It is well known that the spatial biology distribution (e.g., clonogen density, radiosensitivity, tumor proliferation rate, functional importance) in most tumors and sensitive structures is heterogeneous. Recent progress in biological imaging is making the mapping of this distribution increasingly possible. The purpose of this work is to establish a theoretical framework to quantitatively incorporate the spatial biology data into intensity modulated radiation therapy (IMRT) inverse planning. In order to implement this, we first derive a general formula for determining the desired dose to each tumor voxel for a known biology distribution of the tumor based on a linear-quadratic model. The desired target dose distribution is then used as the prescription for inverse planning. An objective function with the voxel-dependent prescription is constructed with incorporation of the nonuniform dose prescription. The functional unit density distribution in a sensitive structure is also considered phenomenologically when constructing the objective function. Two cases with different hypothetical biology distributions are used to illustrate the new inverse planning formalism. For comparison, treatments with a few uniform dose prescriptions and a simultaneous integrated boost are also planned. The biological indices, tumor control probability (TCP) and normal tissue complication probability (NTCP), are calculated for both types of plans and the superiority of the proposed technique over the conventional dose escalation scheme is demonstrated. Our calculations revealed that it is technically feasible to produce deliberately nonuniform dose distributions with consideration of biological information. Compared with the conventional dose escalation schemes, the new technique is capable of generating biologically conformal IMRT plans that significantly improve the TCP while reducing or keeping the NTCPs at their current levels. Biologically conformal radiation therapy (BCRT) incorporates patient-specific biological information and provides an outstanding opportunity for us to truly individualize radiation treatment. The proposed formalism lays a technical foundation for BCRT and allows us to maximally exploit the technical capacity of IMRT to more intelligently escalate the radiation dose.