Search results for: 1D inversion

Authors: Jiaying Zhang, Xin Mu, Chang Ni, Jeff L. Zhang

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Magnetic resonance elastography (MRE) non-invasively assesses tissue elastic properties, such as shear modulus, by measuring tissue’s displacement in response to mechanical waves. The estimated metrics on tissue elasticity or stiffness have been shown to be valuable for monitoring physiologic or pathophysiologic status of tissue, such as a tumor or fatty liver. To quantify tissue shear modulus from MRE-acquired displacements (essentially an inverse problem), multiple approaches have been proposed, including Local Frequency Estimation (LFE) and Direct Inversion (DI). However, one common problem with these methods is that the estimates are severely noise-sensitive due to either the inverse-problem nature or noise propagation in the pixel-by-pixel process. With the advent of deep learning (DL) and its promise in solving inverse problems, a few groups in the field of MRE have explored the feasibility of using DL methods for quantifying shear modulus from MRE data. Most of the groups chose to use real MRE data for DL model training and to cut training images into smaller patches, which enriches feature characteristics of training data but inevitably increases computation time and results in outcomes with patched patterns. In this study, simulated wave images generated by Finite Differential Time Domain (FDTD) simulation are used for network training, and U-Net is used to extract features from each training image without cutting it into patches. The use of simulated data for model training has the flexibility of customizing training datasets to match specific applications. The proposed method aimed to estimate tissue shear modulus from MRE data with high robustness to noise and high model-training efficiency. Specifically, a set of 3000 maps of shear modulus (with a range of 1 kPa to 15 kPa) containing randomly positioned objects were simulated, and their corresponding wave images were generated. The two types of data were fed into the training of a U-Net model as its output and input, respectively. For an independently simulated set of 1000 images, the performance of the proposed method against DI and LFE was compared by the relative errors (root mean square error or RMSE divided by averaged shear modulus) between the true shear modulus map and the estimated ones. The results showed that the estimated shear modulus by the proposed method achieved a relative error of 4.91%±0.66%, substantially lower than 78.20%±1.11% by LFE. Using simulated data, the proposed method significantly outperformed LFE and DI in resilience to increasing noise levels and in resolving fine changes of shear modulus. The feasibility of the proposed method was also tested on MRE data acquired from phantoms and from human calf muscles, resulting in maps of shear modulus with low noise. In future work, the method’s performance on phantom and its repeatability on human data will be tested in a more quantitative manner. In conclusion, the proposed method showed much promise in quantifying tissue shear modulus from MRE with high robustness and efficiency.

Keywords: deep learning, magnetic resonance elastography, magnetic resonance imaging, shear modulus estimation

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Authors: Riadh Zorgati, Thomas Triboulet

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In quite diverse application areas such as astronomy, medical imaging, geophysics or nondestructive evaluation, many problems related to calibration, fitting or estimation of a large number of input parameters of a model from a small amount of output noisy data, can be cast as inverse problems. Due to noisy data corruption, insufficient data and model errors, most inverse problems are ill-posed in a Hadamard sense, i.e. existence, uniqueness and stability of the solution are not guaranteed. A wide class of inverse problems in physics relates to the Fredholm equation of the first kind. The ill-posedness of such inverse problem results, after discretization, in a very ill-conditioned linear system of equations, the condition number of the associated matrix can typically range from 109 to 1018. This condition number plays the role of an amplifier of uncertainties on data during inversion and then, renders the inverse problem difficult to handle numerically. Similar problems appear in other areas such as numerical optimization when using interior points algorithms for solving linear programs leads to face ill-conditioned systems of linear equations. Devising efficient solution approaches for such system of equations is therefore of great practical interest. Efficient iterative algorithms are proposed for solving a system of linear equations. The approach is based on a preconditioning of the initial matrix of the system with an approximation of a generalized inverse leading to a stochastic preconditioned matrix. This approach, valid for non-negative matrices, is first extended to hermitian, semi-definite positive matrices and then generalized to any complex rectangular matrices. The main results obtained are as follows: 1) We are able to build a generalized inverse of any complex rectangular matrix which satisfies the convergence condition requested in iterative algorithms for solving a system of linear equations. This completes the (short) list of generalized inverse having this property, after Kaczmarz and Cimmino matrices. Theoretical results on both the characterization of the type of generalized inverse obtained and the convergence are derived. 2) Thanks to its properties, this matrix can be efficiently used in different solving schemes as Richardson-Tanabe or preconditioned conjugate gradients. 3) By using Lp norms, we propose generalized Kaczmarz’s type matrices. We also show how Cimmino's matrix can be considered as a particular case consisting in choosing the Euclidian norm in an asymmetrical structure. 4) Regarding numerical results obtained on some pathological well-known test-cases (Hilbert, Nakasaka, …), some of the proposed algorithms are empirically shown to be more efficient on ill-conditioned problems and more robust to error propagation than the known classical techniques we have tested (Gauss, Moore-Penrose inverse, minimum residue, conjugate gradients, Kaczmarz, Cimmino). We end on a very early prospective application of our approach based on stochastic matrices aiming at computing some parameters (such as the extreme values, the mean, the variance, …) of the solution of a linear system prior to its resolution. Such an approach, if it were to be efficient, would be a source of information on the solution of a system of linear equations.

