Radiation therapy uses radiation to kill cancer cells but at the same time tries to save normal tissues. This is based on the fact that ionizing particles (radiation) can break the DNA strands in cells and thus damage the cells, but cells also respond to radiation in various ways and can survive from radiation damage in certain situations. Radiobiology provides a good understanding of cell responding mechanism, and radiation therapy can utilize radiobiology to develop new treatment techniques and modalities to maximize cancer killing and normal tissue sparing.

The response of cells to radiation is complex and includes the 4Rs that stand for repair, repopulation, redistribution, and reoxygenation of cells. Repair describes that a cell recovers from radiation damage to its genetic structure before further damage makes recovery impossible. Cells that are not damaged by radiation, divide and replace damaged cells and will divide at a faster rate with irradiation. This is cell repopulation. In general, cells grow through a cycle that includes four phases: Gap 1 (G₁), Synthesis (S), Gap 2 (G₂), and Mitosis (M). Late G₂ and M are most sensitive to radiation while late S and early G₂ are most resistant to radiation. Cells usually stay in different phases during irradiation. However, after irradiation, cells surviving from a single dose of irradiation in radiation resistant phase tend to be partially synchronized and move into radiation sensitive phase. This is redistribution or reassortment. It has also been realized that oxygen as a powerful radiation sensitizer plays an important role in responding irradiation. Cells lacking oxygen are resistant to radiation and called hypoxic cells. The fraction of hypoxic cells is expected to increase after irradiation, but the hypoxic cell fraction can rapidly return to its pre-irradiation level. This is referred to reoxygenation.

The 4Rs affect the results of cell irradiation and thus affect radiation treatment. This review will discuss the effects of the 4Rs and how they are utilized in radiation therapy.

1 The 4Rs in linear quadratic equation (LQ)

The quantitative analysis of the dose-response usually is based on the linear-quadratic equation (LQ) that establishes the quantitative relationship between cell survival fraction S and radiation dose D. LQ can be derived by fitting the experimental data and using theoretical models^[1-3]. The basic form of LQ is expressed as

$ S = \exp \left( { - \alpha D - \beta {D^2}} \right) $

(1)

The biological parameters α and β are determined by experiment.

Two important quantities, biological effective dose (BED) and biological equivalent dose (EQD), are defined based on LQ. BED is defined by

$ {\rm{BED}} = - \ln S/\alpha = D + {D^2}/\left( {\alpha /\beta } \right) = D \cdot RE $

(2)

$ RE = 1 + D/\left( {\alpha /\beta } \right) $

(3)

BED quantitatively describes cell killing. For two different treatment modalities or schemes, to compare which is more effective in treating cancer, one just compares the BED values. If the BED values are equal, or BED₁=BED₂, the corresponding prescription doses D₁, and D₂, are equivalent to each other and called equivalent dose for each other.

The 4Rs are not taken into account in Equation (1). Repair was first considered in the equation by including a factor G, the Lea-Catcheside function^[4], which modifies the quadratic term

$ S = \exp \left( { - \alpha D - G\beta {D^2}} \right) $

(4)

G is defined by

$ G\left( T \right) = \left( {\frac{2}{{{D^2}}}} \right)\int\limits_0^T {duR\left( u \right)} \int\limits_0^u {dwR\left( w \right)\mathit{\Phi }\left( {u, w} \right)} $

(5)

where Φ(u, w)=exp[-(u-w)/T], T is irradiation time, and R(t) is the dose rate.

If μ is the repair rate constant,

$ G = 2/\left( {\mu \cdot T} \right)\left\{ {1 - \left( {1 - \mathit{exp}\left( { - \mu \cdot T} \right)} \right)/\left( {\mu \cdot T} \right)} \right\} $

(6)

G=1 if all β-type damage expressed (T→0), and 0 if all damages are repaired (T→∞).

Repopulation is introduced by an independent term, K_p·T^[5],

$ S = \exp \left( { - \alpha D - G\beta {D^2} + {K_{\rm{p}}} \cdot T} \right) $

(7)

where K_p=ln(2)/T_d, K_p is repopulation rate constant, and T_d is cell doubling time.

