OPINION
SILER, Circuit Judge.James Scott, a prisoner who is serving a life sentence, alleges that the defendants, all of them physicians, were deliberately indifferent to his medical needs in connection with his treatment for prostate cancer. Defendants filed motions to dismiss pursuant to Rule 12(b)(6) and motions for summary judgment. The district court dismissed Scott’s claims against all defendants. We affirm the district court’s judgment as to Drs. Ambani, Faghihnia, and Sullivan, vacate the judgment as to Dr. Antonini, and remand for further proceedings.
*645FACTUAL AND PROCEDURAL BACKGROUND
In March 2002, Scott was informed by Dr. Ambani that he had an elevated prostate-specific antigen (PSA), indicating a possibility of prostate cancer. Dr. Ambani performed a biopsy but did not find any cancer. Dr. Ambani recommended that Scott follow up with his regular physician in approximately one year. Scott alleges that Dr. Ambani refused to pursue additional testing for prostate cancer. He also alleges that Dr. Ambani failed to comply with Michigan Department of Corrections (MDOC) policy directives requiring him to place Scott in a “chronic care clinic” and to place him on a therapeutic diet. As a result, Scott claims that he suffered distress from “thinking that he could be dying from cancer” and experienced a delay in receiving proper treatment for his condition. Dr. Ambani also refused to prescribe pain medication to treat Scott’s lower back pain.
Scott was transferred to another facility and came under the care of Dr. Faghihnia from October 2002 until February 2004. He alleges that Dr. Faghihnia was deliberately indifferent to his medical needs by denying him an annual health screening in 2002, refusing his requests for additional cancer testing, and denying him lab work at his 2003 screening.
Scott’s annual screening in October 2004 revealed an elevated PSA level. He also complained of pain in his upper thigh and lower back. As a result, he was referred back to Dr. Ambani for a second biopsy. In January 2005, Dr. Ambani performed the biopsy which revealed prostate cancer. Scott was then referred to Dr. Sullivan, a radiation oncologist, for treatment.
Scott indicated to Dr. Sullivan that for religious reasons, he did not wish to undergo any treatment which might affect his fertility. Dr. Sullivan told him that if the cancer was located only in the prostate, he would not receive radiation treatment to his seminal vesicle. Scott alleges that additional testing showed that his cancer was confined to the prostate but that, nonetheless, his seminal vesicle was exposed to radiation treatment.
Once Scott’s treatment was complete in August 2005, he was referred to Dr. Antonini to monitor his health for side effects from the radiation. In February 2006, Scott reported to Dr. Antonini that he was in great pain and had developed a hard testicular lump. Dr. Antonini denied Scott’s request to refer him back to Dr. Sullivan and also refused to prescribe pain medication. Instead, Dr. Antonini referred him to another doctor for a colonoscopy.
In May 2006, Scott saw a nurse because he had a lump on his eyelid and was still in great pain from his testicular lump. The nurse communicated Scott’s problems to Dr. Antonini, but he said that he did not have time to examine Scott. His pain eventually dissipated.
In June 2006, Scott underwent a colonoscopy. The colonoscopy indicated that his previous pain was the result of radiological side effects from cancer treatment. In August 2006, Dr. Antonini examined Scott’s testicular lump and ordered an ultrasound. The ultrasound indicated that the lump was a cyst that had burst.
Scott filed his complaint in January 2007. The defendants are named in their individual and official capacities and, with the exception of Dr. Sullivan, were employed by or under contract with MDOC. Dr. Sullivan was employed by the University of Michigan.
The district court granted Drs. Faghihnia and Antonini’s motion to dismiss, Dr. Sullivan’s motion for summary judgment, and Dr. Ambani’s motion to dismiss.
