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PURPOSE: Deformable image registration (DIR) has been increasingly used in radiation therapy (RT). The accuracy of DIR algorithms and how it impacts on the RT plan dosimetrically were examined in our study for abdominal sites using biomechanically modeled deformations. METHODS: Five pancreatic cancer patients were enrolled in this study. Following the guidelines of AAPM TG-132, a patient-specific quality assurance (QA) workflow was developed to evaluate DIR for the abdomen using the TG-132 recommended virtual simulation software ImSimQA (Shrewsbury, UK). First, the planning CT was deformed to simulate respiratory motion using the embedded biomechanical model in ImSimQA. Additionally, 5 mm translational motion was added to the stomach, duodenum, and small bowel. The original planning CT and the deformed CT were then imported into Eclipse and MIM to perform DIR. The output displacement vector fields (DVFs) were compared with the ground truth from ImSimQA. Furthermore, the original treatment plan was recalculated on the ground-truth deformed CT and the deformed CT (with Eclipse and MIM DVF). The dose errors were calculated on a voxel-to-voxel basis. RESULTS: Data analysis comparing DVF from Eclipse versus MIM show the average mean DVF magnitude errors of 2.8 ± 1.0  versus 1.1 ± 0.7 mm for stomach and duodenum, 5.2 ± 4.0  versus 2.5 ± 1.0 mm for small bowel, and 4.8 ± 4.1  versus 2.7 ± 1.1 mm for the gross tumor volume (GTV), respectively, across all patients. The mean dose error on stomach+duodenum and small bowel were 2.3 ± 0.6% for Eclipse, and 1.0 ± 0.3% for MIM. As the DIR magnitude error increases, the dose error range increase, for both Eclipse and MIM. CONCLUSION: In our study, an initial assessment was conducted to evaluate the accuracy of DIR and its dosimetric impact on radiotherapy. A patient-specific DIR QA workflow was developed for pancreatic cancer patients. This workflow exhibits promising potential for future implementation as a clinical workflow.

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It has been found that the intraday dynamics of body temperature in small mammal and bird species on the adjacent day are similar. Therefore, by focusing on the body temperature dynamics of the previous day, it is possible to predict with a high degree of accuracy the periods of increase and decrease in body temperature for the current day. This phenomenon was observed when animals were kept under natural illumination and under artificial illumination when the phase of the intrinsic circadian rhythm shifted by 1-2 h every day. When analyzing this phenomenon in birds, it has been shown that the best match for body temperature dynamics occurs when comparing adjacent days based on sidereal days (a period of 23 h and 56 min). Over time, after several days, the daily patterns of body temperature fluctuation take on a completely different form and frequency. These facts suggest a connection between ultradian rhythms and the rotation of the Earth around its axis, and consequently, the position of animals on the surface of the planet relative to space objects.

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OBJECTIVE: The most recent edition of the International Clinical Practice Guideline for the Prevention and Treatment of Pressure Ulcers/Injuries was released in 2019. Shortly after, in 2020, the first edition of the SECURE Prevention expert panel report, focusing on device-related pressure ulcers/injuries, was published as a special issue in the Journal of Wound Care. A second edition followed in 2022. This article presents a comprehensive summary of the current understanding of the causes of pressure ulcers/injuries (PU/Is) as detailed in these globally recognised consensus documents. METHOD: The literature reviewed in this summary specifically addresses the impact of prolonged soft tissue deformations on the viability of cells and tissues in the context of PU/Is related to bodyweight or medical devices. RESULTS: Prolonged soft tissue deformations initially result in cell death and tissue damage on a microscopic scale, potentially leading to development of clinical PU/Is over time. That is, localised high tissue deformations or mechanical stress concentrations can cause microscopic damage within minutes, but it may take several hours of continued mechanical loading for this initial cell and tissue damage to become visible and clinically noticeable. Superficial tissue damage primarily stems from excessive shear loading on fragile or vulnerable skin. In contrast, deeper PU/Is, known as deep tissue injuries, typically arise from stress concentrations in soft tissues at body regions over sharp or curved bony prominences, or under stiff medical devices in prolonged contact with the skin. CONCLUSION: This review promotes deeper understanding of the pathophysiology of PU/Is, indicating that their primary prevention should focus on alleviating the exposure of cells and tissues to stress concentrations. This goal can be achieved either by reducing the intensity of stress concentrations in soft tissues, or by decreasing the exposure time of soft tissues to such stress concentrations.

