Objective assessment of tumour response to therapy based on tumour growth kinetics

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1 Briish Journal of Cancer (2011) 105, All righs reserved /11 Objecive assessmen of umour response o herapy based on umour growh kineics E Mehrara*,1, E Forssell-Aronsson 1 and P Bernhard 1 1 Deparmen of Radiaion Physics, Universiy of Gohenburg, Sahlgrenska Universiy Hospial, SE Göeborg, Sweden BACKGROUND: Curren sandards for assessmen of umour response o herapy (a) caegorise herapeuic efficacy values, inappropriae for paien-specific and deerminisic sudies, (b) neglec he naural growh characerisics of umours, (c) are based on umour shrinkage, inappropriae for cyosaic herapies, and (d) do no accommodae inegraion of funcional/biological means of herapeuic efficacy assessed wih, for example, posiron emission omography or magneic resonance imaging, wih daa from anaomical changes in umour. METHODS: A quaniy for umour response was formulaed assuming ha an effecive reamen may decrease he cell proliferaion rae (cyosaic) and/or increase he cell loss rae (cyooxic) of he umour. Tumour response values were analysed for 11 non-hodgkin s lymphoma paiens reaed wih 131 I-labelled ani-b1 anibody and 12 prosae cancer paiens reaed wih a nuriional supplemen. RESULTS: Tumour response was found o be equal o he logarihm of he raio of pos-reamen umour volume o he volume of corresponding unreaed umour. Neglecing he naural growh characerisics of umours resuls in underesimaion of reamen effeciveness based on currenly used mehods. The model also faciliaes he inegraion of daa from umour volume changes, wih daa from funcional imaging. CONCLUSION: Tumour response o herapy can be assessed wih a coninuous dimensionless quaniy for boh cyooxic and cyosaic reamens. Briish Journal of Cancer (2011) 105, doi: /bjc Published online 26 July 2011 Keywords: umour; response; herapy; growh kineics; cyooxic; cyosaic Assessmen of umour response () o herapy is necessary for evaluaion of he efficacy of novel anicancer drugs in clinical rials. Furhermore, response evaluaion wih high individual precision may faciliae individualised herapy raher han sandardised reamen regimen in daily clinical pracice. Tumour shrinkage has been radiionally used as a measure of reamen efficacy. For example, he response evaluaion crieria in solid umours (RECIST) is currenly adoped by academic and indusrial groups (Miller e al, 1981; Therasse e al, 2000), where response o herapy is caegorised as follows: complee response (CR), he disappearance of all arge lesions; parial response (PR), a leas a 30% decrease in he sum of he longes diameer of all arge lesions; progressive disease (PD), a leas a 20% increase in he sum of he longes diameer of all arge lesions or he appearance of one or more new lesions; and sable disease (SD), neiher sufficien shrinkage o qualify for PR nor sufficien increase o qualify for PD (Therasse e al, 2000; Eisenhauer e al, 2009). Appropriaeness of RECIST crieria, for example, wheher he change in umour size is a proper end poin for response assessmen, has been widely discussed (Barnacle and McHugh, 2006; Tuma, 2006; Twombly, 2006; Eisenhauer, 2007). The specific crieria have been developed for differen ypes of cancers, for *Correspondence: Dr E Mehrara; esmaeil.mehrara@gu.se Received 20 May 2011; revised 10 June 2011; acceped 23 June 2011; published online 26 July 2011 example, prosae cancer (Scher e al, 2008) and malignan lymphoma (Cheson e al, 2007). However, his sudy was focused only on quanificaion of o herapy, regardless of he ype of umour and clinical measures oher han umour response. The following limiaions can be idenified in curren sandards for quanificaion of o herapy: (1) Tradiional sandards may no be appropriae o assess he efficacy of emerging numbers of cyosaic agens, which do no resul in umour regression o a poin of PR or CR. Proposals of a general means of assessmen of boh cyocidal and cysosaic effecs mus be developed (Michaelis and Raain, 2006; Gwyher and Schwarz, 2008). (2) The naural growh rae of umour is no considered. A cerain reamen ha kills he same raio