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Papers by mazen ali

Lecture Notes in Computational Science and Engineering

A (multi-)wavelet expansion is used to derive a rigorous bound for the (dual) norm Reduced Basis ... more A (multi-)wavelet expansion is used to derive a rigorous bound for the (dual) norm Reduced Basis residual. We show theoretically and numerically that the error estimator is online efficient, reliable and rigorous. It allows to control the exact error (not only with respect to a "truth" discretization).

Advances in Computational Mathematics, 2020

This paper is concerned with the construction, analysis and realization of a numerical method to ... more This paper is concerned with the construction, analysis and realization of a numerical method to approximate the solution of high dimensional elliptic partial differential equations. We propose a new combination of an Adaptive Wavelet Galerkin Method (AWGM) and the wellknown Hierarchical Tensor (HT) format. The arising HT-AWGM is adaptive both in the wavelet representation of the low dimensional factors and in the tensor rank of the HT representation. The point of departure is an adaptive wavelet method for the HT format using approximate Richardson iterations from [1] and an AWGM method as described in [13]. HT-AWGM performs a sequence of Galerkin solves based upon a truncated preconditioned conjugate gradient (PCG) algorithm from [33] in combination with a tensor-based preconditioner from [3]. Our analysis starts by showing convergence of the truncated conjugate gradient method. The next step is to add routines realizing the adaptive refinement. The resulting HT-AWGM is analyzed concerning convergence and complexity. We show that the performance of the scheme asymptotically depends only on the desired tolerance with convergence rates depending on the Besov regularity of low dimensional quantities and the low rank tensor structure of the solution. The complexity in the ranks is algebraic with powers of four stemming from the complexity of the tensor truncation. Numerical experiments show the quantitative performance.

Advances in Computational Mathematics, 2016

We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) for... more We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot (i.e., parameter-dependent) do not permit the standard RB 'truth space', but allow for error estimation of the RB approximation with respect to the exact solution of the considered parameterized partial differential equation. The residual-based a posteriori error estimators are computed by an adaptive dual wavelet expansion, which allows us to compute a surrogate of the dual norm of the residual. The resulting adaptive RBM is analyzed. We show the convergence of the resulting adaptive greedy method. Numerical experiments for stationary and instationary problems underline the potential of this approach.

We use asymptotically optimal adaptive numerical solvers (here specifically a wavelet scheme) wit... more We use asymptotically optimal adaptive numerical solvers (here specifically a wavelet scheme) within the offline phase of the Reduced Basis Method (RBM). Those different discretizations for each parameter require also an adaptive evaluation of residual-based error estimators. The corresponding scheme is analyzed. It allows an error estimate of the RB approximation with respect to the exact solution of the parameterized partial differential equation to be treated by the RBM. We show that mul

International Journal of Molecular Sciences, 2017

Recent research has confirmed the presence of Mesenchymal stem cell (MSC)-like progenitors (MPC) ... more Recent research has confirmed the presence of Mesenchymal stem cell (MSC)-like progenitors (MPC) in both normal and osteoarthritic cartilage. However, there is only limited information concerning how MPC markers are expressed with osteoarthritis (OA) progression. The purpose of this study was to compare the prevalence of various MPC markers in different OA grades. Human osteoarthritic tibial plateaus were obtained from ten patients undergoing total knee replacement. Each sample had been classified into a mild or severe group according to OARSI scoring. Tissue was taken from each specimen and mRNA expression levels of CD105, CD166, Notch 1, Sox9, Acan and Col II A1 were measured at day 0 and day 14 (2 weeks in vitro). Furthermore, MSC markers: Nucleostemin, CD90, CD73, CD166, CD105 and Notch 1 were studied by immunofluorescence. mRNA levels of MSC markers did not differ between mild and severe OA at day 0. At day 14, protein analysis showed that proliferated cells from both sources expressed all 6 MSC markers. Only cells from the mild OA subjects resulted in a significant increase of mRNA CD105 and CD166 after in vitro expansion. Moreover, cells from the mild OA subjects showed significantly higher levels of CD105, Sox9 and Acan compared with those from severe OA specimens. Results confirmed the presence of MSC markers in mild and severe OA tissue at both mRNA and protein levels. We found significant differences between cells obtained from mild compared to severe OA specimens suggests that mild OA derived cells may have a greater MSC potential.

