25 m of grain depth), or by 37.4%. Keywords: Grain bed, Image analysis, Pore structure, Porosity, Tortuosity.

Compact Empirical Model for Droplet Generation in a Lab-on-Chip Cytometry System

This study describes the construction of a compact empirical mathematical model for a flow-focusing microfluidic droplet generator. The application case is a portable, low-cost flow cytometry system for microbiological applications, with water droplet sizes of 50-70 micrometer range and droplet generation rates of 500-1500 per second. In this study, we demonstrate that for the design of reliable microfluidic systems, the availability of an empirical model of droplet generation is a mandatory precondition that cannot be achieved by time-consuming simulations based on detailed physical models. When introducing the concept of a compact empirical model, we refer to a mathematical model that considers general theoretical estimates and describes experimental behavioral trends with a minimal set of easily measurable parameters. By interpreting the experimental results for different water- and oil-phase flow rates, we constructed a minimal 3-parameter droplet generation rate model for every fixed water flow rate by relying on submodels of the water droplet diameter and effective ellipticity. As a result, we obtained a compact model with an estimated 5-10% accuracy for the planned typical application modes. The main novelties of this study are the demonstration of the applicability of the linear approximation model for droplet diameter suppression by the oil flow rate, introduction of an effective ellipticity parameter to describe the droplet form transformation from a bullet-like shape to a spherical shape, and introduction of a machine learning correction function that could be used to fine-tune the model during the real-time operation of the system.

Empirical mathematical model of change in the actual contact area of metals depending on the friction path

Empirical mathematical model of change in the actual contact area of metals depending on the friction path

Modeling and Simulation of Rock Bits Based on Mega Drilling Data

Rock bits directly undertake the task of fracturing rock under earth during drilling operation. Accurate prediction of Rate of penetration (ROP) play an important role in reducing drilling costs and shortening the drilling cycle. This paper introduces ROP prediction methods including empirical mathematical modeling, computer simulation of bit-rock interaction and BP neural network model based on mega drilling data. The most significant factors affecting ROP are summarized as follows: weight on bit(WOB), rotation speed, rock formation properties, bit cutting structure, etc., which have a complex multi-parameter nonlinear relationship with ROP. The drilling data features complexity and big volume. Therefore machine learning is a best way to model the relationship between main factors and ROP. The advantages and disadvantages of the different ROP modeling methods are analyzed and compared. It shows that the BP neural network model based on mega drilling data demonstrates high accuracy, and is the future development direction in ROP prediction.

Exploring strategies to control the cost of food security: Evidence from Bangladesh

CONTEXTA classical challenge in the search for principles and guidelines to protect food security affordably in the developing world comes from the well-known dilemma faced by farmers who incur economic losses from low prices brought on by excess production combined with poorly developed policies to anticipate, adapt to, and manage production and price fluctuations. This challenge is elevated in the face of growing evidence of climate change. OBJECTIVEThis work performs a series of policy experiments to discover an affordable set of measures to protect food grain security as well as assure profitability of high valued crops in Bangladesh. METHODSThis work uses primary and secondary data from Bangladesh agriculture to develop an empirical mathematical programming economic optimization model to achieve each of four alternative food policy objectives. RESULTS AND CONCLUSIONSResults show total economic welfare achievable under each policy objectives: protecting baseline observed farm sector outcomes, minimum protection of food grain security, protection of farm income from producing high value crops, and unconstrained food welfare optimization. The application is to an important farming region of northwest Bangladesh. We find that policymakers can achieve both food grain security and farm income from high value crops at a minimum cost of economic welfare displaced. SIGNIFICANCEThe use of empirical models that describe and predict farm economic optimization behavior can provide guidance in the search for affordable policies for protecting food grain security while protecting farm income in the developing world.

A Study on the Relationships between Water Film Thickness, Fresh Properties, and Mechanical Properties of Cement Paste Containing Superfine Basalt Powder (SB).

In this paper, the effect of a newly developed superfine basalt powder (SB) on the fresh and mechanical properties of cement paste was studied. The concept of water film thickness (WFT) was cited to explain the influence of SB on fresh and mechanical properties and related mathematical model formulas were established. In addition, the relationship between the fresh properties and mechanical properties of paste was also explored. The results indicated that SB can improve the segregation resistance and cohesiveness. The maximum improvement rate relative to the control cement paste was 75.4% and 50.4%, respectively. The 5% SB and 10% SB reduced the fluidity in the range of 4.1–68.7% but increased the early and late compressive strength in the range of 1.2–25.7% compared to control cement paste under different water/cementitious materials (W/CM) ratios. However, the influence of 20% SB on fluidity and compressive strength was opposite to the above behavior, and the increase rate and decrease rate were 1.8–11.8% and 1.1–13.9% respectively. The WFT was the most important factor that determined the compressive strength, rheological parameters, and flow parameters of paste containing SB, while the substitute content of SB and WFT together determined the bleeding rate and cohesiveness. Among them, the correlation between bleeding rate and WFT increased with time. The empirical mathematical models between WFT, fresh properties, and compressive strength were established and verified by other mineral admixtures, which were successfully extended and applied to the entire field of cement-based materials.