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PURPOSE: Spinal flexion exposure (SFE) leads to alterations in neuromuscular and mechanical properties of the trunk. While several studies reported changes in intrinsic trunk stiffness following SFE, there is a lack of studies evaluating the effects on lumbar muscle shear modulus (SM). Therefore, the aim of our study was to investigate the effects of SFE on lumbar muscle SM and posture. METHODS: Sixteen young volunteers were included in this clinical study. Passive lumbar muscle SM, lumbar lordosis, lumbar flexion range of motion and sitting height were measured prior to and following a 60-min SFE protocol. RESULTS: For SM, our results did not show a significant muscle × time interaction effect (p = 0.40). However, we found increased SM (from 6.75 to 15.43% - all p < 0.02) and maximal lumbar flexion (15.91 ± 10.88%; p < 0.01), whereas lumbar lordosis ( - 7.67 ± 13.97%; p = 0.03) and sitting height ( - 0.57 ± 0.32%; p < 0.01) decreased following SFE. Our results showed no significant correlations between the changes in the included outcome measures (p = 0.10-0.83). CONCLUSION: We hypothesized that increased lumbar muscle SM following SFE might be a compensation for decreased passive stability due to viscoelastic deformations of connective tissues, which are indicated by increased maximal lumbar flexion and decreased sitting height. However, there were no significant correlations between the changes of the included outcome measures, which implies that increased muscle SM and reduced lumbar lordosis are more likely an independent consequence of SFE.

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OBJECTIVE: The aim of this study is to evaluate the deformations of the femoropopliteal (FP) arterial segment due to knee flexion in patients suffering from popliteal aneurysm before and after endovascular treatment (ET). DESIGN AND METHODS: Nine patients were prospectively evaluated. Pre-operative and post-operative computed tomography angiography (CTA) scans were performed on the leg of each patient in both a flexed and extended knee position. The images were employed to reconstruct the FP segment through segmentation and the resulting models were subsequently used to calculate the average diameter, length, and tortuosity of both the superficial femoral artery (SFA) and popliteal artery (PA). Furthermore, the overall PA tortuosity was decomposed into 2 components, ie, antero-posterior and lateral direction. RESULTS: Following knee flexion, both arterial segments experienced shortening in the pre-operative and post-operative phases. Specifically, the SFA was shortened by 3.5% in pre (p<0.001) and 1.21% in post-stenting (p<0.001), while the PA was shortened by 4.8% (p<0.001) and 5.63% (p<0.001), respectively. Tortuosity significantly increased in all considered segments; in particular, in SFA there was a pre-intervention increase of 85.2% (p=0.002) and an increase of 100% post-intervention (p=0.004), whereas in the PA, there was an increase of 128.9% (p<0.001) and 254.8% (p<0.001), respectively. The only diameter variation occurred in the SFA pre-operatively with an increase of 11.9% (p=0.007). Tortuosity decomposition revealed significant differences between the 2 planes during the pre-operative and post-operative phases in both extended and flexed configurations, confirming a change in artery position and geometry due to treatment. CONCLUSIONS: Knee flexion induces arterial shortening and increased tortuosity in both the pre- and post-operative configuration. Stent placement does not induce significant geometric differences between pre-treatment and post-treatment. These results seem to indicate that the geometry of the covered stent is not affected by the flexion of the knee joint. Despite this, a more detailed analysis of arterial tortuosity showed a change in artery deformation following treatment. CLINICAL IMPACT: This study aimed to evaluate femoropopliteal arterial deformations in nine patients with popliteal aneurysm before and after endovascular treatment (ET) during knee flexion, using a standardized protocol for CTA acquisition and analysis. The result can be useful in procedure planning and have shown that the Viabahn stent used can adapt to the morphological variations induced by limb flexion. Consequently, device failure does not be attributed to stent compression but rather to other factors, such as alterations in hemodynamic and biomechanical forces on the implant due to the significant changes in tortuosity observed, or biological causes.