Revue de Chirurgie Orthopédique et Traumatologique, 2017

s des communications particulières / Revue de chirurgie orthopédique et traumatologique 103S (201... more s des communications particulières / Revue de chirurgie orthopédique et traumatologique 103S (2017) S27-S145 CO-69 Morbi-mortalité d'une série observationnelle monocentrique rétrospective de 18 patients victimes d'une fracture inter-prothétique fémorale Morbi-mortality of 18 patients with inter-prosthetic femoral fracture

Cureus, 2020

Issaoui et al. This is an open access article distributed under the terms of the Creative Commons... more Issaoui et al. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Revue de Chirurgie Orthopédique et Traumatologique, 2011

Revue de Chirurgie Orthopédique et Traumatologique, 2012

International Wound Journal, 2013

Negative pressure wound therapy combined with timed, cyclical instillation (NPWTi) of topical wou... more Negative pressure wound therapy combined with timed, cyclical instillation (NPWTi) of topical wound solutions has been recently presented as a new adjunctive modality for treating wounds with signs of infection. Normal saline, antiseptics and antimicrobials all have been proposed in scientific and clinical studies as potentially effective when used with NPWTi for treating heavily infected wounds. This is a prospective clinical study of 131 patients with 131 wounds treated with NPWTi using saline between January 2012 and December 2012 in two orthopaedic centres and one surgical wound healing centre in France. Saline was exclusively used. Results were favourable: in 98% of the cases, the wounds could be closed after debridement and following the use of NPWTi. Mean duration of NPWTi was 12·19 days. This does not preclude the need for treating the biofilm appropriately with more active antibacterial products when biofilm has been documented.

Revue de Chirurgie Orthopédique et Réparatrice de l'Appareil Moteur, 2007

ABSTRACT Les pertes de substance cutanées de la cheville et du pied posent un problème de couvert... more ABSTRACT Les pertes de substance cutanées de la cheville et du pied posent un problème de couverture du fait de la pauvreté de la vascularisation cutanée distale et du faible environnement musculaire, limitant les possibilités de plasties cutanées locales et de l’absence de lambeaux musculaires facilement mobilisables et fiables sur le plan vasculaire. À partir d’une série continue, nous avons analysé les résultats de couvertures par lambeaux, et nous avons essayé d’en préciser les indications. Matériels et Méthodes Une série rétrospective de 32 patients (11 femmes et 21 hommes) avec une moyenne d’âge de 35 ans. La localisation de la perte de substance était : face antérieure de la cheville 14 cas ; face interne de la cheville 5 cas ; face dorsale du pied 7 cas ; face postérieure du talon 6 cas. Les dimensions moyennes de la PDS étaient de 8,5 x 5,5 cm. 21 Lambeaux étaient homo latéraux, 5 lambeaux libres et 6 lambeaux controlatéraux (cross-leg). Résultats À 34 mois de recul 28 lambeaux ont cicatrisés en première intention, 1 lambeau s’est compliqué par un hématome et 2 avec nécrose partielle qui ont guéri après reprise chirurgicale. 1 lambeau s’est compliqué d’une nécrose complète repris par un autre lambeau. La cicatrisation a été obtenue dans un délai de 3 semaines, 3 reprises ont été nécessaires pour complication septique. Discussion La couverture de perte de substance initiale a été obtenue totalement dans tous les cas. Le lambeau sural est un procédé très utile pour assurer la couverture de la PSD de la cheville et du pied. Dans notre série, 5 lambeaux cross-leg ont été réalisés avec succès, la seule alternative étant un lambeau libre musculaire, avec un terrain d’anastomose vasculaire défavorable. Conclusion Le lambeau neuro-cutané sural à pédicule distal est une technique de choix pour la reconstruction des pertes de substance de la cheville et de la face dorsale du pied, c’est un lambeau fiable, sans séquelles majeures, et de faible rançon cicatricielle. Il peut être utilisé en version croisée comme alternative d’un lambeau libre musculaire avec un terrain d’anastomose vasculaire défavorable. Toutefois, l’utilisation du système VAC a considérablement restreint les indications de lambeaux et permet de solutionner des situations difficiles à traiter dans les pertes de substances de la cheville et du pied.

The Journal of Foot and Ankle Surgery, 2010

We present the case of a 64-year-old woman with a subcutaneous vascular leiomyoma in the tarsal t... more We present the case of a 64-year-old woman with a subcutaneous vascular leiomyoma in the tarsal tunnel in the ankle. The patient presented with pain of several years' duration in the medial aspect of the ankle in the retromalleolar region corresponding to the tarsal tunnel and associated with a subcutaneous mass. We report the clinical manifestation, the imaging and histopathologic features, and a review of the literature. Vascular leiomyomas are part of the differential diagnosis of painful subcutaneous masses in the lower extremity.

Foot and Ankle Surgery, 2007

Posterior tibial nerve entrapment can be caused by extrinsic compression in the tarsal tunnel. We... more Posterior tibial nerve entrapment can be caused by extrinsic compression in the tarsal tunnel. We report a nerve compression due to a chondroma in the tarsal tunnel. To our knowledge it is a very rare cause of tarsal tunnel syndrome.

