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Atypical femoral fracture (AFF) often appears with bisphosphonate use. Teriparatide (TPTD) treatment may promote AFF healing, but few controlled or comparative studies have examined the effects of TPTD on healing of bisphosphonate-associated AFF. We retrospectively reviewed the medical records of 45 consecutive AFFs in 34 Japanese patients who had received oral bisphosphonates (alendronate or risedronate) for osteoporosis before AFF and had been followed for ≥12 months (range, 12-90 months). Thirty-seven complete or incomplete AFFs (82 %) were treated surgically and eight incomplete AFFs (18 %) were treated conservatively. Bisphosphonates were stopped at diagnosis. Based on TPTD use after fracture, AFFs were divided into non-TPTD (n = 24) and TPTD (n = 21) groups. Time to fracture-healing and frequency of delayed healing or non-union were compared between groups. Because fracture type (complete or incomplete) differed significantly between groups, only subanalyses for all surgically treated AFFs (complete and incomplete), surgically treated complete AFFs, and conservatively treated incomplete AFFs were performed. In subanalyses for all AFFs treated surgically, mean (± standard deviation) time to fracture healing was significantly better in the TPTD group (5.4 ± 1.5 months) than in the non-TPTD group (8.6 ± 4.7 months; P = 0.012), and the frequency of delayed healing or non-union was significantly lower in the TPTD group than in the non-TPTD group (P = 0.014). Subanalyses for surgically treated complete AFFs yielded similar results, but subanalyses for incomplete AFFs treated conservatively showed no significant differences between groups. TPTD treatment appears to significantly shorten the postoperative time to fracture healing and reduce rates of delayed healing or non-union after bisphosphonate-associated AFF.

This paper proposes a method for reconstructing the positions, strengths, and number of point sources in a three-dimensional (3D) Poisson field from boundary measurements. Algebraic relations are obtained, based on multipole moments determined by the sources and data on the boundary of a domain. To solve for the source parameters with efficient use of data, we select the necessary number of equations from them in the following two ways: (1) the use of those starting from lower-degree multipole moments; and (2) the use of combined ones involving infinitely higher-degree multipole moments. We show that both methods are based on the projection of 3D sources onto a two-dimensional space: the xy-plane for the first one and the Riemann sphere which is set to contain the domain for the second one. We also show that they share the same fundamental equations which can be solved by a procedure proposed by El-Badia and Ha-Duong (2000 Inverse Problems 16 651–63). Numerical simulations show that projection onto the xy-plane is more appropriate for sources scattered in the middle of the domain, whereas projection onto the Riemann sphere is more appropriate for sources concentrated close to the boundary of the domain. We also give an appropriate method of measurement for the Riemann sphere projection.

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