Keywords: conditioning, generalized inverse, linear system, norms, stochastic matrix

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Authors: Istvan Szilagyi, Marko Pavlovic, Paul Rouster

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Antioxidant enzymes are the most efficient defense systems against reactive oxygen species, which cause severe damage in living organisms and industrial products. However, their supplementation is problematic due to their high sensitivity to the environmental conditions. Immobilization on carrier nanoparticles is a promising research direction towards the improvement of their functional and colloidal stability. In that way, their applications in biomedical treatments and manufacturing processes in the food, textile and cosmetic industry can be extended. The main goal of the present research was to prepare and formulate antioxidant bionanocomposites composed of superoxide dismutase (SOD) enzyme, anionic clay (layered double hydroxide, LDH) nanoparticle and heparin (HEP) polyelectrolyte. To characterize the structure and the colloidal stability of the obtained compounds in suspension and solid state, electrophoresis, dynamic light scattering, transmission electron microscopy, spectrophotometry, thermogravimetry, X-ray diffraction, infrared and fluorescence spectroscopy were used as experimental techniques. LDH-SOD composite was synthesized by enzyme immobilization on the clay particles via electrostatic and hydrophobic interactions, which resulted in a strong adsorption of the SOD on the LDH surface, i.e., no enzyme leakage was observed once the material was suspended in aqueous solutions. However, the LDH-SOD showed only limited resistance against salt-induced aggregation and large irregularly shaped clusters formed during short term interval even at lower ionic strengths. Since sufficiently high colloidal stability is a key requirement in most of the applications mentioned above, the nanocomposite was coated with HEP polyelectrolyte to develop highly stable suspensions of primary LDH-SOD-HEP particles. HEP is a natural anticoagulant with one of the highest negative line charge density among the known macromolecules. The experimental results indicated that it strongly adsorbed on the oppositely charged LDH-SOD surface leading to charge inversion and to the formation of negatively charged LDH-SOD-HEP. The obtained hybrid materials formed stable suspension even under extreme conditions, where classical colloid chemistry theories predict rapid aggregation of the particles and unstable suspensions. Such a stabilization effect originated from electrostatic repulsion between the particles of the same sign of charge as well as from steric repulsion due to the osmotic pressure raised during the overlap of the polyelectrolyte chains adsorbed on the surface. In addition, the SOD enzyme kept its structural and functional integrity during the immobilization and coating processes and hence, the LDH-SOD-HEP bionanocomposite possessed excellent activity in decomposition of superoxide radical anions, as revealed in biochemical test reactions. In conclusion, due to the improved colloidal stability and the good efficiency in scavenging superoxide radical ions, the developed enzymatic system is a promising antioxidant candidate for biomedical or other manufacturing processes, wherever the aim is to decompose reactive oxygen species in suspensions.

Keywords: clay, enzyme, polyelectrolyte, formulation

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Authors: I. Stathopoulos, V. Syrgiamiotis, E. Karavasilis, A. Ploussi, I. Nikas, C. Hatzigiorgi, K. Platoni, E. P. Efstathopoulos

