1
|
de Hoop H, Petterson NJ, van de Vosse FN, van Sambeek MRHM, Schwab HM, Lopata RGP. Multiperspective Ultrasound Strain Imaging of the Abdominal Aorta. IEEE TRANSACTIONS ON MEDICAL IMAGING 2020; 39:3714-3724. [PMID: 32746118 DOI: 10.1109/tmi.2020.3003430] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Current decision-making for clinical intervention of abdominal aortic aneurysms (AAAs) is based on the maximum diameter of the aortic wall, but this does not provide patient-specific information on rupture risk. Ultrasound (US) imaging can assess both geometry and deformation of the aortic wall. However, low lateral contrast and resolution are currently limiting the precision of both geometry and local strain estimates. To tackle these drawbacks, a multiperspective scanning mode was developed on a dual transducer US system to perform strain imaging at high frame rates. Experimental imaging was performed on porcine aortas embedded in a phantom of the abdomen, pressurized in a mock circulation loop. US images were acquired with three acquisition schemes: Multiperspective ultrafast imaging, single perspective ultrafast imaging, and conventional line-by-line scanning. Image registration was performed by automatic detection of the transducer surfaces. Multiperspective images and axial displacements were compounded for improved segmentation and tracking of the aortic wall, respectively. Performance was compared in terms of image quality, motion tracking, and strain estimation. Multiperspective compound displacement estimation reduced the mean motion tracking error over one cardiac cycle by a factor 10 compared to conventional scanning. Resolution increased in radial and circumferential strain images, and circumferential signal-to-noise ratio (SNRe) increased by 10 dB. Radial SNRe is high in wall regions moving towards the transducer. In other regions, radial strain estimates remain cumbersome for the frequency used. In conclusion, multiperspective US imaging was demonstrated to improve motion tracking and circumferential strain estimation of porcine aortas in an experimental set-up.
Collapse
|
2
|
Reproducibility assessment of ultrasound-based aortic stiffness quantification and verification using Bi-axial tensile testing. J Mech Behav Biomed Mater 2020; 103:103571. [DOI: 10.1016/j.jmbbm.2019.103571] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2018] [Revised: 09/10/2019] [Accepted: 11/29/2019] [Indexed: 01/04/2023]
|
3
|
Wang Y, Li H, Guo Y, Lee WN. Bidirectional Ultrasound Elastographic Imaging Framework for Non-invasive Assessment of the Non-linear Behavior of a Physiologically Pressurized Artery. ULTRASOUND IN MEDICINE & BIOLOGY 2019; 45:1184-1196. [PMID: 30876671 DOI: 10.1016/j.ultrasmedbio.2019.01.014] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2018] [Revised: 01/10/2019] [Accepted: 01/15/2019] [Indexed: 06/09/2023]
Abstract
Studies of non-destructive bidirectional ultrasound assessment of non-linear mechanical behavior of the artery are scarce in the literature. We hereby propose derivation of a strain-shear modulus relationship as a new graphical diagnostic index using an ultrasound elastographic imaging framework, which encompasses our in-house bidirectional vascular guided wave imaging (VGWI) and ultrasound strain imaging (USI). This framework is used to assess arterial non-linearity in two orthogonal (i.e., longitudinal and circumferential) directions in the absence of non-invasive pressure measurement. Bidirectional VGWI estimates longitudinal (μL) and transverse (μT) shear moduli, whereas USI estimates radial strain (ɛr). Vessel-mimicking phantoms (with and without longitudinal pre-stretch) and in vitro porcine aortas under static and/or dynamic physiologic intraluminal pressure loads were examined. ɛr was found to be a suitable alternative to intraluminal pressure for representation of cyclic loading on the artery wall. Results revealed that μT values of all samples examined increased non-linearly with εr magnitude and more drastically than μL, whereas μL values of only the pre-stretched phantoms and aortas increased with ɛr magnitude. As a new graphical representation of arterial non-linearity and function, strain-shear modulus loops derived by the proposed framework over two consecutive dynamic loading cycles differentiated sample pre-conditions and corroborated direction-dependent non-linear mechanical behaviors of the aorta with high estimation repeatability.
