• Participants must have biopsy-proven adenocarcinoma of the prostate, as determined by medical chart review.

• For:

‣ Part 1: Participants post-radiation therapy or currently considering SBRT.

⁃ Part 2A: Participants currently scheduled for or considering SBRT (no neo-adjuvant therapy planned).

⁃ Part 2B: Participants currently scheduled for or considering SBRT and neo-adjuvant therapy is planned. The participant has biopsy-proven adenocarcinoma of the prostate with high-risk disease, defined by the presence of at least two of following criteria: a tumor stage of T3 or T4, a Gleason score of 8 to 10, or a PSA level ≥40 ng/mL) and the participant must be planning to receive androgen deprivation therapy (ADT) with an Luteinizing hormone-releasing hormone (LHRH) agonist or antagonist. The addition of an androgen-receptor (AR) signaling inhibitor (e.g., abiraterone, bicalutamide,apalutamide, enzalutamide or darolutamide) will be allowed.

⁃ Part 3: Participants who have previously received radiation treatment to the prostate and are exhibiting signs of biochemical failure, with planned fusion biopsy within 12 weeks following completion of baseline HP 13C pyruvate +/-urea mpMRI.

• Participant is able and willing to comply with study procedures and provide signed and dated informed consent.

• Eastern Cooperative Oncology Group (ECOG) performance status \<= 1.

• Age \>= 18 years old at time of study entry.

• Ability to understand and the willingness to sign a written informed consent document.

• Demonstrates adequate organ function as defined below:

‣ White Blood Cell count (WBC) \>=4000 cells/μL.

⁃ Hemoglobin ≥9.0 gm/dL.

⁃ Platelets ≥75,000 cells/μL.

⁃ Renal Function \> 30 Epithelial Growth Factor Receptor (eGFR).