*646STANDARD OF REVIEW
This court uses a de novo standard when reviewing a district court’s dismissal of a complaint pursuant to either Rule 12(b)(6) or Rule 56(c) of the Federal Rules of Civil Procedure. See Kottmyer v. Maas, 436 F.3d 684, 688 (6th Cir.2006); Ciminillo v. Streicher, 434 F.3d 461, 464 (6th Cir.2006).
In reviewing a dismissal under Rule 12(b)(6), all allegations in the complaint should be taken as true, and the complaint is to be construed liberally in favor of the party opposing the motion to dismiss. Westlake v. Lucas, 537 F.2d 857, 858 (6th Cir.1976); Davis H. Elliot Co. v. Caribbean Utils. Co., Ltd,., 513 F.2d 1176, 1182 (6th Cir.1975). “Dismissals of complaints under the civil rights statutes are scrutinized with special care.” Westlake, 537 F.2d at 858.
DISCUSSION
A. Dr. Ambani
In dismissing Scott’s deliberate indifference claim against Dr. Ambani, the district court concluded that the claim arose in 2002 and was, therefore, untimely. Scott does not challenge the conclusion that whatever events occurred in 2002 are barred by the statute of limitations. Instead, he challenges the district court’s conclusion that the complaint did not contain an allegation that Dr. Ambani denied Scott pain medication in 2005.
Both parties agree that Scott’s claims are subject to a three-year statute of limitations. See Mich. Comp. Laws § 600.5801(10); Wolfe v. Perry, 412 F.3d 707, 713-14 (6th Cir.2005) (applying Michigan’s three-year statute of limitations to a § 1983 claim). In actions brought under § 1983, the statute of limitations begins to run when the plaintiff knows or has reason to know of the injury that is the basis of the action. Kelly v. Burks, 415 F.3d 558, 561 (6th Cir.2005). “A plaintiff has reason to know of his injury when he should have discovered it through the exercise of reasonable diligence.” Sevier v. Turner, 742 F.2d 262, 273 (6th Cir.1984).
The district court correctly concluded that Scott’s claim against Dr. Am-bani accrued in 2002, and is therefore untimely. In 2002, Dr. Ambani refused Scott’s requests for further cancer testing and for therapeutic treatment. According to the complaint, it was this denial which caused Scott to experience mental and emotional distress regarding the uncertainty of his diagnosis. This mental and emotional distress forms the basis of Scott’s claim against Dr. Ambani, and Scott was aware of this distress at or very near the time in which Dr. Ambani refused Scott’s requests. Similarly, Dr. Ambani’s alleged failure to comply with prison procedures requiring Scott to be placed in a chronic care program due to his elevated PSA level should reasonably have been known to Scott at or near the time of the denial. See Hermansen v. Schickel, 202 F.3d 268 (6th Cir.1999) (concluding that prisoner’s cause of action for deliberate indifference accrued on the date that he was denied medical care, even though the full extent of his injury was not known until later).
Scott argues that the district court erred when it concluded that the complaint failed to allege that Dr. Ambani denied Scott pain medication in 2005. His argument is without merit. In the section of the complaint entitled “Facts,” Scott lays out the events surrounding his encounter with Dr. Ambani in March 2002. Scott alleges that Dr. Ambani (1) denied his requests for additional cancer testing, (2) refused to place Scott in a chronic care program, (3) denied Scott’s request to be placed on a therapeutic diet, and (4) refused to pre*647scribe pain medication for Scott’s lower back and upper thigh pain.
The complaint also states that in January 2005, Dr. Ambani performed a second biopsy and in February 2005, referred Scott to Dr. Sullivan for treatment. Nowhere in the discussion of the second biopsy or in the discussion of the referral does Scott mention either requesting pain medication or being refused pain medication by Dr. Ambani in 2005.
