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In this paper we address the constrained longest common subsequence problem. Given two sequences $X$, $Y$ and a constrained sequence $P$, a sequence $Z$ is a constrained longest common subsequence for $X$ and $Y$ with respect to $P$ if $Z$ is the longest subsequence of $X$ and $Y$ such that $P$ is a subsequence of $Z$. Recently, Tsai \cite{Tsai} proposed an $O(n^2 \cdot m^2 \cdot r)$ time algorithm to solve this problem using dynamic programming technique, where $n$, $m$ and $r$ are the lengths of $X$, $Y$ and $P$, respectively. In this paper, we present a simple algorithm to solve the constrained longest common subsequence problem in $O(n \cdot m \cdot r)$ time and show that the constrained longest common subsequence problem is equivalent to a special case of the constrained multiple sequence alignment problem which can also be solved., Comment: https://doi.org/10.1016/j.ipl.2004.02.008

Background: Extended polyethylene terephthalate mesh (PET, Dacron) can provide containment of compressed particulate allograft and autograft. This study assessed if PET mesh would interfere with osteoprogenitor cell migration from vertebral plates through particulate graft, and its effect on osteoblast differentiation or the quality of bone forming within fusing vertebra during vertebral interbody fusion. Methods: The impact of PET mesh on the biological response of normal human osteoblasts (NHOst cells) and bone marrow stromal cells (MSCs) to particulate bone graft was examined in vitro. Cells were cultured on rat bone particles +/− mesh; proliferation and osteoblast differentiation were assessed. The interface between the vertebral endplate, PET mesh, and newly formed bone within consolidated allograft contained by mesh was examined in a sheep model via microradiographs, histology, and mechanical testing. Results: Growth on bone particles stimulated proliferation and early differentiation of NHOst cells and MSCs, but delayed terminal differentiation. This was not negatively impacted by mesh. New bone formation in vivo was not prevented by use of a PET mesh graft containment device. Fusion was improved in sites containing allograft/demineralized bone matrix (DBM) versus autograft and was further enhanced when stabilized using pedicle screws. Only sites treated with allograft/DBM+screws exhibited greater percent bone ingrowth versus discectomy or autograft. These results were mirrored biomechanically. Conclusions: PET mesh does not negatively impact cell attachment to particulate bone graft, proliferation, or initial osteoblast differentiation. The results demonstrated that bone growth occurs from vertebral endplates into graft material within the PET mesh. This was enhanced by stabilization with pedicle screws leading to greater bone ingrowth and biomechanical stability across the fusion site. Clinical Relevance: The use of extended PET mesh allows containment of bone graft material during vertebral interbody fusion without inhibiting migration of osteoprogenitor cells from vertebral end plates in order to achieve fusion. Level of Evidence: 5.

INTRODUCTION: The objectives of this paper were to identify and explain specific design factors for lumbar interbody fusion (IBF) devices that can influence bone exchange and stability at the vertebral endplate interface and to provide supporting evidence of these factors through both laboratory and clinical data. The laboratory study (Part 1) compared the pressure profiles and contact areas for a minimally invasive, expandable, and conformable porous mesh (CPM) IBF device and a rigid monolithic lateral PEEK cage (LPC). Furthermore, to demonstrate how these laboratory results translate clinically, a quantitative and qualitative assessment of subject x-rays and computed tomography (CT) scans from a US Food and Drug Administration (FDA) investigational device exemption (IDE) trial of the CPM was performed (Part 2). METHODS: Part 1: Load profile testing. Either CPM or LPC was sandwiched between 2 flat or shaped Grade 15 foam blocks. Each implant type was compressed at a rate of 0.1 mm/s for 3 loads (1100, 2000, or 3000 N). Device and bone graft contact area were analyzed for each test condition, and corresponding load profiles were quantified and mapped using pressure film. Part 2: Radiographic fusion assessment. Two independent radiologists analyzed 12- and 24-month motion studies and CTs for fusion, defined as bridging bone across the intervertebral space. The same CTs were assessed for qualitative biomechanical signs of bone healing. RESULTS: CPM demonstrated significant direct loading on the bone graft across all tested loading conditions, while the LPC graft registered a negligible amount of pressure at only the extreme load of 3000 N. Contact area was in turn statistically greater (P < .05) for CPM. CPM fusion rates were 97.9% and 99% at 12 and 24 months, respectively. Radiographic signs of bone healing are described in terms of radiating bone struts and regions of greater intensity. CONCLUSIONS: CPM allows for an optimized contact area for bone exchange and graft incorporation. The load profiles demonstrate widespread load sharing across the device. The expandable, compliant, porous mesh provides a unique area for bone exchange, contributing to qualitative biomechanical radiographic evidence of bone healing that ultimately leads to clinically acceptable fusion rates as observed in the FDA IDE trial.

