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AIDS patients undergoing autologous transplantation for lymphoma were treated with gene-modified peripheral blood derived (CD34+) hematopoietic progenitor cells (HPC) expressing 3 RNA-based anti-HIV moieties (Tat/Rev shRNA, TAR decoy and CCR5 ribozyme). In vitro analysis of gene-modified HPC showed no differences in the hematopoietic potential compared with non-transduced cells. In vitro estimates of gene marking were as high as 22% but declined to ~1% over 4 weeks of culture. Ethical study design required that patients were transplanted with both gene modified and unmanipulated hematopoietic progenitor cell apheresis products (HPC-A). All 4 infused patients engrafted (ANC>500) by day 11 post-infusion and showed no unexpected infusion related toxicities. Persistent vector marking in multiple cell lineages has been observed at low levels for up to 24 months as has expression of siRNA and ribozyme. This is the first demonstration of siRNA expression in human blood cells following transplantation of autologous gene-modified CD34+ HPC. These results support the development of an RNA-based cell therapy platform for HIV. Summary Stem cell gene therapy for HIV results in sustained RNA expression in the blood of patients for up to 2 years following transplant.

An hp-adaptive pseudospectral method is presented for numerically solving optimal control problems. The method presented in this paper iteratively determines the number of segments, the width of each segment, and the polynomial degree required in each segment in order to obtain a solution to a userspecified accuracy. Starting with a global pseudospectral approximation for the state, on each iteration the method determines locations for the segment breaks and the polynomial degree in each segment for use on the next iteration. The number of segments and the degree of the polynomial on each segment continue to be updated until a user-specified tolerance is met. The terminology 'hp' is used because the segment widths (denoted h) and the polynomial degree (denoted p) in each segment are determined simultaneously. It is found that the method developed in this paper leads to higher accuracy solutions with less computational effort and memory than is required in a global pseudospectral method. Consequently, the method makes it possible to solve complex optimal control problems using pseudospectral methods in cases where a global pseudospectral method would be computationally intractable. Finally, the utility of the method is demonstrated on a variety of problems of varying complexity. Determining locations of new segments or increase in number of collocation pointsLet be a user-defined tolerance and assume that the maximum entry of Equation (27) is greater than . In this case, the segment either needs to be divided into more segments or the degree of

A method is presented for direct trajectory optimization and costate estimation using global collocation at Legendre-Gauss-Radau (LGR) points. The method is formulated first by casting the dynamics in integral form and computing the integral from the initial point to the interior LGR points and the terminal point. The resulting integration matrix is nonsingular and thus can be inverted so as to express the dynamics in inverse integral form. Then, by appropriate choice of the approximation for the state, a pseudospectral (i.e., differential) form that is equivalent to the inverse integral form is derived. As a result, the method presented in this paper can be thought of as either a global implicit integration method or a pseudospectral method. Moreover, the formulation derived in this paper enables solving general finite-horizon problems using global collocation at the LGR points. A key feature of the method is that it provides an accurate way to map the KKT multipliers of the nonlinear programming problem (NLP) to the costates of the optimal control problem. Finally, * M.S. Student, Dept. it is shown that a previously developed Radau collocation method, which is restricted to infinite-horizon problems, is subsumed by the method presented in this paper. The results of this paper show that the use of LGR collocation as described in this paper leads to the ability to determine accurate primal and dual solutions to general finite-horizon optimal control problems.

Estimation of muscle forces during motion involves solving an indeterminate problem (more unknown muscle forces than joint moment constraints), frequently via optimization methods. When the dynamics of muscle activation and contraction are modeled for consistency with muscle physiology, the resulting optimization problem is dynamic and challenging to solve. This study sought to identify a robust and computationally efficient formulation for solving these dynamic optimization problems using direct collocation optimal control methods. Four problem formulations were investigated for walking based on both a two and three dimensional model. Formulations differed in the use of either an explicit or implicit representation of contraction dynamics with either muscle length or tendon force as a state variable. The implicit representations introduced additional controls defined as the time derivatives of the states, allowing the nonlinear equations describing contraction dynamics to be imposed as algebraic path constraints, simplifying their evaluation. Problem formulation affected computational speed and robustness to the initial guess. The formulation that used explicit contraction dynamics with muscle length as a state failed to converge in most cases. In contrast, the two formulations that used implicit contraction dynamics converged to an optimal solution in all cases for all initial guesses, with tendon force as a state generally being the fastest. Future work should focus on comparing the present approach to other approaches for computing muscle forces. The present approach lacks some of the major limitations of established methods such as static optimization and computed muscle control while remaining computationally efficient.Electronic Supplementary MaterialThe online version of this article (doi:10.1007/s10439-016-1591-9 contains supplementary material, which is available to authorized users.