If cells are not fully reoxygenated and redistributed, the survival fraction would be increased by adding the term, (σ²/2)G_sD². Then, we have

$ S = \exp \left[ { - \alpha D - \beta {G_{\rm{r}}}{D^2} + \left( {{\sigma ^2}/2} \right){G_{\rm{s}}}{D^2} + {K_{\rm{p}}} \cdot T} \right] $

(8)

The term σ²/2 represents an increase in survival fraction due to partial reoxygenation and redistribution associated with cell-to-cell diversity. Brenner et al^[6] call the equation (8) the extended LQ equation that includes all the 4Rs.The LQ including the 4Rs should be more accurate and more realistic in estimation of biological effectiveness.

2 The 4Rs in dose fractionation

Killing cancers while sparing normal tissues is critical for the success of radiation therapy. Dose fractionation as an effective way to balance cancer killing and normal tissue sparing was realized not long after radiation therapy began. Just about one month after the discovery of X-rays was announced in 1895, Orton^[7] had started using X-rays to treat breast cancer, but it was found that radiation would cause virulent dermatitis. Then, a question was raised: is it possible to damage tumors while sparing normal tissues? About ten years later, Withers^[8] observed in an animal study that irradiation of the testes of the animals with a series of fractionated doses resulted in infertility without damage of the skin of the scrotum, but this could not be achieved using single irradiations. This result led to the assumption that dose fractionation would be the answer to the above question. On the contrary, many people believed that a single-fraction dose would be better in treating cancer because multi-fractionation would allow cancer to recover from radiation damage^[7].The single fraction treatment was favored in the early practice. However, extensive normal tissue damages caused by radiation pushed radiation therapy practitioners back to dose fractionation techniques.

Dose fractionation was also supported by a cell experiment which found that X-rays were more damaging to mitotic than to interphase cells. Based on that, Schwarz reasoned that treatment with multiple fractions rather than single fraction would increase the chances of irradiating tumor cells in mitosis.In 1932, excellent results using fractionated radiation therapy were published and thus established as a standard of practice of radiation therapy.

A better understanding of dose fractionation was achieved by radiobiological studies. Systematic radiobiological studies started in the 1950s with the advent of cell cloning techniques^[9-10] and the development of quantitative assays of normal tissue^[11] and tumor responses^[12].The rationale for dose fractionation has been fully understood with the advances in radiobiology, especially, the advanced study of the 4Rs.

Of the 4Rs, repair is the most important in understanding fractionation. Late-responding normal tissue cells usually have greater repair capability than cancer cells, but this capability will drop below that of cancer cells when dose is greater than 4 Gy based on the linear quadratic model. Therefore, to protect normal tissues, it is better to keep dose below 4 Gy. Meanwhile, we also need high dose to control cancer. The solution is to fractionate treatment with a very high total dose and a fractional dose less than 4 Gy. This leads to 2 Gy as a standard fractional dose at which the difference in survival fraction between normal cells and cancer cells can be maximized.

On the other hand, all cells can divide and cancer cells divide much faster than normal cells. Also, accelerated repopulation may occur after the first 2 to 4 weeks of treatment. Therefore, there is more repopulation of cancer cells than normal cells during radiation treatment. This indicates that the longer the treatment course, the more difficult to control tumor without exceeding the tolerance of normal tissues. Hence, the length of treatment course and number of fractions should be limited to be effective in killing cancer cells. This contradicts to repair. However, repopulation may benefit acute-responding normal tissues in recovering from cell loss. The question now is how to balance repair and repopulation to optimize fractionation. A recent study shows that the optimal number of fractions should be less than 15 for a head and neck cancer case^[13].

Oxygen is the most powerful radiation sensitizer. But many human cancers contain hypoxic cells that are deprived of oxygen become resistant to radiation. Since reoxygenation would occur after irradiation, reoxygenation between irradiations for fractionated treatments would enhance cancer control and thus support fractionation. Similarly, redistribution would help sensitize radiation resistant cells when those cells enter the mitotic (M) phase of the cell cycle. However, since there are too many uncertainties in determining if the cells enter the M phase, redistribution has not been considered in fractionation.