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Introduction: Brain and central nervous system (CNS) tumors form the second most common group of cancer in children, accounting for 30% of all childhood cancers. MRI is the key imaging technique used for the visualization and management of pediatric brain tumors. Initial characterization of tumors from MRI scans is usually performed via a radiologist’s visual assessment. However, different brain tumor types do not always demonstrate clear differences in visual appearance. Using only conventional MRI to provide a definite diagnosis could potentially lead to inaccurate results, and so histopathological examination of biopsy samples is currently considered to be the gold standard for obtaining definite diagnoses. Machine learning is defined as the study of computational algorithms that can use, complex or not, mathematical relationships and patterns from empirical and scientific data to make reliable decisions. Concerning the above, machine learning techniques could provide effective and accurate ways to automate and speed up the analysis and diagnosis for medical images. Machine learning applications in radiology are or could potentially be useful in practice for medical image segmentation and registration, computer-aided detection and diagnosis systems for CT, MR or radiography images and functional MR (fMRI) images for brain activity analysis and neurological disease diagnosis. Purpose: The objective of this study is to provide an automated tool, which may assist in the imaging evaluation and classification of brain neoplasms in pediatric patients by determining the glioma type, grade and differentiating between different brain tissue types. Moreover, a future purpose is to present an alternative way of quick and accurate diagnosis in order to save time and resources in the daily medical workflow. Materials and Methods: A cohort, of 80 pediatric patients with a diagnosis of posterior fossa tumor, was used: 20 ependymomas, 20 astrocytomas, 20 medulloblastomas and 20 healthy children. The MR sequences used, for every single patient, were the following: axial T1-weighted (T1), axial T2-weighted (T2), FluidAttenuated Inversion Recovery (FLAIR), axial diffusion weighted images (DWI), axial contrast-enhanced T1-weighted (T1ce). From every sequence only a principal slice was used that manually traced by two expert radiologists. Image acquisition was carried out on a GE HDxt 1.5-T scanner. The images were preprocessed following a number of steps including noise reduction, bias-field correction, thresholding, coregistration of all sequences (T1, T2, T1ce, FLAIR, DWI), skull stripping, and histogram matching. A large number of features for investigation were chosen, which included age, tumor shape characteristics, image intensity characteristics and texture features. After selecting the features for achieving the highest accuracy using the least number of variables, four machine learning classification algorithms were used: k-Nearest Neighbour, Support-Vector Machines, C4.5 Decision Tree and Convolutional Neural Network. The machine learning schemes and the image analysis are implemented in the WEKA platform and MatLab platform respectively. Results-Conclusions: The results and the accuracy of images classification for each type of glioma by the four different algorithms are still on process.

Keywords: image classification, machine learning algorithms, pediatric MRI, pediatric oncology

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Authors: Bidisha Chatterjee, Sonal Grover, Rekha Gurung

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Postpartum dissection of the internal carotid artery is a relatively rare condition and is considered as an underlying aetiology in 5% to 25% of strokes under the age of 30 to 45 years. However, 86% of these cases recover completely and 14% have mild focal neurological symptoms. Prognosis is generally good with early intervention. The risk quoted for a repeat carotid artery dissection in subsequent pregnancies is less than 2%. 36-year Caucasian primipara presented on postnatal day one of forceps delivery with tachycardia. In the intrapartum period she had a history of prolonged rupture of membranes and developed intrapartum sepsis and was treated with antibiotics. Postpartum ECG showed septal inferior T wave inversion and a troponin level of 19. Subsequently Echocardiogram ruled out post-partum cardiomyopathy. Repeat ECG showed improvement of the previous changes and in the absence of symptoms no intervention was warranted. On day 4 post-delivery, she had developed symptoms of droopy right eyelid, pain around the right eye and itching in the right ear. On examination, she had developed right sided ptosis, unequal pupils (Rt miotic pupil). Cranial nerve examination, reflexes, sensory examination and muscle power was normal. Apart from migraine, there was no medical or family history of note. In view of Horner’s on the right, she had a CT Angiogram and subsequently MR/MRA and was diagnosed with dissection of the cervical portion of the right internal carotid artery. She was discharged on a course of Aspirin 75mg. By 6 week post-natal follow up patient had recovered significantly with occasional episodes of unequal pupils and tingling of right toes which resolved spontaneously. Cervical artery dissection, including VAD and carotid artery dissection, are rare complications of pregnancy with an estimated annual incidence of 2.6–3 per 100,000 pregnancy hospitalizations. Aetiology remains unclear though trauma during straining at labour, underlying arterial disease and preeclampsia have been implicated. Hypercoagulable state during pregnancy and puerperium could also be an important factor. 60-90% cases present with severe headache and neck pain and generally precede neurological symptoms like ipsilateral Horner’s syndrome, retroorbital pain, tinnitus and cranial nerve palsy. Although rare, the consequences of delayed diagnosis and management can lead to severe and permanent neurological deficits. Patients with a strong index of suspicion should undergo an MRI or MRA of head and neck. Antithrombotic and antiplatelet therapy forms the mainstay of therapy with selected cases needing endovascular stenting. Long term prognosis is favourable with either complete resolution or minimal deficit if treatment is prompt. Patients should be counselled about the recurrence risk and possibility of stroke in future pregnancy. Coronary artery dissection is rare and treatable but needs early diagnosis and treatment. Post-partum headache and neck pain with neurological symptoms should prompt urgent imaging followed by antithrombotic and /or antiplatelet therapy. Most cases resolve completely or with minimal sequelae.

