A pharmaceutical composition comprising a Bruton's Tyrosine Kinase inhibitor for use in restoring or improving hematopoiesis in a subject in need thereof and for reducing the extent or duration of leukopenia and neutropenia resulting from chemotherapy, radiation therapy or accidental radiation exposure in a subject, said use comprising administering to said subject said pharmaceutical composition in an amount effective to mobilize hematopoietic stem and/or progenitor cells into the peripheral blood of said subject, wherein the BTK inhibitor is selected from Formula I: wherein: La is CH 2, O, NH or S; Ar is a substituted or unsubstituted aryl, unsubstituted phenyl, or a substituted or unsubstituted heteroaryl; Y is a 4-, 5-, 6-, or 7-membered cycloalkyl ring, or Y is a 4-, 5-, 6-, or 7-membered monocyclic nitrogen containing heterocycloalkyl ring; Z is C(=O), OC(=O), NHC(=O), NRC(=O), C(=S), S(=O) x, OS(=O) x, NHS(=O) x, where x is 1 or 2; R 7 and R 8 are independently selected from among H, unsubstituted C 1 -C 4 alkyl, substituted C 1 -C 4 alkyl, C 1 -C 6 alkoxyalkyl, C 1 -C 8 alkylaminoalkyl, C 1 -C 4 alkyl(phenyl), unsubstituted C 1 -C 4 heteroalkyl, substituted C 1 -C 4 heteroalkyl, unsubstituted C 3 -C 6 cycloalkyl, substituted C 3 -C 6 cycloalkyl, unsubstituted C 2 -C 6 heterocycloalkyl, and substituted C 2 -C 6 heterocycloalkyl; or R 7 and R 8 taken together form a bond; R 6 is H, substituted or unsubstituted C 1 -C 4 alkyl, substituted or unsubstituted C 1 -C 4 heteroalkyl, C 1 -C 6 alkoxyalkyl, C 1 -C 8 alkylaminoalkyl, substituted or unsubstituted C 3 -C 6 cycloalkyl, substituted or unsubstituted aryl, substituted or unsubstituted C 2 -C 8 heterocycloalkyl, substituted or unsubstituted heteroaryl, C 1 -C 4 alkyl(aryl), C 1 -C 4 alkyl(phenyl), C 1 -C 4 alkyl(heteroaryl), C 1 -C 4 alkyl(C 3 -C 8 cycloalkyl), or C 1 -C 4 alkyl(C 2 -C 8 heterocycloalkyl), or C 1 -C 8 alkylaminoalkyl; R is H, or C 1 -C 6 alkyl and pharmaceutically acceptable solvates or pharmaceutically acceptable salts thereof. La is CH 2, O, NH or S; Ar is a substituted or unsubstituted aryl, unsubstituted phenyl, or a substituted or unsubstituted heteroaryl; Y is a 4-, 5-, 6-, or 7-membered cycloalkyl ring, or Y is a 4-, 5-, 6-, or 7-membered monocyclic nitrogen containing heterocycloalkyl ring; Z is C(=O), OC(=O), NHC(=O), NRC(=O), C(=S), S(=O) x, OS(=O) x, NHS(=O) x, where x is 1 or 2; R 7 and R 8 are independently selected from among H, unsubstituted C 1 -C 4 alkyl, substituted C 1 -C 4 alkyl, C 1 -C 6 alkoxyalkyl, C 1 -C 8 alkylaminoalkyl, C 1 -C 4 alkyl(phenyl), unsubstituted C 1 -C 4 heteroalkyl, substituted C 1 -C 4 heteroalkyl, unsubstituted C 3 -C 6 cycloalkyl, substituted C 3 -C 6 cycloalkyl, unsubstituted C 2 -C 6 heterocycloalkyl, and substituted C 2 -C 6 heterocycloalkyl; or R 7 and R 8 taken together form a bond; R 6 is H, substituted or unsubstituted C 1 -C 4 alkyl, substituted or unsubstituted C 1 -C 4 heteroalkyl, C 1 -C 6 alkoxyalkyl, C 1 -C 8 alkylaminoalkyl, substituted or unsubstituted C 3 -C 6 cycloalkyl, substituted or unsubstituted aryl, substituted or unsubstituted C 2 -C 8 heterocycloalkyl, substituted or unsubstituted heteroaryl, C 1 -C 4 alkyl(aryl), C 1 -C 4 alkyl(phenyl), C 1 -C 4 alkyl(heteroaryl), C 1 -C 4 alkyl(C 3 -C 8 cycloalkyl), or C 1 -C 4 alkyl(C 2 -C 8 heterocycloalkyl), or C 1 -C 8 alkylaminoalkyl; R is H, or C 1 -C 6 alkyl and