In a section of the complaint titled, “Cause of Action, Count I,” Scott makes his deliberate indifference claim against Dr. Ambani. Scott alleges that Dr. Ambani was deliberately indifferent to Scott’s medical needs by denying his requests for additional cancer testing and refusing to prescribe pain medication for Scott’s lower back and upper thigh pain. The only allegation made by Scott regarding Dr. Ambani’s refusal to prescribe pain medication alleges that the refusal occurred in March 2002. Therefore, Scott’s deliberate indifference claim, insofar as it is based upon Dr. Ambani’s refusal to prescribe pain medication, must be referring to the refusal which allegedly occurred in March 2002.
Since Scott’s claim against Dr. Ambani accrued in 2002, it should have been brought by 2005 in order to comply with the three-year statute of limitations. Scott filed the complaint in 2007. Therefore, the claim is untimely.
B. Dr. Faghihnia
The district court granted Dr. Faghihnia’s motion to dismiss on the basis that Scott failed to exhaust his administrative remedies. Scott filed a grievance against Dr. Faghihnia contending that Dr. Faghihnia violated the Eighth Amendment by failing to give Scott an annual health care screening from October 2002 to February 2004. He did not file his grievance until 2006. The grievance against Dr. Faghihnia was denied during the administrative process because it was untimely. Scott contends that the denial of his grievance was improper because it was filed soon after he received his medical records.
Under the Prison Litigation Reform Act of 1995 (PLRA), prison litigation brought under 42 U.S.C. § 1983 may only be brought after a prisoner has exhausted the available administrative remedies. See 42 U.S.C. § 1997e(a) (“[n]o action shall be brought with respect to prison conditions under section 1983 of this title, or any other Federal law, by a prisoner ... until such administrative remedies as are available are exhausted”).
“Proper exhaustion demands compliance with an agency’s deadlines and other critical procedural rules because no adjudicative system can function effectively without imposing some orderly structure on the course of its proceedings.” Woodford v. Ngo, 548 U.S. 81, 90-91, 126 S.Ct. 2378, 165 L.Ed.2d 368 (2006). In Wood-ford, the Supreme Court held that a prisoner’s § 1983 action must be dismissed for failure to exhaust administrative remedies where the underlying grievance was denied as untimely even though the claim would not have been barred by the applicable statute of limitations. Woodford makes clear that a prisoner cannot satisfy the PLRA exhaustion requirement by filing an untimely or otherwise procedurally defective administrative grievance. Id. at 83, 126 S.Ct. 2378.
Here, Scott’s grievance against Dr. Faghihnia was rejected as untimely during the administrative process. Therefore, under Woodford, he failed to exhaust his administrative remedies.
C. Dr. Antonini
Scott appeals the district court’s dismissal of his deliberate indifference claim against Dr. Antonini under Rule 12(b)(6) of the Federal Rules of Civil Pro*648cedure. The district court concluded that these claims were not time-barred and were properly exhausted. However, it granted Dr. Antonini’s motion to dismiss on the basis that Scott’s allegations did not rise to the level of deliberate indifference. Dismissal was erroneous.
A prisoner has adequately stated a cause of action “when he alleges that prison authorities have denied reasonable requests for medical treatment in the face of an obvious need for such attention where the inmate is thereby exposed to undue suffering or the threat of tangible residual injury.” Westlake, 537 F.2d at 860. The inquiry into whether a prison official acted with deliberate indifference has both an objective and subjective component. Comstock v. McCrary, 273 F.3d 693, 702 (6th Cir.2001). In order to satisfy the objective component, the prisoner must show that the medical need is “sufficiently serious.” Id. at 702-03 (quoting Farmer v. Brennan, 511 U.S. 825, 834, 114 S.Ct. 1970, 128 L.Ed.2d 811 (1994)). To satisfy the subjective component, the prisoner must allege facts which show that the prison official had a “sufficiently culpable state of mind.” Farmer, 511 U.S. at 834, 114 S.Ct. 1970; Comstock, 273 F.3d at 703. It must be shown that the official acted with reckless disregard for a substantial risk to the prisoner, that he drew the inference, and that’ he disregarded the risk. Farmer, 511 U.S. at 836-37, 114 S.Ct. 1970.