Collapse
Affiliation(s)
- Yahua Wang
- Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong
| | - He Li
- Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong
| | - Yuexin Guo
- Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong
| | - Wei-Ning Lee
- Department of Electrical and Electronic Engineering, University of Hong Kong, Hong Kong; Medical Engineering Programme, University of Hong Kong, Hong Kong.
| |
Collapse
|
4
|
Mix DS, Stoner MC, Day SW, Richards MS. Manufacturing Abdominal Aorta Hydrogel Tissue-Mimicking Phantoms for Ultrasound Elastography Validation. J Vis Exp 2018. [PMID: 30295670 PMCID: PMC6235247 DOI: 10.3791/57984] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
Ultrasound (US) elastography, or elasticity imaging, is an adjunct imaging technique that utilizes sequential US images of soft tissues to measure the tissue motion and infer or quantify the underlying biomechanical characteristics. For abdominal aortic aneurysms (AAA), biomechanical properties such as changes in the tissue's elastic modulus and estimates of the tissue stress may be essential for assessing the need for the surgical intervention. Abdominal aortic aneurysms US elastography could be a useful tool to monitor AAA progression and identify changes in biomechanical properties characteristic of high-risk patients. A preliminary goal in the development of an AAA US elastography technique is the validation of the method using a physically relevant model with known material properties. Here we present a process for the production of AAA tissue-mimicking phantoms with physically relevant geometries and spatially modulated material properties. These tissue phantoms aim to mimic the US properties, material modulus, and geometry of the abdominal aortic aneurysms. Tissue phantoms are made using a polyvinyl alcohol cryogel (PVA-c) and molded using 3D printed parts created using computer aided design (CAD) software. The modulus of the phantoms is controlled by altering the concentration of PVA-c and by changing the number of freeze-thaw cycles used to polymerize the cryogel. The AAA phantoms are connected to a hemodynamic pump, designed to deform the phantoms with the physiologic cyclic pressure and flows. Ultra sound image sequences of the deforming phantoms allowed for the spatial calculation of the pressure normalized strain and the identification of mechanical properties of the vessel wall. Representative results of the pressure normalized strain are presented.
Collapse
Affiliation(s)
- Doran S Mix
- Division of Vascular Surgery, University of Rochester Medical Center
| | - Michael C Stoner
- Division of Vascular Surgery, University of Rochester Medical Center
| | - Steven W Day
- Department of Biomedical Engineering, Rochester Institute of Technology
| | | |
Collapse
|
5
|
Mix DS, Yang L, Johnson CC, Couper N, Zarras B, Arabadjis I, Trakimas LE, Stoner MC, Day SW, Richards MS. Detecting Regional Stiffness Changes in Aortic Aneurysmal Geometries Using Pressure-Normalized Strain. ULTRASOUND IN MEDICINE & BIOLOGY 2017; 43:2372-2394. [PMID: 28728780 PMCID: PMC5562537 DOI: 10.1016/j.ultrasmedbio.2017.06.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2016] [Revised: 04/26/2017] [Accepted: 06/02/2017] [Indexed: 06/07/2023]
Abstract
Transabdominal ultrasound elasticity imaging could improve the assessment of rupture risk for abdominal aortic aneurysms by providing information on the mechanical properties and stress or strain states of vessel walls. We implemented a non-rigid image registration method to visualize the pressure-normalized strain within vascular tissues and adapted it to measure total strain over an entire cardiac cycle. We validated the algorithm's performance with both simulated ultrasound images with known principal strains and anatomically accurate heterogeneous polyvinyl alcohol cryogel vessel phantoms. Patient images of abdominal aortic aneurysm were also used to illustrate the clinical feasibility of our imaging algorithm and the potential value of pressure-normalized strain as a clinical metric. Our results indicated that pressure-normalized strain could be used to identify spatial variations in vessel tissue stiffness. The results of this investigation were sufficiently encouraging to warrant a clinical study measuring abdominal aortic pressure-normalized strain in a patient population with aneurysmal disease.
