In this note a graph G is a finite 1-complex, and an imbedding of G in an orientable 2-manifold M is a geometric realization of G in M.The letter G will also be used to designate the set in M which is the realization of G. Manifolds will always be orientable 2-manifolds, and y(M) will stand for the genus of M. Given a graph G the genus y(G) of G is the smallest number y(M), for M in the collection of manifolds in which G can be imbedded.A block of G is a subgraph B of G maximal with respect to the property that removing any single vertex of B does not disconnect 5, (A block with more than two vertices is a "true cyclic element" in Whyburn

PurposeMedial meniscus posterior root tears (MMPRT) induce medial meniscus extrusion (MME). However, the time-dependent extent of MME in patients suffering from the MMPRT remains unclear. This study evaluated the extent of MME after painful popping events that occurred at the onset of the MMPRT.Materials and MethodsThirty-five patients who had an episode of posteromedial painful popping were investigated. All the patients were diagnosed as having an MMPRT by magnetic resonance imaging (MRI) within 12 months after painful popping. Medial meniscus body width (MMBW), absolute MME, and relative MME (100×absolute MME/MMBW) were assessed among three groups divided according to the time after painful popping events: early period (<1 month), subacute period (1–3 months), and chronic period (4–12 months).ResultsIn the early period, absolute and relative MMEs were 3.0 mm and 32.7%, respectively. Absolute MME increased up to 4.2 mm and 5.8 mm during the subacute and chronic periods, respectively. Relative MME also progressed to 49.2% and 60.3% in the subacute and chronic periods, respectively.ConclusionsThis study demonstrated that absolute and relative MMEs increased progressively within the short period after the onset of symptomatic MMPRT. Our results suggest that early diagnosis of an MMPRT may be important to prevent progression of MME following the MMPRT.

Background: Lateral meniscus (LM) posterior root tears (PRT) are often associated with anterior cruciate ligament (ACL) injury and can result in rotational instability, joint overloading, and degenerative changes in the knee. Improved rotational stability and kinematics have been reported after LMPRT repair. However, it is unclear which repair technique can achieve the greatest reduction in lateral meniscus extrusion (LME).Hypothesis: We hypothesized that transtibial pullout repair would decrease LME to a greater extent than other repair techniques.Patients and Methods: Seventeen patients with ACL injury but complete LM posterior root were evaluated. Nine underwent ACL reconstruction (ACLR) and transtibial pullout repair, and eight underwent ACLR and other repairs such as inside-out suturing. Double-bundle ACLR was performed using hamstring tendons, and LMPRT pullout was performed through the bone tunnel for the PL bundle. Magnetic resonance imaging was performed immediately preoperatively and at >6 months postoperatively, and LME was measured from coronal images only.Results: A significant decrease in the size of LME from pre-to postoperative measurement was observed in the transtibial pullout repair group (−0.5 ± 0.7 mm) than the other-repair group (1.0 ± 0.9 mm, P < 0.01). Pre-and postoperative LME measurements were not significantly different between the two groups.Discussion: The most important finding of this study is that transtibial pullout repair results in Transtibial pullout repair of LMPRT combined with ACLR reduces LM extrusion a greater decrease in LME than other repair techniques in patients with ACL injury and LMPRT. This technique might be useful for restoring hoop tension by decreasing LME.

This study demonstrated that our semi-quantitative scoring system of meniscal healing correlated with the KOOS QOL subscale following MMPRT transtibial pullout repair. Our results suggest that the second-look arthroscopic score using this system may be a useful scale to determine and compare the healing status of the MM posterior root.

A medial meniscus posterior root tear (MMPRT) may increase the tibiofemoral contact pressure by decreasing the tibiofemoral contact area. Meniscal dysfunction induced by posterior root injury may lead to the development of osteoarthritic knees. Repair of a MMPRT can restore medial meniscus (MM) function and prevent knee osteoarthritis progression. Several surgical procedures have been reported for treating a MMPRT. However, these procedures are associated with several technical difficulties. Here, we describe a technique to stabilize a torn MM posterior root using the FasT-Fix all-inside meniscal suture device and a new aiming device. The uncut free-end of the FasT-Fix suture can be used as a thread for transtibial pullout repair. Our procedure might help overcome the technical difficulties in arthroscopic treatment of a MMPRT.