Various fractionation schemes have been used for different purposes based on biological principles. The most common fractionation is called conventional fractionation with 1.8 to 2.2 Gy/fraction delivered five times a week. It is effective as it delivers high tumoricidal dose while keeping normal tissue doses within tolerance. It is also efficient as it uses all weekdays. Moreover, it is convenient as it saves weekends for both patients and medical staff. Most importantly, a lot of clinical experience has been obtained from such fractionated treatments^{[7, 14]}.

Of course, conventional fractionation is not the only fractionation scheme for radiation therapy. Hyperfractionation increases number of fractions delivering two fractions per day with fractional dose 1.2 to 1.3 Gy and an increase of 20% of total dose. The main reason for hyperfractionation is to maximize the difference in repair capacity between normal tissues and tumor to improve treatment efficiency. Another potential advantage of hyperfractionation might be the reduced oxygen enhancement ratio at low dose/fraction. This could help with the treatment of hypoxic cancers^[14-15].

For rapidly growing tumors with short potential doubling time, accelerated fractionation has been applied by increasing number of fractions or fractional dose. A potential risk for this scheme is that increasing number of fractions and treatment frequency would exceed normal tissue tolerance and reduce the repair capacity of normal cells. To get around this problem, accelerated hyperfractionation scheme has been proposed attempting to complete treatments in such a short time before acute reactions reach their peak. This is called continuous hyperfractionated accelerated radiation therapy (CHART)^[16-17]. With CHART, treatments are delivered three times a day, 6 hours apart, and 7 days a week. With a fractional dose of 1.5 Gy and a total dose of 54 Gy, the treatments can be completed within 12 days. To reduce complications and inconvenience, weekend treatments are removed and daily fractions are increased to 3. This is called CHARTWEL (CHART weekend less)^[18].Recent studies have shown that hyperfractionation and acceleration by delivering two or more fractions per day are successful and can increase 2% survival rate for head and neck cancer treatment^[19-20].

Other than increasing the number of fractions, hypofractionation reduces the number of fractions and the total dose of treatments^[21-23]. According to the linear quadratic model, the cell survival fraction decreases with fractional dose and total dose or the number of fractions but decreases with α/β. Thus, the decrease in number of fractions or total dose can reduce normal tissue complications but also reduce the effectiveness of cancer treatment. In addition, tumors usually have a higher α/β value (e.g., 10 Gy) than normal tissues (e.g., 3 Gy), which indicates that for the same dose, tumors may have lower BED (higher survival fraction) than normal tissues, thus less sensitive to radiation and less effective in cell killing than normal tissues. Therefore, hypofractionation was initially proposed for patients who do not need cure but palliation or adjuvant treatment. Things have changed since the discovery of low α/β values for prostate cancer, though. Brenner and Hall^[22] proposed that the prostate cancer can have very low α/β values with a mean of 1.5 Gy, which is much lower than most cancer cells. With such low values, the same or even higher BED can be achieved with less fractions and total dose than conventional or hyperfractional schemes. As a result, various hypofractionation schemes for cure purpose have been proposed and applied in clinical practice. Typically, hypofractionation schemes range from a single fraction of 10 Gy to 28 fractions of about 2.5 Gy, with one to five fractions per week^[24].

Many studies on hypogfractionation schemes for various sites have been reported recently. For prostate, moderate hypofractionation schemes range from 28×2.5 Gy to 25×3.2 Gy^[24]. Polack et al^[25] used 26×2.7 Gy to compare conventional 38×2 Gy and found Grade 2 gastrointestinal toxicities were 5.0% and 6.8% of the conventional and hypofractionated groups. The rates of local regional failure were comparable between the hypofractionation and the conventional radiation groups^[26]. Hypofraction has also used for breast treatment^[27-28]. It was found that the risk of local recurrence with 16×2.65 Gy was similar to that with conventional radiation therapy^[28]. Hypofractionation can significantly improve the effectiveness and efficiency of radiation therapy and greatly benefit patients in every aspect.