Lecture Notes in Computational Science and Engineering

A (multi-)wavelet expansion is used to derive a rigorous bound for the (dual) norm Reduced Basis ... more A (multi-)wavelet expansion is used to derive a rigorous bound for the (dual) norm Reduced Basis residual. We show theoretically and numerically that the error estimator is online efficient, reliable and rigorous. It allows to control the exact error (not only with respect to a "truth" discretization).

Advances in Computational Mathematics, 2020

This paper is concerned with the construction, analysis and realization of a numerical method to ... more This paper is concerned with the construction, analysis and realization of a numerical method to approximate the solution of high dimensional elliptic partial differential equations. We propose a new combination of an Adaptive Wavelet Galerkin Method (AWGM) and the wellknown Hierarchical Tensor (HT) format. The arising HT-AWGM is adaptive both in the wavelet representation of the low dimensional factors and in the tensor rank of the HT representation. The point of departure is an adaptive wavelet method for the HT format using approximate Richardson iterations from [1] and an AWGM method as described in [13]. HT-AWGM performs a sequence of Galerkin solves based upon a truncated preconditioned conjugate gradient (PCG) algorithm from [33] in combination with a tensor-based preconditioner from [3]. Our analysis starts by showing convergence of the truncated conjugate gradient method. The next step is to add routines realizing the adaptive refinement. The resulting HT-AWGM is analyzed concerning convergence and complexity. We show that the performance of the scheme asymptotically depends only on the desired tolerance with convergence rates depending on the Besov regularity of low dimensional quantities and the low rank tensor structure of the solution. The complexity in the ranks is algebraic with powers of four stemming from the complexity of the tensor truncation. Numerical experiments show the quantitative performance.

Advances in Computational Mathematics, 2016

We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) for... more We use asymptotically optimal adaptive numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot (i.e., parameter-dependent) do not permit the standard RB 'truth space', but allow for error estimation of the RB approximation with respect to the exact solution of the considered parameterized partial differential equation. The residual-based a posteriori error estimators are computed by an adaptive dual wavelet expansion, which allows us to compute a surrogate of the dual norm of the residual. The resulting adaptive RBM is analyzed. We show the convergence of the resulting adaptive greedy method. Numerical experiments for stationary and instationary problems underline the potential of this approach.

We use asymptotically optimal adaptive numerical solvers (here specifically a wavelet scheme) wit... more We use asymptotically optimal adaptive numerical solvers (here specifically a wavelet scheme) within the offline phase of the Reduced Basis Method (RBM). Those different discretizations for each parameter require also an adaptive evaluation of residual-based error estimators. The corresponding scheme is analyzed. It allows an error estimate of the RB approximation with respect to the exact solution of the parameterized partial differential equation to be treated by the RBM. We show that mul

International Journal of Molecular Sciences, 2017

Recent research has confirmed the presence of Mesenchymal stem cell (MSC)-like progenitors (MPC) ... more Recent research has confirmed the presence of Mesenchymal stem cell (MSC)-like progenitors (MPC) in both normal and osteoarthritic cartilage. However, there is only limited information concerning how MPC markers are expressed with osteoarthritis (OA) progression. The purpose of this study was to compare the prevalence of various MPC markers in different OA grades. Human osteoarthritic tibial plateaus were obtained from ten patients undergoing total knee replacement. Each sample had been classified into a mild or severe group according to OARSI scoring. Tissue was taken from each specimen and mRNA expression levels of CD105, CD166, Notch 1, Sox9, Acan and Col II A1 were measured at day 0 and day 14 (2 weeks in vitro). Furthermore, MSC markers: Nucleostemin, CD90, CD73, CD166, CD105 and Notch 1 were studied by immunofluorescence. mRNA levels of MSC markers did not differ between mild and severe OA at day 0. At day 14, protein analysis showed that proliferated cells from both sources expressed all 6 MSC markers. Only cells from the mild OA subjects resulted in a significant increase of mRNA CD105 and CD166 after in vitro expansion. Moreover, cells from the mild OA subjects showed significantly higher levels of CD105, Sox9 and Acan compared with those from severe OA specimens. Results confirmed the presence of MSC markers in mild and severe OA tissue at both mRNA and protein levels. We found significant differences between cells obtained from mild compared to severe OA specimens suggests that mild OA derived cells may have a greater MSC potential.