A Mathematical Model for Dehydration by Successive Pressure Drops: Simulation of Discarded Potatoes Dehydration

Dehydration by Successive Pressure Drops (SPD) is a process with high potential for treating heat-sensitive materials; this includes agro-industry by-products. However, the response of drying kinetics to operating conditions of SPD is not fully understood. The present manuscript refers to mathematical simulations to describe drying kinetics of discarded potatoes using SPD. While there are numerous theoretical, semi-theorical and empirical mathematical models, the selection of the appropriate model is a rigorous process. In this paper, the Thompson thin-layer semi-theoretical model was chosen since the assumptions for this model (e.g., product is arranged in thin layers) are fulfilled for the SPD. As a result of mathematical simulation, it was possible to describe the drying kinetics in terms of the major parameters of SPD namely pressurizing level (Pa) and the Frequency of Pressure Drop (FPD). The dehydration by SPD allows the removal of water from the material, mainly at the pressure drop. If this stage occurs more frequently, the drying rate increases. The model developed describes at less 91% of the variability of the experimental data. It is recommended to use high FPD and Pa equals to 0.50 MPa.

Determination of the Sun‐Climate Relationship Using Empirical Mathematical Models for Climate Data Sets

AbstractPrevious studies have reported that human influences are required to explain the observed global warming using a linear model (LM) that relates change in solar forcing to change in global mean temperature (GMT) . This model has the shortcoming of assuming a given causes the same irrespective of the value of the initial global warming rate . Analysis of the GMT data showed that this warming rate has been increasing linearly since steady state ( for year ) as given by , where °C/year2 is the secular GMT acceleration and is the number of years of the change. The secular solar forcing due to 18% of the 11 yr solar cycle forcing of 0.19 W/ (0.08% of Total Solar Irradiance) was expressed as . Defining the climate sensitivity as °C/year per W/ removed the shortcoming of the LM and integration of the model for above and then simplifying gave a secular GMT‐solar forcing model given by that explained all of the observed global warming and increase in atmospheric , sea level and ocean heat content. Therefore, for this nonlinear empirical model, invoking human influences to explain climate change was not required. The annual GMT model predicts a pause in global warming until 2040.

Development of a modified serum-free medium for Vero cell cultures: effects of protein hydrolysates, l-glutamine and SITE liquid media supplement on cell growth.

Vero cells have been widely used in the viral vaccine production due to the recommendation of the World Health Organization regarding its safety and non-tumorigenicity. The aim of this study was to describe the development a modified serum-free medium for Vero cell cultures. Two protein hydrolysates (Bacto™ soytone and Bacto™ yeast extract), vitamin C, vitamin B12, SITE liquid media supplement, and recombinant human epidermal growth factor (rEGF) were investigated as serum substitutes. A sequential experiment of fractional factorial and central composite design was applied. A modified serum-free medium obtained (named as SFM01-M) was verified. Contrary to P0, the cell yields obtained at P1, P2, and P3 decreased continuously during the verification experiments indicating that Vero cells could not adapt to SFM01-M as expected according to the empirical mathematical model. To improve cell growth after P0, protein hydrolysates, l-glutamine, and SITE liquid media supplement were further investigated. The results showed that cell yields gradually decreased from P1 to P3 when a fixed concentration of Bacto™ yeast extract (7.0g/L) combined with various concentrations of Bacto™ soytone (0.1-7.0g/L) in SFM01-M were used. Similarly, cell yields also gradually decreased from P1 to P3 when a fixed concentration of Bacto™ soytone (7.0g/L) combined with various concentrations of Bacto™ yeast extract (0.1-7.0g/L) in SFM01-M were used. However, the combination of Bacto™ soytone at 0.1g/L and Bacto™ yeast extract at 7.0g/L or Bacto™ soytone at 7.0g/L and Bacto™ yeast extract at 0.1g/L in SFM01-M could give the maximum cell yield at P3 when compared with other combinations. In addition, the addition of SITE liquid media supplement (0.1-2.0% v/v) in SFM01-M in which the concentrations of Bacto™ soytone, Bacto™ yeast extract, and l-glutamine were fixed at 0.1g/L, 0.1g/L, and 4.0mM, respectively, the results showed that the cell yields obtained at P3 were not significantly different. From this study, the optimum concentrations of SFM01-M components were as follows: Bacto™ soytone (0.1g/L), Bacto™ yeast extract (0.1g/L), vitamin C (9.719mg/L), vitamin B12 (0.1725mg/L), SITE liquid media supplement (0.1-2.0% v/v), rEGF (0.05756mg/L), l-glutamine (4.0mM), MEM non-essential amino acids (1.0% v/v), sodium pyruvate (1.0mM), MEM (9.4g/L), and sodium hydrogen carbonate (2.2g/L). However, to evaluate SFM01-M in the long-term subculture of Vero cells, the efficiency of SFM01-M will be further investigated.