3 The 4Rs in stereotactic radiation therapy

Stereotactic radiation therapy (SRT) uses an external three-dimensional (3D) reference system (stereotactic system) to achieve highly accurate target localization and delivers a single high dose to kill all the cells in the irradiated volume. SRT was initially developed to treat intracranial diseases during the 1950s to the 1970s^[29-30]. It was suggested as an alternative to neurosurgery and thus called stereotactic radiosurgery (SRS). In the early 1990s, SRT was also introduced to treat extracranial tumors. The SRT for extracranial tumors is called stereotactic body radiation therapy (SBRT)^[31-33].

SBRT attempts to increase tumor control rate while sparing normal tissues utilizing radiobiological principles. SBRT uses hypofractionation schemes with dramatically increased fractional dose^[34]. Reducing the number of fractions can restrict tumor cell repair and repopulation. Compared to SRS with single fractions, SBRT usually includes 3-5 fractions to keep normal tissue repair. Hypofractionation schemes for SBRT use much higher fractional doses and thus have higher BED than conventional fractionation scheme. Meanwhile, advanced localization and immobilization techniques and imaging technologies with high accuracy have been used for SRBT. The damages of normal tissues can be significantly reduced. Therefore, SBRT is expected to achieve higher tumor control rate than conventional treatment while reducing normal tissue toxicity or keeping the toxicity as the same as for conventional treatment.

SBRT has been used to treat many different sites of tumors, mainly in the thoracic, abdominal, and pelvicregions. The lung was one of the first SBRT-treated sites and is also the site most frequently treated with SBRT. Conventional radiation therapy for lung cancer was disappointing. The 5-year overall survival rates were only 10%-30%^[35-37] However, a dosimetric study based on clinical data shows that the dose to achieve significant probability of tumor control for non-small cell lung cancer (NSCLC) conventional treatment should be on the order of 84 Gy to achieve longer (>30 months) local progression-free survival^[38]. On the other hand, dose escalation using conventional fractionation would increase overall treatment time and result in a negative effect on tumor control and normal tissue complications^[39-40]. SBRT has thus been used for lung cancer treatment. Table 1 compares conventional fractionation and SBRT and indicates SBRT has advantages in terms of estimated progression-free survival rate^[41]. Recent clinical studies also supported lung SBRT. Inoue et al^[42] reported a 5-year overall survival rate of 89.8% with a 3.4% grade 2 pulmonary complications for tumor size less than 2 cm. Onishi et al^[43] reported a 5-year local control rate of 92% for T1 tumors with only 1.1% grade 2 pulmonary complications. Zheng et al^[44] showed there were no significant difference in overall survival and disease free survival between SBRT and surgery. Lee et al^[45] found that total does of 43-50 Gy with 3-5 fractions increased cure rate of lung cancer.

Prostate SBRT is getting more interesting. King et al^[46] reported the prostate SBRT results for 67 patients treated with 5×7.25 Gy from 2003 to 2009, and found that the 4-year Kaplan-Meier PSA relapse-free survival was 94%, and significant late bladder and rectal toxicities are infrequent. Kotecha et al^[47] reported a 95.8% 2-year prostate specific antigen relapse-free survival rate. In 2018, Meier et al^[48] published very good results from a multicenter clinical trial showing that the actuarial 5-year overall survival rate was 95.6% and the DFS rate was 97.1% for 309 prostate patients treated by SBRT.

SBRT has been found to be more effective in treating hypoxic tumors than expected because SBRT can cause devascularization that would lead to indirect cell death. Also, extensive cell death can initiate antitumor immune response that would lead to further cell death^[49-50]. This has led to the debate on the validity of LQ for SBRT with very high fractional doses^[51-53].