Keywords: postpartum, dissection of internal carotid artery, magnetic resonance angiogram, magnetic resonance imaging, antiplatelet, antithrombotic

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Authors: Deon Bezuidenhout

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Pre-seeding with autologous endothelial cells improves the long-term patency of synthetic vascular grafts levels obtained with autografts, but is limited to a single centre due to resource, time and other constraints. Spontaneous in vivo endothelialization would obviate the need for pre-seeding, but has been shown to be absent in man due to limited transanastomotic and fallout healing, and the lack of transmural ingrowth due to insufficient porosity. Two types of graft scaffolds with increased interconnected porosity for improved tissue ingrowth and healing are thus proposed and described. Foam-type polyurethane (PU) scaffolds with small, medium and large, interconnected pores were made by phase inversion and spherical porogen extraction, with and without additional surface modification with covalently attached heparin and subsequent loading with and delivery of growth factors. Fibrillar scaffolds were made either by standard electrospinning using degradable PU (Degrapol®), or by dual electrospinning using non-degradable PU. The latter process involves sacrificial fibres that are co-spun with structural fibres and subsequently removed to increased porosity and pore size. Degrapol samples were subjected to in vitro degradation, and all scaffold types were evaluated in vivo for tissue ingrowth and vascularization using rat subcutaneous model. The foam scaffolds were additionally evaluated in a circulatory (rat infrarenal aortic interposition) model that allows for the grafts to be anastomotically and/or ablumenally isolated to discern and determine endothelialization mode. Foam-type grafts with large (150 µm) pores showed improved subcutaneous healing in terms of vascularization and inflammatory response over smaller pore sizes (60 and 90µm), and vascularization of the large porosity scaffolds was significantly increased by more than 70% by heparin modification alone, and by 150% to 400% when combined with growth factors. In the circulatory model, extensive transmural endothelialization (95±10% at 12 w) was achieved. Fallout healing was shown to be sporadic and limited in groups that were ablumenally isolated to prevent transmural ingrowth (16±30% wrapped vs. 80±20% control; p<0.002). Heparinization and GF delivery improved both mural vascularization and lumenal endothelialization. Degrapol electrospun scaffolds showed decrease in molecular mass and corresponding tensile strength over the first 2 weeks, but very little decrease in mass over the 4w test period. Studies on the effect of tissue ingrowth with and without concomitant degradation of the scaffolds, are being used to develop material models for the finite element modelling. In the case of the dual-spun scaffolds, the PU fibre fraction could be controlled shown to vary linearly with porosity (P = −0.18FF +93.5, r2=0.91), which in turn showed inverse linear correlation with tensile strength and elastic modulus (r2 > 0.96). Calculated compliance and burst pressures of the scaffolds increased with fibre fraction, and compliances matching the human popliteal artery (5-10 %/100 mmHg), and high burst pressures (> 2000 mmHg) could be achieved. Increasing porosity (76 to 82 and 90%) resulted in increased tissue ingrowth from 33±7 to 77±20 and 98±1% after 28d. Transmural endothelialization of highly porous foamed grafts is achievable in a circulatory model, and the enhancement of porosity and tissue ingrowth may hold the key the development of spontaneously endothelializing electrospun grafts.

Keywords: electrospinning, endothelialization, porosity, scaffold, vascular graft

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Authors: Francisco J. Ortega, Claudia Roman, Moisés García-Morales, Francisco J. Navarro