Revue de Chirurgie Orthopédique et Traumatologique, 2017

s des communications particulières / Revue de chirurgie orthopédique et traumatologique 103S (201... more s des communications particulières / Revue de chirurgie orthopédique et traumatologique 103S (2017) S27-S145 CO-69 Morbi-mortalité d'une série observationnelle monocentrique rétrospective de 18 patients victimes d'une fracture inter-prothétique fémorale Morbi-mortality of 18 patients with inter-prosthetic femoral fracture

Cureus, 2020

Issaoui et al. This is an open access article distributed under the terms of the Creative Commons... more Issaoui et al. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Revue de Chirurgie Orthopédique et Traumatologique, 2011

Revue de Chirurgie Orthopédique et Traumatologique, 2012

International Wound Journal, 2013

Negative pressure wound therapy combined with timed, cyclical instillation (NPWTi) of topical wou... more Negative pressure wound therapy combined with timed, cyclical instillation (NPWTi) of topical wound solutions has been recently presented as a new adjunctive modality for treating wounds with signs of infection. Normal saline, antiseptics and antimicrobials all have been proposed in scientific and clinical studies as potentially effective when used with NPWTi for treating heavily infected wounds. This is a prospective clinical study of 131 patients with 131 wounds treated with NPWTi using saline between January 2012 and December 2012 in two orthopaedic centres and one surgical wound healing centre in France. Saline was exclusively used. Results were favourable: in 98% of the cases, the wounds could be closed after debridement and following the use of NPWTi. Mean duration of NPWTi was 12·19 days. This does not preclude the need for treating the biofilm appropriately with more active antibacterial products when biofilm has been documented.

Revue de Chirurgie Orthopédique et Réparatrice de l'Appareil Moteur, 2007

ABSTRACT Les pertes de substance cutanées de la cheville et du pied posent un problème de couvert... more ABSTRACT Les pertes de substance cutanées de la cheville et du pied posent un problème de couverture du fait de la pauvreté de la vascularisation cutanée distale et du faible environnement musculaire, limitant les possibilités de plasties cutanées locales et de l’absence de lambeaux musculaires facilement mobilisables et fiables sur le plan vasculaire. À partir d’une série continue, nous avons analysé les résultats de couvertures par lambeaux, et nous avons essayé d’en préciser les indications. Matériels et Méthodes Une série rétrospective de 32 patients (11 femmes et 21 hommes) avec une moyenne d’âge de 35 ans. La localisation de la perte de substance était : face antérieure de la cheville 14 cas ; face interne de la cheville 5 cas ; face dorsale du pied 7 cas ; face postérieure du talon 6 cas. Les dimensions moyennes de la PDS étaient de 8,5 x 5,5 cm. 21 Lambeaux étaient homo latéraux, 5 lambeaux libres et 6 lambeaux controlatéraux (cross-leg). Résultats À 34 mois de recul 28 lambeaux ont cicatrisés en première intention, 1 lambeau s’est compliqué par un hématome et 2 avec nécrose partielle qui ont guéri après reprise chirurgicale. 1 lambeau s’est compliqué d’une nécrose complète repris par un autre lambeau. La cicatrisation a été obtenue dans un délai de 3 semaines, 3 reprises ont été nécessaires pour complication septique. Discussion La couverture de perte de substance initiale a été obtenue totalement dans tous les cas. Le lambeau sural est un procédé très utile pour assurer la couverture de la PSD de la cheville et du pied. Dans notre série, 5 lambeaux cross-leg ont été réalisés avec succès, la seule alternative étant un lambeau libre musculaire, avec un terrain d’anastomose vasculaire défavorable. Conclusion Le lambeau neuro-cutané sural à pédicule distal est une technique de choix pour la reconstruction des pertes de substance de la cheville et de la face dorsale du pied, c’est un lambeau fiable, sans séquelles majeures, et de faible rançon cicatricielle. Il peut être utilisé en version croisée comme alternative d’un lambeau libre musculaire avec un terrain d’anastomose vasculaire défavorable. Toutefois, l’utilisation du système VAC a considérablement restreint les indications de lambeaux et permet de solutionner des situations difficiles à traiter dans les pertes de substances de la cheville et du pied.

The Journal of Foot and Ankle Surgery, 2010

We present the case of a 64-year-old woman with a subcutaneous vascular leiomyoma in the tarsal t... more We present the case of a 64-year-old woman with a subcutaneous vascular leiomyoma in the tarsal tunnel in the ankle. The patient presented with pain of several years' duration in the medial aspect of the ankle in the retromalleolar region corresponding to the tarsal tunnel and associated with a subcutaneous mass. We report the clinical manifestation, the imaging and histopathologic features, and a review of the literature. Vascular leiomyomas are part of the differential diagnosis of painful subcutaneous masses in the lower extremity.

Foot and Ankle Surgery, 2007

Posterior tibial nerve entrapment can be caused by extrinsic compression in the tarsal tunnel. We... more Posterior tibial nerve entrapment can be caused by extrinsic compression in the tarsal tunnel. We report a nerve compression due to a chondroma in the tarsal tunnel. To our knowledge it is a very rare cause of tarsal tunnel syndrome.