Collapse
Affiliation(s)
- Doran S Mix
- Division of Vascular Surgery, Department of Surgery, University of Rochester Medical Center, Rochester, New York, USA; Department of Biomedical Engineering, Rochester Institute of Technology, Rochester, New York, USA.
| | - Ling Yang
- Department of Biomedical Engineering, University of Rochester, Rochester, New York, USA
| | - Camille C Johnson
- Department of Biomedical Engineering, Rochester Institute of Technology, Rochester, New York, USA
| | - Nathan Couper
- Division of Vascular Surgery, Department of Surgery, University of Rochester Medical Center, Rochester, New York, USA; Department of Biomedical Engineering, University of Rochester, Rochester, New York, USA
| | - Ben Zarras
- Department of Biomedical Engineering, University of Rochester, Rochester, New York, USA
| | - Isaac Arabadjis
- Department of Biomedical Engineering, Rochester Institute of Technology, Rochester, New York, USA
| | - Lauren E Trakimas
- Division of Vascular Surgery, Department of Surgery, University of Rochester Medical Center, Rochester, New York, USA
| | - Michael C Stoner
- Division of Vascular Surgery, Department of Surgery, University of Rochester Medical Center, Rochester, New York, USA
| | - Steven W Day
- Department of Biomedical Engineering, Rochester Institute of Technology, Rochester, New York, USA
| | - Michael S Richards
- Division of Vascular Surgery, Department of Surgery, University of Rochester Medical Center, Rochester, New York, USA; Department of Biomedical Engineering, Rochester Institute of Technology, Rochester, New York, USA
| |
Collapse
|
6
|
Carotid Artery Plaque Vulnerability Assessment Using Noninvasive Ultrasound Elastography: Validation With MRI. AJR Am J Roentgenol 2017. [PMID: 28639927 DOI: 10.2214/ajr.16.17176] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
OBJECTIVE Vulnerable and nonvulnerable carotid artery plaques have different tissue morphology and composition that may affect plaque biomechanics. The objective of this study is to evaluate plaque vulnerability with the use of ultrasound noninvasive vascular elastography (NIVE). MATERIALS AND METHODS Thirty-one patients (mean [± SD] age, 69 ± 7 years) with stenosis of the internal carotid artery of 50% or greater were enrolled in this cross-sectional study. Elastography parameters quantifying axial strain, shear strain, and translation motion were used to characterize carotid artery plaques as nonvulnerable, neovascularized, and vulnerable. Maximum axial strain, cumulated axial strain, mean shear strain, cumulated shear strain, cumulated axial translation, and cumulated lateral translations were measured. Cumulated measurements were summed over a cardiac cycle. The ratio of cumulated axial strain to cumulated axial translation was also evaluated. The reference method used to characterize plaques was high-resolution MRI. RESULTS According to MRI, seven plaques were vulnerable, 12 were nonvulnerable without neovascularity, and 12 were nonvulnerable with neovascularity (a precursor of vulnerability). The two parameters cumulated axial translation and the ratio of cumulated axial strain to cumulated axial translation could discriminate between nonvulnerable plaques and vulnerable plaques or determine the presence of neovascularity in nonvulnerable plaques (which was also possible with the mean shear strain parameter). All parameters differed between the non-vulnerable plaque group and the group that combined vulnerable plaques and plaques with neovascularity. The most discriminating parameter for the detection of vulnerable neovascularized plaques was the ratio of cumulated axial strain to cumulated axial translation (expressed as percentage per millimeter) (mean ratio, 39.30%/mm ± 12.80%/mm for nonvulnerable plaques without neovascularity vs 63.79%/mm ± 17.59%/mm for vulnerable plaques and nonvulnerable plaques with neovascularity, p = 0.002), giving an AUC value of 0.886. CONCLUSION The imaging parameters cumulated axial translation and the ratio of cumulated axial strain to cumulated axial translation, as computed using NIVE, were able to discriminate vulnerable carotid artery plaques characterized by MRI from nonvulnerable carotid artery plaques. Consideration of neovascularized plaques improved the performance of NIVE. NIVE may be a valuable alternative to MRI for carotid artery plaque assessment.