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Asphaltic bitumen has been largely used in both industrial and civil engineering, mostly in pavement construction and roofing membrane manufacture. However, bitumen as such is greatly susceptible to temperature variations, and dramatically changes its in-service behavior from a viscoelastic liquid, at medium-high temperatures, to a brittle solid at low temperatures. Bitumen modification prevents these problems and imparts improved performance. Isocyanates like polymeric MDI (mixture of 4,4′-diphenylmethane di-isocyanate, 2,4’ and 2,2’ isomers, and higher homologues) have shown to remarkably enhance bitumen properties at the highest in-service temperatures expected. This comes from the reaction between the –NCO pendant groups of the oligomer and the most polar groups of asphaltenes and resins in bitumen. In addition, oxygen diffusion and/or UV radiation may provoke bitumen hardening and ageing. With the purpose of minimizing these effects, nano-layered-silicates (nanoclays) are increasingly being added to bitumen formulations. Montmorillonites, a type of naturally occurring mineral, may produce a nanometer scale dispersion which improves bitumen thermal, mechanical and barrier properties. In order to increase their lipophilicity, these nanoclays are normally treated so that organic cations substitute the inorganic cations located in their intergallery spacing. In the present work, the combined effect of polymeric MDI and the commercial montmorillonite Cloisite® 20A was evaluated. A selected bitumen with penetration within the range 160/220 was modified with 10 wt.% Cloisite® 20A and 2 wt.% polymeric MDI, and the resulting ternary composites were characterized by linear rheology, X-ray diffraction (XRD) and Atomic Force Microscopy (AFM). The rheological tests evidenced a notable solid-like behavior at the highest temperatures studied when bitumen was just loaded with 10 wt.% Cloisite® 20A and high-shear blended for 20 minutes. However, if polymeric MDI was involved, the sequence of addition exerted a decisive control on the linear rheology of the final ternary composites. Hence, in bitumen/Cloisite® 20A/polymeric MDI formulations, the previous solid-like behavior disappeared. By contrast, an inversion in the order of addition (bitumen/polymeric MDI/ Cloisite® 20A) enhanced further the solid-like behavior imparted by the nanoclay. In order to gain a better understanding of the factors that govern the linear rheology of these ternary composites, a morphological and microstructural characterization based on XRD and AFM was conducted. XRD demonstrated the existence of clay stacks intercalated by bitumen molecules to some degree. However, the XRD technique cannot provide detailed information on the extent of nanoclay delamination, unless the entire fraction has effectively been fully delaminated (situation in which no peak is observed). Furthermore, XRD was unable to provide precise knowledge neither about the spatial distribution of the intercalated/exfoliated platelets nor about the presence of other structures at larger length scales. In contrast, AFM proved its power at providing conclusive information on the morphology of the composites at the nanometer scale and at revealing the structural modification that yielded the rheological properties observed. It was concluded that high-shear blending brought about a nanoclay-reinforced network. As for the bitumen/Cloisite® 20A/polymeric MDI formulations, the solid-like behavior was destroyed as a result of the agglomeration of the nanoclay platelets promoted by chemical reactions.

Keywords: Atomic Force Microscopy, bitumen, composite, isocyanate, montmorillonite.

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Authors: Divya SY. Ang, Mark B. Tan, Nicholas EM. Yeo, Siti RB. Sudirman, Khong Yik Chew

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Introduction: The importance of the amalgamation of technological and engineering advances with surgical principles of reconstruction cannot be overemphasized. With earlier detection of cancer, consequences of high-speed living and neglect, like traumatic injuries and infection, resulting in increasingly younger patients with bone defects. This may result in malformations and suboptimal function that is more noticeable and palpable in the younger, active demographic. Our team proposes a technique that encapsulates a mesh of multidisciplinary effort, tissue engineering and reconstructive principles. Methods/Materials: Our patient was a young competitive footballer in his early 30s who was diagnosed with submandibular adenoid cystic carcinoma with bony involvement. He was thus counselled for a right hemi mandibulectomy, the floor of mouth resection, right selective neck dissection, tracheostomy, and free fibular flap reconstruction of his mandible and required post-operative radiotherapy. Being young and in his prime sportsman years, he was unable to accept the morbidities associated with using his fibula to reconstruct his mandible despite it being the gold standard reconstructive option. The fibula is an ideal vascularized bone flap because it’s reliable and easily shaped with relatively minimal impact on functional outcomes. The fibula contributes to 30% of weightbearing and is the attachment for the lateral compartment muscles; it is stronger in footballers concerning lateral bending. When harvesting the fibula, the distal 6-8cm and up to 10% of the total length is preserved to maintain the ankle’s stability, thus, minimizing the impact on daily activities. There are studies that have noted gait variability post-operatively. Therefore, returning to a premorbid competitive level may be doubtful. To improve his functional outcomes, the decision was made to try and restore the fibula's form and function. Using the concept of Fused Deposition Modelling (FDM), our team comprising of Plastics, Otolaryngology, Orthopedics and Radiology, worked with Osteopore to design a 3D bioresorbable implant to regenerate the fibula defect (14.5cm). Bone marrow was harvested via reaming the contralateral hip prior to the wide resection. 30mls of his blood was obtained for extracting platelet rich plasma. These were packed into the Osteopore 3D-printed bone scaffold. This was then secured into the fibula defect with titanium plates and screws. The flexor hallucis longus and soleus were anchored along the construct and intraosseous membrane, done in a single setting. Results: He was reviewed closely as an outpatient over 10 months post operatively. He reported no discernable loss or difference in ankle function. He is satisfied and back in training and our team has video and photographs that substantiate his progress. Conclusion: FDM allows regeneration of long bone defects. However, we aimed to also restore his eversion and inversion that is imperative for footballers and hence reattached his previously dissected muscles along the length of the Osteopore implant. We believe that the reattachment of the muscle stabilizes not only the construct but allows optimum muscle tensioning when moving his ankle. This is a simple but effective technique in restoring complete function and form in a young patient whose minute muscle control is imperative to life.

