Combined OX40 Agonist and PD-1 Inhibitor Immunotherapy Improves the Efficacy of Vascular Targeted Photodynamic Therapy in a Urothelial Tumor Model

Purpose: Vascular targeted photodynamic therapy (VTP) is a nonsurgical tumor ablation approach used to treat early-stage prostate cancer and may also be effective for upper tract urothelial cancer (UTUC) based on preclinical data. Toward increasing response rates to VTP, we evaluated its efficacy in combination with concurrent PD-1 inhibitor/OX40 agonist immunotherapy in a urothelial tumor-bearing model. Experimental design: In mice allografted with MB-49 UTUC cells, we compared the effects of combined VTP with PD-1 inhibitor/OX40 agonist with those of the component treatments on tumor growth, survival, lung metastasis, and antitumor immune responses. Results: The combination of VTP with both PD-1 inhibitor and OX40 agonist inhibited tumor growth and prolonged survival to a greater degree than VTP with either immunotherapeutic individually. These effects result from increased tumor infiltration and intratumoral proliferation of cytotoxic and helper T cells, depletion of Treg cells, and suppression of myeloid-derived suppressor cells. Conclusions: Our findings suggest that VTP synergizes with PD-1 blockade and OX40 agonist to promote strong antitumor immune responses, yielding therapeutic efficacy in an animal model of urothelial cancer.     

N. N. Bogolyubov's research in mathematics and theoretical physics

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 9, pp. 1156–1164, September, 1989.     

Boltzmann-Enskog limit for equilibrium states of systems of hard spheres in the framework of a canonical ensemble

We prove the existence of the Boltzmann-Enskog limit for an equilibrium system of hard spheres. On the basis of analysis of the Kirkwood-Salsburg equations, we show that the limit distribution functions are constants that can be represented as series in density. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1195–1205, September, 1997.     

Methods for derivation of the stochastic Boltzmann hierarchy

We consider different methods for the derivation of the stochastic Boltzmann hierarchy corresponding to the stochastic dynamics that is the Boltzmann-Grad limit of the Hamiltonian dynamics of hard spheres. Solutions of the stochastic Boltzmann hierarchy are the Boltzmann-Grad limit of solutions of the BBGKY hierarchy of hard spheres in the entire phase space. A new concept of reduced distribution functions corresponding to the stochastic dynamics are introduced. They take into account the contribution of the hyperplanes of lower dimension where stochastic point particles interact with one another. The solutions of the Boltzmann equation coincide with one-particle distribution functions of the stochastic Boltzmann hierarchy and are represented by integrals over the hyperplanes where the stochastic point particles interact with one another.     

Existence of equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit within the frame work of the grand canonical ensemble

We study equilibrium states of systems of hard spheres in the Boltzmann-Enskog limit (d→0, 1/v→∞ (z→∞), and d ³ (1/v)=const (d ³ z=const)). For this purpose, we use the Kirkwood-Salsburg equations. We prove that, in the Boltzmann-Enskog limit, solutions of these equations exist and the limit distribution functions are constant. By using the cluster and compatibility conditions, we prove that all distribution functions are equal to the product of one-particle distribution functions, which can be represented as power series in z=d ³ z with certain coefficients. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 1, pp. 112–121, January, 1997.     

Stochastic dynamics as a limit of Hamiltonian dynamics of hard spheres

We consider the stochastic dynamics that is the Boltzmann-Grad limit of the Hamiltonian dynamics of a system of hard spheres. A new concept of averages over states of stochastic systems is introduced, in which the contribution of the hypersurfaces on which stochastic point particles interact is taken into account. We give a rigorous derivation of the infinitesimal operators of the semigroups of evolution operators.

---

Стохастична динаміка як границя гамільтонової динаміки пружних куль

Визначена стохаатична динаміка, яка є границею Больцмана-Греда від гамільтонової динаміки системи пружних куль. Введено нову концепцію середніх від спостережуваних за станами стохастичних систем. В ньому враховуються вклади від гіперповерхонь, на яких взаємодіуть точкові стохастичні частки. Дано строге визначення інфінітезімальних операторов для півгрупи еволюційних операторів.

---

---

This work was performed during the stay May–June 1997 of D. Ya. Petrina and during the stay September–December 1997 of K. D. Petrina as visiting professors at the Politecnico di Milano, supported by the Italian Consiglio Nazionale delle Ricerche. The authors would like to thank Prof. C. Cercignani for his comments and support.