Collapse
|
7
|
Mascarenhas EJ, Peters MF, Nijs J, Rutten MC, van de Vosse FN, Lopata RG. Assessment of mechanical properties of porcine aortas under physiological loading conditions using vascular elastography. J Mech Behav Biomed Mater 2016; 59:185-196. [DOI: 10.1016/j.jmbbm.2015.12.009] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2015] [Revised: 12/01/2015] [Accepted: 12/10/2015] [Indexed: 01/11/2023]
|
8
|
Nauta FJ, Conti M, Marconi S, Kamman AV, Alaimo G, Morganti S, Ferrara A, van Herwaarden JA, Moll FL, Auricchio F, Trimarchi S. An experimental investigation of the impact of thoracic endovascular aortic repair on longitudinal strain. Eur J Cardiothorac Surg 2016; 50:955-961. [DOI: 10.1093/ejcts/ezw180] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/17/2016] [Accepted: 04/26/2016] [Indexed: 11/13/2022] Open
|
9
|
Huang C, Pan X, He Q, Huang M, Huang L, Zhao X, Yuan C, Bai J, Luo J. Ultrasound-Based Carotid Elastography for Detection of Vulnerable Atherosclerotic Plaques Validated by Magnetic Resonance Imaging. ULTRASOUND IN MEDICINE & BIOLOGY 2016; 42:365-377. [PMID: 26553205 DOI: 10.1016/j.ultrasmedbio.2015.09.023] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2015] [Revised: 08/27/2015] [Accepted: 09/23/2015] [Indexed: 06/05/2023]
Abstract
Ultrasound-based carotid elastography has been developed to estimate the mechanical properties of atherosclerotic plaques. The objective of this study was to evaluate the in vivo capability of carotid elastography in vulnerable plaque detection using high-resolution magnetic resonance imaging as reference. Ultrasound radiofrequency data of 46 carotid plaques from 29 patients (74 ± 5 y old) were acquired and inter-frame axial strain was estimated with an optical flow method. The maximum value of absolute strain rate for each plaque was derived as an indicator for plaque classification. Magnetic resonance imaging of carotid arteries was performed on the same patients to classify the plaques into stable and vulnerable groups for carotid elastography validation. The maximum value of absolute strain rate was found to be significantly higher in vulnerable plaques (2.15 ± 0.79 s(-1), n = 27) than in stable plaques (1.21 ± 0.37 s(-1), n = 19) (p < 0.0001). Receiver operating characteristic curve analysis was performed, and the area under the curve was 0.848. Therefore, the in vivo capability of carotid elastography to detect vulnerable plaques, validated by magnetic resonance imaging, was proven, revealing the potential of carotid elastography as an important tool in atherosclerosis assessment and stroke prevention.
Collapse
Affiliation(s)
- Chengwu Huang
- Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China; Center for Biomedical Imaging Research, Tsinghua University, Beijing, China
| | - Xiaochang Pan
- Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China; Center for Biomedical Imaging Research, Tsinghua University, Beijing, China
| | - Qiong He
- Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China; Center for Biomedical Imaging Research, Tsinghua University, Beijing, China
| | - Manwei Huang
- Department of Sonography, China Meitan General Hospital, Beijing, China
| | - Lingyun Huang
- Clinical Sites Research Program, Philips Research China, Shanghai, China
| | - Xihai Zhao
- Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China; Center for Biomedical Imaging Research, Tsinghua University, Beijing, China.
| | - Chun Yuan
- Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China; Center for Biomedical Imaging Research, Tsinghua University, Beijing, China; Department of Radiology, University of Washington, Seattle, Washington, USA
| | - Jing Bai
- Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China
| | - Jianwen Luo
- Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing, China; Center for Biomedical Imaging Research, Tsinghua University, Beijing, China.
| |
Collapse
|
10
|
Boekhoven RW, Peters MFJ, Rutten MCM, van Sambeek MR, van de Vosse FN, Lopata RGP. Inflation and Bi-Axial Tensile Testing of Healthy Porcine Carotid Arteries. ULTRASOUND IN MEDICINE & BIOLOGY 2016; 42:574-585. [PMID: 26598396 DOI: 10.1016/j.ultrasmedbio.2015.09.019] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2014] [Revised: 09/16/2015] [Accepted: 09/16/2015] [Indexed: 06/05/2023]
Abstract
Knowledge of the intrinsic material properties of healthy and diseased arterial tissue components is of great importance in diagnostics. This study describes an in vitro comparison of 13 porcine carotid arteries using inflation testing combined with functional ultrasound and bi-axial tensile testing. The measured tissue behavior was described using both a linear, but geometrically non-linear, one-parameter (neo-Hookean) model and a two-parameter non-linear (Demiray) model. The shear modulus estimated using the linear model resulted in good agreement between the ultrasound and tensile testing methods, GUS = 25 ± 5.7 kPa and GTT = 23 ± 5.4 kPa. No significant correspondence was observed for the non-linear model aUS = 1.0 ± 2.7 kPa vs. aTT = 17 ± 8.8 kPa, p ∼ 0); however, the exponential parameters were in correspondence (bUS = 12 ± 4.2 vs. bTT = 10 ± 1.7, p > 0.05). Estimation of more complex models in vivo is cumbersome considering the sensitivity of the model parameters to small changes in measurement data and the absence of intraluminal pressure data, endorsing the use of a simple, linear model in vivo.