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Accurate transverse deformation measurements are required for the estimation of the Poisson function and volume ratio. In this study, pure silicone and soft composite specimens were subjected to uniaxial tension, and the digital image correlation method was used to measure longitudinal and in- and out-of-plane transverse stretches. To minimize the effects of measurement errors on parameter estimation, the measured transverse stretches were defined in terms of the longitudinal stretch using a new formulation based on Poisson's ratios and two stretch-dependent parameters. From this formulation, Poisson functions and volume ratio for soft materials under large deformations were obtained. The results showed that pure silicone can be considered isotropic and nearly incompressible under large deformations, as expected. In contrast, Poisson's ratio of silicone reinforced with extensible fabric can exceed classical bounds, including negative value (auxetic behavior). The incompressibility assumption can be employed for describing the stress-stretch curve of pure silicone, while volume ratios are required for soft composites. Data of human skin, aortic wall, and annulus fibrosus from the literature were selected and analyzed. Except for the aortic wall, which can be considered nearly incompressible, the studied soft tissues must be regarded as compressible. All tissues presented anisotropic behavior.

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The interactions between fluid flow and structural components of collapsible tubes are representative of those in several physiological systems. Although extensively studied, there exists a lack of characterization of the three-dimensionality in the structural deformations of the tube and its influence on the flow field. This experimental study investigates the spatio-temporal relationship between 3D tube geometry and the downstream flow field under conditions of fully open, closed, and slamming-type oscillating regimes. A methodology is implemented to simultaneously measure three-dimensional surface deformations in a collapsible tube and the corresponding downstream flow field. Stereophotogrammetry was used to measure tube deformations, and simultaneous flow field measurements included pressure and planar Particle Image Velocimetry (PIV) data downstream of the collapsible tube. The results indicate that the location of the largest collapse in the tube occurs close to the downstream end of the tube. In the oscillating regime, sections of the tube downstream of the largest mean collapse experience the largest oscillations in the entire tube that are completely coherent and in phase. At a certain streamwise distance upstream of the largest collapse, a switch in the direction of oscillations occurs with respect to those downstream. Physically, when the tube experiences constriction downstream of the location of the largest mean collapse, this causes the accumulation of fluid and build-up of pressure in the upstream regions and an expansion of these sections. Fluctuations in the downstream flow field are significantly influenced by tube fluctuations along the minor axes. The fluctuations in the downstream flowfield are influenced by the propagation of disturbances due to oscillations in tube geometry, through the advection of fluid through the tube. Further, the manifestation of the LU-type pressure fluctuations is found to be due to the variation in the propagation speed of the disturbances during the different stages within a period of oscillation of the tube.

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Membrane-induced interactions play an important role in organizing membrane proteins. Measurements of the interactions between two and three membrane deforming objects have revealed their nonadditive nature. They are thought to lead to complex many-body effects, however, experimental evidence is lacking. We here present an experimental method to measure many-body effects in membrane-mediated interactions using colloidal spheres placed between a deflated giant unilamellar vesicles and a planar substrate. The confined colloidal particles cause a large deformation of the membrane while not being physicochemically attached to it and interact through it. Two particles attract with a maximum force of 0.2 pN. For three particles, compact equilateral triangles were preferred over linear arrangements. We use numerical energy minimization to establish that the attraction stems from a reduction in the membrane-deformation energy caused by the particles. Confining up to 36 particles, we find a preference for hexagonally close packed clusters. However, with increasing number of particles the order of the confined particles decreases, at the same time, diffusivity of the particles increases. Our experiments show that the nonadditive nature of membrane-mediated interactions affects the interactions and arrangements and ultimately leads to spherical aggregates with liquid-like order of potential importance for cellular processes.

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Association was assessed between the data harvested by a long-baseline laser interference deformograph and the dynamics of body temperature (BT) in hamsters deprived of natural daily light-darkness changes. The power spectral data revealed the positive correlation between simultaneous time series of hamster BT and the Earth's crust deformation (ECD). The superposed epoch analysis established an association between abrupt upstrokes of hamster BT and ECD increments. Thus, the direct relationships between BT dynamics (reflecting predominance of sympathetic part of autonomic nervous system) and ECD (according to long-baseline laser interference deformography) were established. The study observed synchronization of the free-running circadian rhythm of hamster BT with the tidal stress in Earth's lithosphere. Further studies are needed to find the physical factor underlying the revealed relationships.