Construing the complaint in the light most favorable to Scott and accepting all factual allegations as true, Scott has sufficiently stated a claim that Dr. Antonini had knowledge of Scott’s serious medical needs and was deliberately indifferent to those needs. Scott alleges that as of February 2006, Dr. Antonini was aware that Scott had been recently treated for prostate cancer, and had severe back and leg pain as well as a testicular lump that was hard and painful. Nevertheless, Dr. Antonini did not provide Scott with medication to treat the pain. In May 2006, when Scott reported to the nurse that the lump was still causing him severe pain, Dr. Antonini said he did not have time to examine the lump, and he did not do so until August 2006.
Given the severity of Scott’s prior medical condition, a refusal to provide pain medication and to examine his testicular lump for three months could lead a trier of fact to conclude that prison officials exposed Scott to “undue suffering or the threat of tangible residual injury.” See Westlake, 537 F.2d at 860 n. 4 (“Whether a prisoner has suffered unduly by the failure to provide medical treatment is to be determined in view of the totality of the circumstances. In making this determination the trier of fact should consider the practicalities of the situation including the extent of the injury, the realistic possibilities of treatment, and the possible consequences to the prisoner of failing to provide immediate medical attention.”) (emphasis added).
Since Scott has adequately stated a claim against Dr. Antonini for deliberate indifference, the district court’s dismissal of the claim must be vacated.
D. Dr. Sullivan
Scott alleges that Dr. Sullivan violated his constitutional rights by treating his seminal vesicle against his wishes resulting in infertility. Dr. Sullivan filed a motion for summary judgment arguing that she was not a state actor and therefore cannot be held liable under 42 U.S.C. § 1983, and that the alleged facts do not support a claim of deliberate indifference. The district court concluded that Dr. Sullivan was not a state actor and dismissed the claim against her. We affirm.
*649The relevant standard for determining whether Dr. Sullivan acted under color of state law focuses on “the relationship among the State, the physician and the prisoner.” West v. Atkins, 487 U.S. 42, 55-56, 108 S.Ct. 2250, 101 L.Ed.2d 40 (1988). In determining whether a doctor acted under color of state law, the primary factor is “the physician’s function within the state system, not the precise terms of his employment.” Id. at 56, 108 S.Ct. 2250.
Dr. Sullivan was employed by the University of Michigan, a public university, as a radiation oncologist. She held medical staff privileges at W.A. Foote Hospital in Jackson, Michigan. She had no contractual relationship with MDOC or Correctional Medical Services. Her care and treatment of all patients, including any prisoners which may have required treatment at Foote Hospital, were determined by her own training, experience, and independent medical judgment. Neither MDOC nor Correctional Medical Services had any influence, direction, or control over the care and treatment of any patient.
In her role as a radiation oncologist providing care to Scott, Dr. Sullivan was not exercising “any power possessed by virtue of state law.” West, 487 U.S. at 49, 108 S.Ct. 2250. Dr. Sullivan’s employment by the University of Michigan did not give her any additional responsibilities or vest her with any additional authority that other physicians who treated patients at Foote Hospital did not enjoy. As with any private physician, Dr. Sullivan provided treatment and care to the patients at the hospital.
Furthermore, Dr. Sullivan was able to treat Scott not because she was “clothed with the authority of state law,” West, 487 U.S. at 49, 108 S.Ct. 2250, but because she had medical staff privileges at Foote Hospital. Upon referral by Dr. Ambani, a physician at the prison hospital, Scott could have been treated by any of the radiation oncologists with medical staff privileges. Dr. Sullivan just happened to be the physician who provided treatment. As such, Dr. Sullivan was not performing her duties as a state actor in her treatment of Scott and dismissal of the claim against her was proper.
AFFIRMED in part, VACATED in part, and REMANDED for further proceedings in connection with the claim against Dr. Antonini only.