Hematopoietic progenitor cell content of vertebral body marrow used for combined solid organ and bone marrow transplantation

While cadaveric vertebral bodies (VB) have long been proposed as a suitable source of bone marrow (BM) for transplantation (BMT), they have rarely been used for this purpose. We have infused VB BM immediately following whole organ (WO) transplantation to augment donor cell chimerism. We quantified the hematopoietic progenitor cell (HPC) content of VB BM as well as BM obtained from the iliac crests (IC) of normal allogeneic donors (ALLO) and from patients with malignancy undergoing autologous marrow harvest (AUTO). Patients undergoing WO/BM transplantation also had AUTO BM harvested in the event that subsequent lymphohematopoietic reconstitution was required. Twenty-four VB BM, 24 IC BM-ALLO, 31 IC AUTO, and 24 IC WO-AUTO were harvested. VB BM was tested 12 to 72 hr after procurement and infused after completion of WO grafting. IC BM was tested and then used or cryopreserved immediately. HPC were quantified by clonal assay measuring CFU-GM, BFU-E, and CFU-GEMM, and by flow cytometry for CD34+ progenitor cells. On an average, 9 VB were processed during each harvest, and despite an extended processing time the number of viable nucleated cells obtained was significantly higher than that from IC. Furthermore, by HPC content, VB BM was equivalent to IC BM, which is routinely used for BMT. We conclude that VB BM is a clinically valuable source of BM for allogeneic transplantation. © 1995 by Williams & Wilkins

Combinatorics of linear iterated function systems with overlaps

Let $\bm p_0,...,\bm p_{m-1}$ be points in ${\mathbb R}^d$, and let $\{f_j\}_{j=0}^{m-1}$ be a one-parameter family of similitudes of ${\mathbb R}^d$: $$f_j(\bm x) = \lambda\bm x + (1-\lambda)\bm p_j, j=0,...,m-1,$$ where $\lambda\in(0,1)$ is our parameter. Then, as is well known, there exists a unique self-similar attractor $S_\lambda$ satisfying $S_\lambda=\bigcup_{j=0}^{m-1} f_j(S_\lambda)$. Each $\bm x\in S_\lambda$ has at least one address $(i_1,i_2,...)\in\prod_1^\infty\{0,1,...,m-1\}$, i.e., $\lim_n f_{i_1}f_{i_2}... f_{i_n}({\bf 0})=\bm x$. We show that for $\lambda$ sufficiently close to 1, each $\bm x\in S_\lambda\setminus\{\bm p_0,...,\bm p_{m-1}\}$ has $2^{\aleph_0}$ different addresses. If $\lambda$ is not too close to 1, then we can still have an overlap, but there exist $\bm x$'s which have a unique address. However, we prove that almost every $\bm x\in S_\lambda$ has $2^{\aleph_0}$ addresses, provided $S_\lambda$ contains no holes and at least one proper overlap. We apply these results to the case of expansions with deleted digits. Furthermore, we give sharp sufficient conditions for the Open Set Condition to fail and for the attractor to have no holes. These results are generalisations of the corresponding one-dimensional results, however most proofs are different.Comment: Accepted for publication in Nonlinearit