Background: Expandable cages that allow for bidirectional expansion, in both height and width, may offer benefits over traditional expandable cages or static cages. Effective stiffness must also be considered, as implants with exceedingly high stiffness may increase subsidence risk and reduce graft loading. Methods: A retrospective case series of 7 patients were assessed with computed tomography (CT) scan at the final 1-year follow-up to evaluate the interbody fusion and configuration of the expandable cage related to the endplates within the intervertebral space. CT scans were reformatted using cage9s tantalum markers as fiducials for single-plane orientation for each intervertebral cage. Device height and width at maximum in situ expansion was measured at its anterior and posterior aspects to evaluate implant deformation. The new bone volume within each cage was measured from the same CT scan data sets and by the Bridwell classification of interbody fusion. Results: The average difference between medial and lateral height measurements was 1.82 mm (±1.08) at the device9s anterior aspect and 1.41 mm (±0.98) at the posterior aspect. The average difference between medial and lateral heights was 18.55% (±9.34) anteriorly and 15.49% (±9.24) posteriorly. There was a successful fusion in all 7 patients, as evidenced by measurable bone volume in the center of each interbody cage with an average of 586.42 mm3 (±237.06). Conclusion: The authors demonstrated the feasibility of successfully using bidirectionally expandable multimaterial cages to achieve interbody fusion. These composite open-architecture cages were found to conform to each patient9s endplate configuration. The authors9 observations support the concept of material selection impacting the effective construct stiffness. The design investigated by the authors provided sufficient anterior column support and successful fusion in all patients. Level of Evidence: 4.

Background: A successful intervertebral fusion requires biomechanical stability created by the structural support of the interbody device and loading of the bone graft material to accelerate mechanotransduction and bone remodeling. The objective of this study was to generate a quantitative map of the contact area and stress profile for 2 implant designs; a rigid monolithic polyetheretherketone (PEEK) lateral cage (MPLC), and a unique hybrid interbody design, which includes PEEK terminal supports surrounding an expandable porous mesh (P+EPM) that serves to contain bone graft. Methods: The construct for each test consisted of a device sandwiched between 2 flat or shaped Grade 15 foam blocks. Pressure sensitive film and thin film sensors were placed between the device and each of the foam blocks. A series of each implant type was compressed at a rate 0.1 mm/second for 2 loads (1100 N and 2000 N) with and without bone graft. Device and bone graft contact area were analyzed for each test condition and corresponding load profiles were quantified and mapped. Results: P+EPM demonstrated 34% greater graft volume than MPLC resulting in a 28% larger area for bone exchange when filled. The load profiles for all applied loading paradigms for P+EPM demonstrated significant direct loading on the bone graft contained within the mesh, resulting in at least 170% greater loaded area than MPLC. Furthermore, the P+EPM demonstrated load sharing with the terminal PEEK supports. MPLC for all loading conditions demonstrated negligible bone graft loading. Conclusions: P+EPM allows for an optimized contact area for bone exchange and graft incorporation. The load profiles confirmed that the filled mesh does not stress shield terminal PEEK supports and will load share. The expandable, compliant, porous mesh provides a greater multiplanar area for bone exchange and allows for direct contact with the viscoelastic vertebral endplates, improving the endplate and graft interface mechanics.

Background: Bidirectional expandable designs for lumbar interbody fusion cages are the latest iteration of expandable spacers employed to address some of the common problems inherent to static interbody fusion cages. Objective: To describe the rationales for contemporary bidirectional, multimaterial expandable lumbar interbody fusion cage designs to achieve in situ expansion for maximum anterior column support while decreasing insertion size during minimal-access surgeries. Methods: The authors summarize the current concepts behind expandable spinal fusion open architecture cage designs focusing on advanced minimally invasive spinal surgery techniques, such as endoscopy. A cage capable of bidirectional expansion in both height and width to address constrained surgical access problems was of particular interest to the authors while they analyzed the relationship between implant material stiffness and geometric design regarding the risk of subsidence and reduced graft loading. Conclusions: Biomechanical advantages of new bidirectional, multimaterial expandable interbody fusion cages allow insertion through minimal surgical access and combine the advantages of proven device configurations and advanced material selection. The final construct stiffness is sufficient to provide immediate anterior column support while accommodating reduced sizes required for minimally invasive surgery applications. Level of Evidence: 7.

Background: Expandable cages have gone through several iterations since they first appeared on the market in the early 2000s. Their development was prompted by some common problems associated with static interbody cages, including migration, expulsion, dural or neural traction injury, and pseudarthrosis. Objective: To summarize current technological advances from earlier expandable lumbar interbody fusion devices to implants with vertical and medial-to-lateral expansion mechanisms. Methods: The authors review the currently available expandable cage designs, the incremental technological advances, and how these devices impact minimally invasive surgery interbody procedures and clinical outcomes. The strategic concepts intended to improve the minimally invasive application of expandable interbody fusion implants are reviewed from a surgeon9s perspective in a clinical context to discuss how their use may improve patient outcomes. Conclusions: The geometrical configuration, effective stiffness of composite multi-material cage designs may impact the bone-implant contact area with the endplates. Hybridization strategies of expandable cage technology with modern minimally invasive and endoscopic spinal surgery techniques are presented by outlining their advantages and disadvantages. Level of Evidence: 1 Clinical Relevance: Systematic review.

The new general data protection regulation requires organizations to conduct a data protection impact assessment (DPIA) when the processing of personal information may result in high risk to individual rights and freedoms. DPIA allows organizations to identify, assess and prioritize the risks related to the processing of personal information and select suitable mitigations to reduce the severity of the risks. The existing DPIA methodologies measure the severity of privacy risks according to analysts’ opinions about the likelihood and the impact factors of the threats. The assessment is therefore subjective to the expertise of the analysts. To reduce subjectivity, we propose a set of well-defined criteria that analysts can use to measure the likelihood and the impact of a privacy risk. Then, we adopt the fuzzy multi-criteria decision-making approach to systematically measure the severity of privacy risks while modeling the imprecision and vagueness inherent in linguistic assessment. Our approach is illustrated for a realistic scenario with respect to LINDDUN threat categories.