4 The 4Rs in brachytherapy

Brachytherapy deals with continuous irradiation with various dose rates. Dose rate affects the 4Rs and thus brachytherapy. The dose rate effects on the 4Rs have been proved by both animal cell and human cell experiments^[54-55]. Dose rate effects have also been shown in clinical outcomes. In interstitial brachytherapy for head and neck patients with T_1-2 squamous cell carcinoma of the tongue and the floor of mouth using ¹⁹²Ir wires, patients were grouped by dose rate higher or lower than 0.5 Gy/h. The results show local control rate for high dose rate was up to 27% higher than low doses rate while complication rate was also high for high dose rate^[56]. The decrease in local recurrence with the increase of dose rate for breast ¹⁹²Ir implant has also been reported^[57]. The 4Rs respond to dose rate in different ways. It was found that dose effect on the 4Rs occurred at different dose rate. Repair starts at dose rate equal or lower than 100 cGy/min, redistribution and reoxygenation occur at equal or lower than 10 cGy/min, and repopulation takes place when dose rate is equal or lower than 1 cGy/min^[58-59].

For brachytherapy, if dose rate is R, and total dose delivered within irradiation time T is D, then D is RT. For high dose rate brachytherapy (HDR, R > 12 Gy/h), irradiation time T is short and comparable to external beam treatment. HDR can be treated as fractionated therapy and the 4Rs can be ignored during irradiation. In this case, BED can be calculated using Equation (2). But for low dose rate brachytherapy (LDR, R < 2 Gy/h), treatment takes as long as several days or even permanent. In this case, the 4Rs would take place during irradiation^[58]. Repair would start almost immediately after exposure to irradiation, reoxygenation and redistribution would occur in about ten minutes, and repopulation would take place in 1 h^[59]. Thus, LQ for LDR should be corrected for the 4Rs as discussed above for fractionated treatment but in different forms.

Considering repair with repair rate constant μ and source decay with decay constant λ for LDR with a single fraction, Dale derived RE as^[60]

$ \begin{array}{l} RE = 1 + \left\{ {2{R_0} \cdot \lambda /\left[ {\left( {\mu - \lambda } \right)\left( {\alpha /\beta } \right)} \right]} \right\} \cdot \left\{ {1/\left[ {1 - \exp \left( { - \lambda \cdot } \right.} \right.} \right.\\ \;\;\;\;\;\;\;\;\;\left. {\left. {\left. T \right)} \right]} \right\} \cdot \left\{ {\left[ {1 - \exp \left( { - 2\lambda \cdot T} \right)} \right]/\left( {2\lambda } \right) - \left\{ {1 - \exp \left[ {1 - T} \right.} \right.} \right.\\ \;\;\;\;\;\;\;\;\;\left. {\left. {\left. {\left( {\mu + \lambda } \right)} \right]} \right\}/\left( {\mu + \lambda } \right)} \right\} \end{array} $

(9)

For permanent implant, RE becomes

$ RE = 1 + {R_0}/\left( {\mu + \lambda } \right) $

(10)

To include repopulation and relative biological effectiveness (RBE) for different isotopes, Dale^[61] and Armpilia et al^[62] have come up with

$ \begin{array}{l} R{E_{{\rm{eff}}}} = {\rm{BB}}{{\rm{E}}_{\max }} + \left\{ {2{R_0} \cdot \lambda /\left[ {\left( {\mu - \lambda } \right)\left( {\alpha /\beta } \right)} \right]} \right\} \cdot \left\{ {1/\left[ {1 - } \right.} \right.\\ \;\;\;\;\;\;\;\;\;\;\;\left. {\left. {\exp \left( { - \lambda \cdot {T_{{\rm{eff}}}}} \right)} \right]} \right\} \cdot \left\{ {\left[ {1 - \exp \left( { - 2\lambda \cdot {T_{{\rm{eff}}}}} \right)} \right]/\left( {2\lambda } \right) - } \right.\\ \;\;\;\;\;\;\;\;\;\;\;\left. {\left\{ {1 - \exp \left[ { - {T_{{\rm{eff}}}}\left( {\mu + \lambda } \right)} \right]} \right\}/\left( {\mu + \lambda } \right)} \right\} \end{array} $

(11)

RBE_max is the maximum value of the RBE and defined by the ratio of α between the given radiation and the reference radiation. T_eff is the effective treatment time for permanent implant and defined at which the dose rate R falls to K [=ln(2)/(α·T_p)]

$ {T_{{\rm{eff}}}} = - \left( {1/\lambda } \right)\ln \left( {K/{R_0}} \right) $

(12)

