A Case-Based Reasoning Approach to Dose Planning in Radiotherapy Xueyan Song1, Sanja Petrovic1, Santhanam Sundar2 1
Automated Scheduling, Optimisation and Planning Research Group School of Computer Science and IT, University of Nottingham, Nottingham, UK. { xxs, sxp}@cs.nott.ac.uk 2
Dept. of Oncology, Nottingham University Hospitals NHS Trust Nottingham, UK
[email protected]
Abstract. This paper concerns the determination of dose plan for prostate cancer in radiotherapy. The determination of dose plan is based on the analysis of trade-off between the expected benefits in terms of the cancer control and the risk in terms of the side effects to rectum caused by the given radiation. A casebased reasoning (CBR) approach to dose planning is proposed, in which fuzzy sets theory is applied in the similarity measure. Dempster-Shafer theory is applied to fuse the dose plans from multiple retrieved similar cases with the aim to strength the agreements and decrease the conflicts in the situations in which oncologists might have different opinions of the same case. Some initial results are presented towards the validation of the approach. Key Words: Case Based Reasoning, Fuzzy Sets, Demspter-Shafer Theory, Prostate Cancer, Radiotherapy
1 Introduction In the UK, nearly 32000 new cases of prostate cancer are diagnosed each year and it is considered to be the most common cancer amongst the male population [8]. Radiotherapy, which uses Gamma and X-rays to kill the prostate cancer cells, is widely applied within prostate cancer treatments. The organs surrounding prostate, namely bladder and rectum, also receive radiation during the treatment procedure, which cause some harmful side effects. The determination of a suitable radiotherapy dose to be used in the prostate cancer treatment is a very important and complex process, since it concerns a trade-off between the expected benefit in terms of the cancer control, and harmful side effects in terms of the patient survival and quality of life. The determination of the dose plan is a complex decision making procedure, which requires a lot of domain knowledge and subjective experience. In order to aid the oncologist in the complex analysis and the calculation of dose plan, and to provide a good decision aid for less experienced oncologists, we develop a case-based reasoning (CBR) system to generate dose plans for prostate cancer patients in collaboration with the City Hospital at the Nottingham University Hospitals NHS
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Trust, UK. A CBR system tries to retrieve a case most similar to the new case from its past experience (cases), and the solution of the retrieved case is reused by revising it to suit the specific need of the new case [7]. The revised solution will be taken for the new case and be retained in the case base for future retrieval [7]. In medical domain, CBR was mostly used for diagnostic purpose [5]. The literature on application of CBR to radiotherapy planning has been very limited so far. To our knowledge, only Berger reported a CBR system which generates a radiotherapy treatment plan for a new patient using the past case (patient) that best match his/her geometry and the treatment constraints [1]. The reasoning in the medical domain is usually characterised by the presence of uncertainty. In general, fuzzy sets have been successfully used for modelling of uncertainties in various application domains [12]. Recent years have seen an increase of interest in fuzzy CBR system, where fuzzy sets are used in the similarity measure [2][6][10]. In our CBR approach to dose planning the dose plans for patients are stored in cases. Fuzzy sets are applied in the formulation of the similarity measure. In practise, we also found that several most similar cases to a new case might propose different treatment plans. Dempster-Shafer theory [4][11] is used to fuse multiple proposals with the aim to increase the non-subjectivity of the oncologist’s opinion. The result after the fusion will be suggested to the oncologist. The paper is organised as follows. The description of the problem is presented in Section 2. Section 3 provides a detailed description of our CBR approach to dose planning. This research is at very early stage and our initial results are given in Section 4 to illustrate our approach. Section 5 concludes our work and proposes future research direction.