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Over the last 50 years resonance Raman spectroscopy has become an invaluable tool for the exploration of chromophores in biological macromolecules. Among them, heme proteins and metal complexes have attracted considerable attention. This interest results from the fact that resonance Raman spectroscopy probes the vibrational dynamics of these chromophores without direct interference from the surrounding. However, the indirect influence via through-bond and through-space chromophore-protein interactions can be conveniently probed and analyzed. This review article illustrates this point by focusing on class 1 cytochrome c, a comparatively simple heme protein generally known as electron carrier in mitochondria. The article demonstrates how through selective excitation of resonance Raman active modes information about the ligation, the redox state and the spin state of the heme iron can be obtained from band positions in the Raman spectra. The investigation of intensities and depolarization ratios emerged as tools for the analysis of in-plane and out-of-plane deformations of the heme macrocycle. The article further shows how resonance Raman spectroscopy was used to characterize partially unfolded states of oxidized cytochrome c. Finally, it describes its use for exploring structural changes due to the protein's binding to anionic surfaces like cardiolipin containing membranes.

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Significance: The accurate correlation between optical measurements and pathology relies on precise image registration, often hindered by deformations in histology images. We investigate an automated multi-modal image registration method using deep learning to align breast specimen images with corresponding histology images. Aim: We aim to explore the effectiveness of an automated image registration technique based on deep learning principles for aligning breast specimen images with histology images acquired through different modalities, addressing challenges posed by intensity variations and structural differences. Approach: Unsupervised and supervised learning approaches, employing the VoxelMorph model, were examined using a dataset featuring manually registered images as ground truth. Results: Evaluation metrics, including Dice scores and mutual information, demonstrate that the unsupervised model exceeds the supervised (and manual) approaches significantly, achieving superior image alignment. The findings highlight the efficacy of automated registration in enhancing the validation of optical technologies by reducing human errors associated with manual registration processes. Conclusions: This automated registration technique offers promising potential to enhance the validation of optical technologies by minimizing human-induced errors and inconsistencies associated with manual image registration processes, thereby improving the accuracy of correlating optical measurements with pathology labels.

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Optical coherence elastography (OCE) demonstrated impressive abilities for diagnosing tissue types/states using differences in their biomechanics. Usually, OCE visualizes tissue deformation induced by some additional stimulus (e.g., contact compression or auxiliary elastic-wave excitation). We propose a new variant of OCE with osmotically induced straining (OIS-OCE) and demonstrate its application to assess various stages of proteoglycan content degradation in cartilage. The information-bearing signatures in OIS-OCE are the magnitude and rate of strains caused by the application of osmotically active solutions onto the sample surface. OCE examination of the induced strains does not require special tissue preparation, the osmotic stimulation is highly reproducible, and strains are observed in noncontact mode. Several minutes suffice to obtain a conclusion. These features are promising for intraoperative method usage when express assessment of tissue state is required during surgical operations. The "waterfall" images demonstrate the development of cumulative osmotic strains in control and degraded cartilage samples.

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Magnetic skyrmions are quasi-particles with a swirling spin texture that form two-dimensional lattices. Skyrmion lattices can exhibit defects in response to geometric constraints, variations of temperature or applied magnetic fields. Measuring deformations in skyrmion lattices is important to understand the interplay between the lattice structure and external influences. Geometric phase analysis (GPA) is a Fourier-based image processing method that is used to measure deformation fields in high resolution transmission electron microscopy (TEM) images of crystalline materials. Here, we show that GPA can be applied quantitatively to Lorentz TEM images of two-dimensional skyrmion lattices obtained from a chiral magnet of FeGe. First, GPA is used to map deformation fields around a 5-7 dislocation and the results are compared with the linear theory of elasticity. Second, rotation angles between skyrmion crystal grains are measured and compared with angles calculated from the density of dislocations. Third, an orientational order parameter and the corresponding correlation function are calculated to describe the evolution of the disorder as a function of applied magnetic field. The influence of sources of artifacts such as geometric distortions and large defoci are also discussed.

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Recent studies have shown that the mechanical properties of bioinspired periodic composite materials can be strongly influenced by finite deformation effects, leading to highly nonlinear static and dynamic behaviors at multiple length scales. For instance, in porous periodic nacre-like microstructures, microscopic and macroscopic instabilities may occur for a given uniaxial loading process and, as a consequence, wave attenuation properties may evolve as a function of the microstructural evolution, designating it as metamaterials. The numerical outcomes provide new opportunities to design bioinspired, soft composite metamaterials characterized by high deformability and enhanced elastic wave attenuation capabilities given by the insertion of voids and lead cores.