T_p is the doubling time of repopulation, and R₀ is the initial dose rate. The BED for permanent implants includes T_p and T_eff,

$ {\rm{BE}}{{\rm{D}}_{{\rm{eff}}}} = {D_{{\rm{eff}}}} \cdot R{E_{{\rm{eff}}}} - \ln \left( 2 \right){T_{{\rm{eff}}}}/\left( {\alpha \cdot {T_{\rm{p}}}} \right) $

(13)

Where

$ {D_{{\rm{eff}}}} = {R_0}\left[ {1 - \exp \left( { - \lambda \cdot {T_{{\rm{eff}}}}} \right)} \right]/\lambda $

(14)

The difference between BED and BED_eff is that, after time T_eff, BED_eff no longer impacts cell survival.

Recently, Luo et al^[63] has combined Brenner′s LQR for fractionated therapy with Dale′s BED formulism so that the BED formulism for permanent implant includes resensitization in the following equation,

$ R{E_{{\rm{eff}}}} = 1 + \left( {\beta /\alpha } \right)G\left( {{\mu _{\rm{r}}}, {T_{{\rm{eff}}}}} \right){D_{{\rm{eff}}}} - {\sigma ^2}/\left( {2\alpha } \right)G\left( {{\mu _{\rm{s}}}, {T_{{\rm{eff}}}}} \right){D_{{\rm{eff}}}} $

(15)

and,

$ \begin{array}{l} G\left( {\mu , {T_{{\rm{eff}}}}} \right) = \lambda /\left\{ {\left( {{\mu ^2} - {\lambda ^2}} \right)\left[ {1 - \exp \left( { - \lambda \cdot {T_{{\rm{eff}}}}} \right)} \right]} \right\}\left\{ {\left[ {1 - } \right.} \right.\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left. {\exp \left( { - \lambda \cdot {T_{{\rm{eff}}}}} \right)} \right]\left( {\mu + \lambda } \right) - 2\lambda \left[ {1 - \exp \left( { - \left( {\mu + } \right.} \right.} \right.\\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left. {\left. {\left. {\left. \lambda \right){T_{{\rm{eff}}}}} \right)} \right]} \right\} \end{array} $

(16)

where μ can be μ_r or μ_s, repair constant or resensitization constant, respectively. Considering RBE, we have

$ \begin{array}{l} R{E_{{\rm{eff}}}} = {\rm{RB}}{{\rm{E}}_{\max }} + \left[ {\left( {\beta /\alpha } \right)G\left( {{\mu _{\rm{r}}}, {T_{{\rm{eff}}}}} \right) - {\sigma ^2}/\left( {2\alpha } \right)G\left( {{\mu _{\rm{s}}}, {T_{{\rm{eff}}}}} \right)} \right]\\ \;\;\;\;\;\;\;\;\;\;\;{D_{{\rm{eff}}}} \end{array} $

(17)

The BED formulism including all the 4Rs is give below

$ {\rm{BE}}{{\rm{D}}_{{\rm{eff}}}} = {D_{{\rm{eff}}}} \cdot R{E_{{\rm{eff}}}} - \ln \left( 2 \right){T_{{\rm{eff}}}}/\left( {\alpha {T_{\rm{p}}}} \right) $

(18)

This formulism has been used to determine prescription dose for ¹³¹Cs and ¹⁰³Pd permanent implant for gynecological malignancies. The results showed the calculation was consistent with the clinical observation^[64-65].

5 Summary

The 4Rs are correlated to cell survival and also correlated to clinical outcomes from radiation therapy. Such correlations have been quantitatively included in LQ and successfully applied to dose fractionation calculation and prescription dose determination in hypo-or hyper-fractionation schemes, SBRT, and permanent implantation. Excellent clinical outcomes have shown that including the 4Rs in radiation therapy would significantly improve the effectiveness and efficiency of radiation therapy. Future studies should focus on more effective and accurate use of the 4Rs to optimize treatment schemes based on both experimental data and clinical outcomes.

Conflict of interest statement There is no conflict of interest
Contribution statement of author Luo Wei is the only author and he designed the study and prepared the manuscript