2 Description of Problem A radiotherapy treatment to prostate cancer is divided into two phases. In phase I, both the prostate and its surrounding area, where the cancer has spread to, will be irradiated, while in phase II, only the prostate will be irradiated. The dose given in phase I is usually in the range of 46-64Gy, while the dose range of phase II is usually 16-24 Gy. Our task is to determine the dose levels for phases I and II, which enable good control of cancer while reduce the risk to rectum. In practise, rectum is primarily concerned because it is far more sensitive to the radiation than bladder. Dose limits are set to different volumes of rectum that have to be respected by oncologists when proposing a dose plan. Ideally, the dose received by the rectum should be within the set limits presented in Table 1. However, for some patients, this condition has to be sacrificed so that adequate dose can be given to fight the cancer. Table 1. Total dose limits for rectum Rectal Volume 66% 50% 25% 10%
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Total dose limits (Gy) 45 55 65 70
The oncologist uses two groups of parameters to determine a dose plan for each patient. The first group of parameters include: the clinical stage, the gleason score and PSA. This group of parameters describes the stage of the cancer and therefore has impact on the required dose level in phase I. The meaning of the medical terms used in this paper is given in Appendix. An example of the parameter values is given in Table 2. Table 2. Parameters which indicate the stage of cancer Case No. Case 1
Clinical Stage T2a
Gleason score 7
PSA 20.1
The second group of parameters describes the degree of radiation received by the rectum. It can be used to calculate the potential risk to the rectum. This group of parameters includes the Distribution Volume Histogram (DVH) of rectum for phases I and II at 66%, 50%, 25% and 10% of the volume, illustrated in Table 3. The DVH is calculated for each patient by a software system for planning called Helax. It takes into consideration the radiotherapy treatment plan including the width and length of the radiation beams, their shaping, weighting, energy and wedges. The DVH describes the received dose level at certain percentage of the volume of the site. For example, if 54Gy is given to a prostate, then the radiation to the 66% volume of the rectum would be 67% of 54 Gy, which is equal to 36Gy. Table 3. Parameters which indicate the risk to the rectum. Case No. Case 1
DVH of phase I 66% 50% 25% 0.67 0.87 0.98
10% 0.99
DVH of phase II 66% 50% 25% 0.44 0.47 0.53
10% 0.77
The determination of dose levels for phases I and II is based on the trade-off analysis of benefits and risk. Table 4 illustrates the Partin table for Case 1, which estimates the degree to which the cancer has spread to the surrounding area. Table 5 presents the 5yr Progress Free Probability (PFP) of Case 1 when difference dose levels are given to the patient. The determination of dose level for phase I and phase II is based on the oncologist subjective judgements on the stage of cancer supported by the Partin table and expected 5 yr PFP. Table 4. MSKCC Partin Table for Case 1 MSKCC Partin Table LNI 51% Risk of Lymph Node Involvement SVI 24% Risk of Seminal Vesicle Invasion ECS 14% Risk of Extracapsular Spread Table 5. MSKCC 5yr PFP for Case 1 MSKCC 5yr PFP
66Gy 30%
70Gy 46%
72Gy 54%
74Gy 60%
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As a general rule, if SVI is less than 15%, the dose for Phase I is usually set to 46 Gy. If SVI is greater than 15%, the dose for phase I is usually set to 46-64 Gy, depending on the degree of the infection of the surrounding area and the risk to rectum. In this example, since the SVI is very high (>15%), the oncologist decides to give 54 Gy in phase I. There is an ongoing European trial which recommends 70Gy to be given to all patients. Thus, 16 Gy will be given in phase II. Using the DVH of rectum, the oncologist can calculate whether the dose limits assigned to the rectum are violated. Table 6 presents the received levels of radiation by the rectum for dose plan 54Gy+16Gy and 56Gy+14Gy, respectively. According to Tables 1 and 6, it can be concluded that the proposed plan is safe because the dose limits to the rectum are not violated. However, if the dose in phase I is increased from 54Gy to 56 Gy, the limit of the dose received by the rectum will be violated. In this case, the oncologist prefers not to violate the dose limits for rectum and will give 54 Gy +16 Gy dose levels for phase I and phase II, respectively. Table 6. Dose received by rectum for dose plan: 54 Gy+16Gy Rectal Volume 66% 50% 25% 10%
DVH: Rectum Phase I Phase II (%) (%) 67% 44% 87% 47% 98% 53% 99% 77%
Dose plan (54Gy+16Gy) Phase I Phase II Total (=54Gy) (=16Gy) (Gy) 36 7 43 47 7.5 54.5 53 8.4 61.4 54 12.3 66.3
Dose plan (56Gy+14Gy) Phase I Phase II Total (=56Gy) (=14Gy) (Gy) 37.52 6.16 43.68 48.72 6.58 55.3 54.88 7.42 62.3 55.44 10.78 66.22
It is worthwhile to mention that only the first group of parameters was considered in the past when generating dose plans for patients. In this research, the DVH of rectum is included to evaluate the risk of the generated plan.