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Flow in a porous medium can be driven by the deformations of the boundaries of the porous domain. Such boundary deformations locally change the volume fraction accessible by the fluid, creating non-uniform porosity and permeability throughout the medium. In this work, we construct a deformation-driven porous medium transport model with spatially and temporally varying porosity and permeability that are dependent on the boundary deformations imposed on the medium. We use this model to study the transport of interstitial fluid along the basement membranes in the arterial walls of the brain. The basement membrane is modeled as a deforming annular porous channel with the compressible pore space filled with an incompressible, Newtonian fluid. The role of a forward propagating peristaltic heart pulse wave and a reverse smooth muscle contraction wave on the flow within the basement membranes is investigated. Our results identify combinations of wave amplitudes that can induce either forward or reverse transport along these transport pathways in the brain. The magnitude and direction of fluid transport predicted by our model can help in understanding the clearance of fluids and solutes along the Intramural Periarterial Drainage route and the pathology of cerebral amyloid angiopathy.

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Objective.Deformable image registration (DIR) is a widely used technique in radiotherapy. Complex deformations, resulting from large anatomical changes, are a regular challenge. DIR algorithms generally seek a balance between capturing large deformations and preserving a smooth deformation vector field (DVF). We propose a novel structure-based term that can enhance the registration efficacy while ensuring a smooth DVF.Approach.The proposed novel similarity metric for controlling structures was introduced as a new term into a commercially available algorithm. Its performance was compared to the original algorithm using a dataset of 46 patients who received pelvic re-irradiation, many of which exhibited complex deformations.Main results.The mean Dice Similarity Coefficient (DSC) under the improved algorithm was 0.96, 0.94, 0.76, and 0.91 for bladder, rectum, colon, and bone respectively, compared to 0.69, 0.89, 0.62, and 0.88 for the original algorithm. The improvement was more pronounced for complex deformations.Significance.With this work, we have demonstrated that the proposed term is able to improve registration accuracy for complex cases while maintaining realistic deformations.

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BACKGROUND: The dosimetric effect of setup uncertainty and tissue deformations in left-sided whole-breast irradiation with complementary surface-guided radiotherapy (SGRT) and cone-beam computed tomography (CBCT) setup was evaluated. METHOD: Treatment courses of 40.05 Gy prescribed dose in 15 fractions were simulated for 29 patients by calculating the dose on deformed CT images, that were based on daily CBCT images, and deforming and accumulating the dose onto the planning CT image. Variability in clinical target volume (CTV) position and shape was assessed as the 95% Hausdorff distance (HD95) between the planning CTV and deformed CTV structures. DVH metrics were evaluated between the planned and simulated cumulative dose distributions using two treatment techniques: tangential volumetric modulated arc therapy (tVMAT) and conventional 3D-conformal radiotherapy (3D-CRT). RESULTS: Based on the HD95 values, the variations in CTV shape and position were enclosed by the 5 mm CTV-PTV margin in 85% of treatment fractions using complementary CBCT and SGRT setup. A residual error of 8.6 mm was observed between the initial SGRT setup and CBCT setup. The median CTV V95% coverage was 98.1% (range 93.1-99.8%) with tVMAT and 98.2% (range 84.5-99.7%) with 3D-CRT techniques with CBCT setup. With the initial SGRT-only setup, the corresponding coverages were 96.3% (range 92.6-99.4%) and 96.6% (range 84.2-99.4%), respectively. However, a considerable bias in vertical residual error between initial SGRT setup and CBCT setup was observed. Clinically relevant changes between the planned and cumulative doses to organs-at-risk (OARs) were not observed. CONCLUSIONS: The CTV-to-PTV margin should not be reduced below 5 mm even with daily CBCT setup. Both tVMAT and 3D-CRT techniques were robust in terms of dose coverage to the target and OARs. Based on the shifts between setup methods, CBCT setup is recommended as a complementary method with SGRT.