Keywords: fused deposition modelling, functional reconstruction, lower limb bony defects, regenerative surgery, 3D printing, tissue engineering

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Authors: Nanine Fouche

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The Cape Flats is a low-lying sand-covered expanse of approximately 460 square kilometres, situated to the southeast of the central business district of Cape Town in the Western Cape of South Africa. The aeolian sands masking this area are often loose and compressible in the upper 1m to 1.5m of the surface, and there is a general exceedance of the maximum allowable settlement in these sands. The settlement of shallow foundations on Cape Flats sands is commonly predicted using the results of in-situ tests such as the SPT or DPSH due to the difficulty of retrieving undisturbed samples for laboratory testing. Varying degrees of accuracy and reliability are associated with these methods. More recently, shear wave velocity (Vs) profiles obtained from seismic testing, such as continuous surface wave tests (CSW), are being used for settlement prediction. Such predictions have the advantage of considering non-linear stress-strain behaviour of soil and the degradation of stiffness with increasing strain. CSW tests are rarely executed in the Cape Flats, whereas SPT’s are commonly performed. For this reason, and to facilitate better settlement predictions in Cape Flats sand, equations representing shear wave velocity (Vs) as a function of SPT blow count (N60) and vertical effective stress (v’) were generated by statistical regression of site investigation data. To reveal the most appropriate method of overburden correction, analyses were performed with a separate overburden term (Pa/σ’v) as well as using stress corrected shear wave velocity and SPT blow counts (correcting Vs. and N60 to Vs1and (N1)60respectively). Shear wave velocity profiles and SPT blow count data from three sites masked by Cape Flats sands were utilised to generate 80 Vs-SPT N data pairs for analysis. Investigated terrains included sites in the suburbs of Athlone, Muizenburg, and Atlantis, all underlain by windblown deposits comprising fine and medium sand with varying fines contents. Elastic settlement analysis was also undertaken for the Cape Flats sands, using a non-linear stepwise method based on small-strain stiffness estimates, which was obtained from the best Vs-N60 model and compared to settlement estimates using the general elastic solution with stiffness profiles determined using Stroud’s (1989) and Webb’s (1969) SPT N60-E transformation models. Stroud’s method considers strain level indirectly whereasWebb’smethod does not take account of the variation in elastic modulus with strain. The expression of Vs. in terms of N60 and Pa/σv’ derived from the Atlantis data set revealed the best fit with R2 = 0.83 and a standard error of 83.5m/s. Less accurate Vs-SPT N relations associated with the combined data set is presumably the result of inversion routines used in the analysis of the CSW results showcasing significant variation in relative density and stiffness with depth. The regression analyses revealed that the inclusion of a separate overburden term in the regression of Vs and N60, produces improved fits, as opposed to the stress corrected equations in which the R2 of the regression is notably lower. It is the correction of Vs and N60 to Vs1 and (N1)60 with empirical constants ‘n’ and ‘m’ prior to regression, that introduces bias with respect to overburden pressure. When comparing settlement prediction methods, both Stroud’s method (considering strain level indirectly) and the small strain stiffness method predict higher stiffnesses for medium dense and dense profiles than Webb’s method, which takes no account of strain level in the determination of soil stiffness. Webb’s method appears to be suitable for loose sands only. The Versak software appears to underestimate differences in settlement between square and strip footings of similar width. In conclusion, settlement analysis using small-strain stiffness data from the proposed Vs-N60 model for Cape Flats sands provides a way to take account of the non-linear stress-strain behaviour of the sands when calculating settlement.

Keywords: sands, settlement prediction, continuous surface wave test, small-strain stiffness, shear wave velocity, penetration resistance

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