3 A Fuzzy CBR Approach to Dose Planning The dose plans for patients are stored in the cases, and the assumption is that by retrieving similar cases the stored experience and judgements can be reused for a new case. 3.1 Representation of Cases and Similarity Measure As explained in Section 2, two groups of parameters are used to analyze the expected benefit v.s. risk situation. Our assumption is that similar cases should have similar benefit versus risk situations. Attributes of a case correspond to two sets of parameters introduced in Section 2: the 1st group of attributes includes clinical stage, gleason score, PSA; the 2nd group of attributes includes DVH of rectum for phase I and phase II;
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Fuzzy Representation of the 1st Group of Attributes. Three fuzzy sets, low, medium and high are assigned to each attribute. Each attribute Ai can be represented by a 3-dimensional vector:
Ai = [ μ low ( Ai ), μ medium ( Ai ), μ high ( Ai )]
(1)
where each element of the vector presents a membership degree of the attribute to the fuzzy set low, medium and high, respectively. These membership functions are defined based on the domain knowledge and oncologist’s preference. Thus, fuzzy representation of the attributes provides more flexibility by allowing the expression of preferences. Since the 1st group of attributes have different scales and representations, fuzzy sets also enable these attributes to work as a group. As an illustration, Figure 1 presents the membership functions for low, medium and high values of clinical stage. Table 7 presents the values of 1st group of attributes of case C1. Low
High
Medium
1.0
Membership
0.8 0.6 0.4 0.2 0.0
T1a
T1b
T1c
T2a
T1d
T3a
T3b
Clinical stage
Fig. 1. Membership functions of fuzzy sets low, medium and high of clinical stage Table 7. Fuzzy representation of the 1st group features Case no. C1
Clinical Stage low med high 0 1 0
Gleason Score low med high 0 1 0
PSA low med 0 0.49
high 0.26
Similarity For The 1st Group of Attributes. Given two cases Ci and C r , the distance between Ci and C r with respect to the 1st group of attributes, denoted by
Dis I (Ci , C r ) , is defined as in many CBR systems: 1/ 2 3 3 2 Dis I (Ci , C r ) = ( ∑ wl ∑ ( vi ,l , m − v r ,l , m ) ) l =1 m =1
(2)
where wl is the weighting of attribute l , l =1,2,3; vi ,l , m and v r ,l ,m are the values of attribute l of Ci and C r with respect to fuzzy sets low (m=1), medium (m=2) and high (m=3);
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The similarity between Ci and C r with respect to the 1st group of attributes, denoted by SimI (Ci , C r ) , is defined as: SimI (Ci , Cr ) =
1 1 + Dis I (Ci , C r )
(3)
Following the oncologist’s practise, the weighting of gleason score, clinical stage, PSA and DVH of rectum in the similarity measure should be non-increasing (currently set to be 0.5, 0.3, 0.2, respectively). Similarity For the 2nd Group of Attributes. The 2nd group of attributes contains the DVHs of rectum at 66%, 50%, 25% and 10% of its volume, for phase I and phase II. Given two cases Ci and C r , the distance between Ci and C r with respect to the 2nd
group of attributes, denoted by Dis II (Ci , Cr ) , is defined as: 1/ 2 2 4 2 Dis II (Ci , Cr ) = ( ∑ ∑ ( vi ,l ,m − v r ,l ,m ) ) l =1 m =1
(4)
where vi ,l , m and v r ,l ,m are the values of dose received in phase l , received by 66% (m=1), 50% (m=2), 25% (m=3) and 10% (m=4) of rectal volume in cases Ci and C r ; The similarity between Ci and C r with respect to the 2st group of attributes, denoted by SimII (Ci , Cr ) , is defined as: SimII (Ci , Cr ) =
1 1 + Dis II (Ci , C r )
(5)
Similarity Measure between Two Cases. The similarity between cases Ci and C r , denoted by Sim(Ci , Cr ) , is defined as:
Sim(Ci , Cr ) = W1 × SimI (Ci , Cr ) + W2 × SimII (Ci , Cr )
(6)
Following the oncologist recommendation, the 1st group of attributes is of higher importance than the 2nd one. At this stage of the development of the system we set the following values for the weights: W1=0.6, W2=0.4.
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3.2 Retrieval
Given a new case, the retrieval process first filters the case base and finds the cases with similar clinical stages. According to the scale of clinical stages published in 1997, a clinical stage of the prostate cancer takes values from the set: {T1a,T1b,T1c,T2a,T2b,T3a,T3b}, indicating the spread of the cancer. These values are sorted in the following order: T1a