Collapse
Affiliation(s)
- Renate W Boekhoven
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Mathijs F J Peters
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Marcel C M Rutten
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Marc R van Sambeek
- Vascular Surgery, Catharina Hospital Eindhoven, Eindhoven, The Netherlands
| | - Frans N van de Vosse
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands
| | - Richard G P Lopata
- Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
| |
Collapse
|
11
|
Akyildiz AC, Hansen HHG, Nieuwstadt HA, Speelman L, De Korte CL, van der Steen AFW, Gijsen FJH. A Framework for Local Mechanical Characterization of Atherosclerotic Plaques: Combination of Ultrasound Displacement Imaging and Inverse Finite Element Analysis. Ann Biomed Eng 2015; 44:968-79. [PMID: 26399991 PMCID: PMC4826666 DOI: 10.1007/s10439-015-1410-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2015] [Accepted: 07/24/2015] [Indexed: 02/07/2023]
Abstract
Biomechanical models have the potential to predict plaque rupture. For reliable models, correct material properties of plaque components are a prerequisite. This study presents a new technique, where high resolution ultrasound displacement imaging and inverse finite element (FE) modeling is combined, to estimate material properties of plaque components. Iliac arteries with plaques were excised from 6 atherosclerotic pigs and subjected to an inflation test with pressures ranging from 10 to 120 mmHg. The arteries were imaged with high frequency 40 MHz ultrasound. Deformation maps of the plaques were reconstructed by cross correlation of the ultrasound radiofrequency data. Subsequently, the arteries were perfusion fixed for histology and structural components were identified. The histological data were registered to the ultrasound data to construct FE model of the plaques. Material properties of the arterial wall and the intima of the atherosclerotic plaques were estimated using a grid search method. The computed displacement fields showed good agreement with the measured displacement fields, implying that the FE models were able to capture local inhomogeneities within the plaque. On average, nonlinear stiffening of both the wall and the intima was observed, and the wall of the atheroslcerotic porcine iliac arteries was markedly stiffer than the intima (877 ± 459 vs. 100 ± 68 kPa at 100 mmHg). The large spread in the data further illustrates the wide variation of the material properties. We demonstrated the feasibility of a mixed experimental–numerical framework to determine the material properties of arterial wall and intima of atherosclerotic plaques from intact arteries, and concluded that, due to the observed variation, plaque specific properties are required for accurate stress simulations.
Collapse
Affiliation(s)
- Ali C. Akyildiz
- />Biomechanics Lab, Department of Biomedical Engineering, Thoraxcenter, Erasmus Medical Center, PO Box 2040, 3000 CA Rotterdam, The Netherlands
- />Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, USA
| | - Hendrik H. G. Hansen
- />Medical UltraSound Imaging Center (MUSIC), Department of Radiology and Nuclear Medicine, Radboud University Medical Center, Nijmegen, The Netherlands
| | - Harm A. Nieuwstadt
- />Biomechanics Lab, Department of Biomedical Engineering, Thoraxcenter, Erasmus Medical Center, PO Box 2040, 3000 CA Rotterdam, The Netherlands
| | - Lambert Speelman
- />Biomechanics Lab, Department of Biomedical Engineering, Thoraxcenter, Erasmus Medical Center, PO Box 2040, 3000 CA Rotterdam, The Netherlands
| | - Chris L. De Korte
- />Medical UltraSound Imaging Center (MUSIC), Department of Radiology and Nuclear Medicine, Radboud University Medical Center, Nijmegen, The Netherlands
| | - Antonius F. W. van der Steen
- />Biomechanics Lab, Department of Biomedical Engineering, Thoraxcenter, Erasmus Medical Center, PO Box 2040, 3000 CA Rotterdam, The Netherlands
- />Department of Applied Sciences, Delft University of Technology, Delft, The Netherlands
| | - Frank J. H. Gijsen
- />Biomechanics Lab, Department of Biomedical Engineering, Thoraxcenter, Erasmus Medical Center, PO Box 2040, 3000 CA Rotterdam, The Netherlands
| |
Collapse
|