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STUDY QUESTION: Could actin-related protein T1 (ACTRT1) deficiency be a potential pathogenic factor of human male infertility? SUMMARY ANSWER: A 110-kb microdeletion of the X chromosome, only including the ACTRT1 gene, was identified as responsible for infertility in two Chinese males with sperm showing acrosomal ultrastructural defects and fertilization failure. WHAT IS KNOWN ALREADY: The actin-related proteins (e.g. ACTRT1, ACTRT2, ACTL7A, and ACTL9) interact with each other to form a multimeric complex in the subacrosomal region of spermatids, which is crucial for the acrosome-nucleus junction. Actrt1-knockout (KO) mice are severely subfertile owing to malformed sperm heads with detached acrosomes and partial fertilization failure. There are currently no reports on the association between ACTRT1 deletion and male infertility in humans. STUDY DESIGN, SIZE, DURATION: We recruited a cohort of 120 infertile males with sperm head deformations at a large tertiary hospital from August 2019 to August 2023. Genomic DNA extracted from the affected individuals underwent whole exome sequencing (WES), and in silico analyses were performed to identify genetic variants. Morphological analysis, functional assays, and ART were performed in 2022 and 2023. PARTICIPANTS/MATERIALS, SETTING, METHODS: The ACTRT1 deficiency was identified by WES and confirmed by whole genome sequencing, PCR, and quantitative PCR. Genomic DNA of all family members was collected to define the hereditary mode. Papanicolaou staining and electronic microscopy were performed to reveal sperm morphological changes. Western blotting and immunostaining were performed to explore the pathological mechanism of ACTRT1 deficiency. ICSI combined with artificial oocyte activation (AOA) was applied for one proband. MAIN RESULTS AND THE ROLE OF CHANCE: We identified a whole-gene deletion variant of ACTRT1 in two infertile males, which was inherited from their mothers, respectively. The probands exhibited sperm head deformations owing to acrosomal detachment, which is consistent with our previous observations on Actrt1-KO mice. Decreased expression and ectopic distribution of ACTL7A and phospholipase C zeta were observed in sperm samples from the probands. ICSI combined with AOA effectively solved the fertilization problem in Actrt1-KO mice and in one of the two probands. LIMITATIONS, REASONS FOR CAUTION: Additional cases are needed to further confirm the genetic contribution of ACTRT1 variants to male infertility. WIDER IMPLICATIONS OF THE FINDINGS: Our results reveal a gene-disease relation between the ACTRT1 deletion described here and human male infertility owing to acrosomal detachment and fertilization failure. This report also describes a good reproductive outcome of ART with ICSI-AOA for a proband. STUDY FUNDING/COMPETING INTEREST(S): This work was supported by the Chongqing medical scientific research project (Joint project of Chongqing Health Commission and Science and Technology Bureau, 2023MSXM008 and 2023MSXM054). There are no competing interests to declare. TRIAL REGISTRATION NUMBER: N/A.

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This study addresses the challenges of modeling flexible connections in composite structures employing a polymeric adhesive layer. These types of connections provide a more uniform stress distribution compared to conventional rigid connectors. However, they lack standardized design rules and still require much research to sufficiently comprehend their properties. The novelty of this research lies in proposing an analytical solution to address these issues. Its aim is to investigate the influence of the stiffness of the polymer adhesive on the girder's deflection and on the maximum stresses in both the adhesive and concrete. The analyzed composite structure consists of a reinforced concrete (RC) slab and an RC beam connected with a layer of flexible polyurethane (FPU) adhesive. Analytical and numerical approaches for the description of the mechanical response of a composite bridge girder are presented. Another objective is to validate the analytical design formulas using 3D nonlinear numerical analysis, both in the case of uncracked and cracked concrete. Seven types of FPUs are tested in the uniaxial tension test, each examined at five strain rates. The obtained data is used to predict the mechanical response of the considered girder using finite element analysis (FEA) as well as with a simplified one-dimensional composite beam theory. Fair agreement is found between the FEA results and theoretical predictions. A comparison of the results obtained for these two models is performed, and the similarities and discrepancies are highlighted and discussed.

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In the modern theory of compressed concrete elements, the most attention is paid to longitudinal deformations, whereas transverse ones are rarely considered and just within Poisson's coefficient limits (i.e., elastic concrete behavior in the transverse direction). However, transverse deformations significantly develop beyond the limits corresponding to Poisson's coefficient, where they lead to longitudinal crack initiation and development. In-depth experimental and numerical investigations of transverse deformations in the inelastic stage showed that it is necessary to consider crack propagation. The present study proposes simultaneous consideration of longitudinal and transverse deformations, as well as the appearance of cracks and their widths and depths. This allowed us to obtain a complete compressed concrete element behavior pattern at all performance stages in two types of limit states (based on longitudinal and transverse deformations). Consequently, new ultimate limit states by the depth and width of cracks caused by transverse deformations are proposed to be included in modern design practices and codes.