Hybrid infrared with hot air drying of Pisang‐Awak banana: Kinetics and shrinkage quality

AbstractThe purpose of this study was to develop the prototype drying system for drying the Pisang‐Awak (PA) banana. It was designed and implemented to study the drying kinetics in each drying mode: hot air drying (HA), infrared drying (IR), and hybrid drying (Hy). The experimental results were fit with simulation results from the finite element method (FEM). Two statistical parameters, the coefficient of determination and the root mean square error , were used to assess the fit between experimental results and simulation results, and their respective ranges were 0.960–0.997 and 0.014–0.050. For PA banana drying the most suitable drying mode is hybrid, combining 1.5 m/s flow of hot air and IR heating at 60°C drying temperature. The axial and radial shrinkages of PA banana were the largest in Hy mode at 60°C, namely 18.2 and 27.3%, respectively, and this choice gave the best/lowest specific energy consumption (SEC) for drying performance and the best final dried PA banana.Practical ApplicationsThe understanding of the drying kinetics and shrinkage properties of the dried PA banana is important for the choice of drying process because these reflect the quality of the dried product and help an engineer to design the drying system. Therefore, the empirical mathematical modeling of the drying process serves a crucial role in the food industry sector. These results can be used to quantify temperature and moisture content as functions of drying time to monitor the drying process of PA banana, saving energy and time.

Mathematical models of water surface for geodetic support of construction in agro-industrial complex

The purpose of the study was to analyze the possibilities of using mathematical models of the water (level) surface of rivers and reservoirs for the transfer of elevations. The use of an empirical mathematical model obtained for the Irtysh River near the city of Omsk makes it possible to determine the heights in the investigated area with an accuracy of about 0.1 m. To determine the level of the water edge at the selected area, it is necessary to obtain: the mark of the water edge at the gauging station; the distance along the river from the gauging station to the work site. It is advisable to fix the water level at the gauging station and the work site simultaneously. For the elevation transfer from one river bank to another by the III class leveling program, the authors propose the technology of laying temporary benchmarks on the banks, fixing the level using special devices, and transferring the elevations of the fixed water level to temporary benchmarks. The technology contains the devices of simple design for accurate level fixing. The factors influencing the accuracy of the height transmission are: fixing the water level, the centrifugal forces of the flow, the Coreolis force caused by the rotation of the Earth, and the wind surge. The authors calculated the expected values of errors determining the accuracy: for fixing the level it was about 1 mm according to the proposed method; the height difference at the banks due to the forces of Coreolis was 0.007 m; the influence of centrifugal forces at a turning radius of 500 m causes a difference in heights at opposite banks of 0.1 m. In the result, the authors proposed the recommendations developed for transferring heights from one river bank to another using a class III leveling program, which ensure the specified accuracy.

Эффективность применения технологии скоростного торцевого фрезерования деталей топливной аппаратуры ГТД из закалённых сталей

There are shown results of high-speed end milling experimental researches of critical hardened steel parts in fuel control equipment of modern aircraft gas turbine engines (GTE) with the purpose of optimum cutting mode definition ensuring the roughness Ra ≤ 0.63 mkm for the surface worked and deviation from the plane not more than 0.015 mm. The empirical mathematical models of high-speed milling are obtained and optimum cutting modes are defined.

Evaluation of the Ability to Accurately Produce Angular Details by 3D Printing of Plastic Parts

3D printing is a process that has become widely used in recent years, allowing the production of parts with relatively complicated shapes from metallic and non-metallic materials. In some cases, it is challenging to evaluate the ability of 3D printers to make fine details of parts. For such an assessment, the printing of samples showing intersections of surfaces with low angle values was considered. An experimental plan was designed and materialized to highlight the influence of different factors, such as the thickness of the deposited material layer, the printing speed, the cooling and filling conditions of the 3D-printed part, and the thickness of the sample. Samples using areas in the form of isosceles triangles with constant height or bases with the same length, respectively, were used. The mathematical processing of the experimental results allowed the determination of empirical mathematical models of the power-function type. It allowed the detection of both the direction of actions and the intensity of the influence exerted by the input factors. It is concluded that the strongest influence on the printer’s ability to produce fine detail, from the point of view addressed in the paper, is exerted by the vertex angle, whose reduction leads to a decrease in printing accuracy.