of umour cells in wo differen umour ypes will give differen resuls if he naural proliferaion raes of umour cells are differen. (3) Adoping he curren sandards will conver a coninuous variable, as, ino a discree variable, resuling in he loss of informaion. This will make comparison of individual, or combinaion of, reamens less accurae. Furhermore, aemps o relae reamen efficacy o molecular or cellular characerisics of umours, for example, by sysems biology approach, will be raher difficul when daa are caegorised. Karrison e al (2007), based on suggesions by Lavin (1981), demonsraed ha clinical rial designs ha rea change in umour size as a coninuous variable are feasible (Karrison e al, 2007). They used he logarihm of he raio of umour volume afer herapy o ha a baseline as an

2 end poin for quanificaion of, denoed as LR (log raio) (Karrison e al, 2007). (4) Many sudies have shown ha he effec of reamen on umours can be assessed by means of changes in umour characerisics oher han size, for example, esimaed by posiron emission omography (PET) or magneic resonance imaging or specroscopy (MRI/MRS) (Padhani and Miles, 2010). Available sandards do no accommodae mahemaical inegraion of physiological or funcional imaging modaliies ino anaomical changes in umour and new mehods mus evolve (Jaffe, 2008). The aim of his sudy was o develop a mahemaically accurae and biologically relevan mehod for assessmen of o any ype of reamen. MATERIALS AND METHODS Kineics of umour growh olumeric growh rae of umours can be quanified wih specific growh rae (SGR), described as relaive volume change per ime uni. Quanificaion of growh rae wih SGR is mahemaically more accurae and biologically more relevan han he widely used parameer umour volume doubling ime (DT) (Mehrara e al, 2007, 2009). The SGR of a umour during ime period from 0 o can be calculaed from umour volumes a he sar and a he end of his period, 0 and, respecively: SGR ¼ lnð= 0Þ ð1þ ð 0 Þ More rapidly growing umours have higher SGR values, SGR ¼ 0 represens non-growing umours, and negaive SGR values can be assigned o umour regression. Specific growh rae is consan for exponenially growing umours; however, if SGR is ime dependen, as for non-exponenially growing umours, he above equaion can be rewrien as follows: ln ¼ SGRðÞd ð2þ 0 0 where SGR() is he SGR a ime. The value of SGR() depends on he level of cell proliferaion rae, CPR(), and cell loss rae, CLR(), a ime : SGRðÞ ¼CPRðÞ CLRðÞ ð3þ o herapy If he naural growh of umour is inerruped by herapy, an effecive herapeuic agen may increase he CLR (cyooxic effec) and/or decrease he CPR (cyosaic effec) of umour. Specific growh rae will hen decrease o SGR 0 regardless of he mechanism of he herapeuic effec: SGR 0 ðþ ¼SGRðÞ DSGRðÞ ð4þ where DSGR() is he effec of reamen a ime. Temporal variaion of SGR 0 depends on all facors ha naurally affec umour growh as well as he effec of herapy. Readjusmen and inegraion of he above equaion over ime gives: DSGRðÞd ¼ SGRðÞd SGR 0 ðþd where and are he ime of herapy iniiaion and efficacy assessmen, respecively. The righ side of he above equaion can be replaced using Equaion (2), which gives: DSGRðÞd ¼ ln ln i i where i is umour volume a he ime of herapy iniiaion, and and are he volume of reaed and corresponding (hypoheical) non-reaed umour a he ime of efficacy assessmen, respecively. The lef side of he above equaion is he overall effec of reamen during ime from reamenniiaion o ime of efficacy assessmen, and can be denoed as. Since ln( / i ) ln( / i ) ¼ ln( / ): ¼ ln ð5þ is a general coninuous dimensionless quaniy for umour response o boh cyooxic and cyosaic herapeuic effecs. can hus be calculaed by he logarihm of he raio beween he pos-reamen volume of umour and he volume ha he umour would have had (a he ime of efficacy assessmen) if he growh was nonfluenced by herapy. The value of canno be defined, bu only esimaed based on he naural growh model of umour. To esimae he following assumpions were used (cf. Figure 1): (1) umour volume a firs diagnosic invesigaion is d ; (2) herapy is iniiaed a a ime poin D pre afer measuremen of d ;(3)umour grows exponenially wih a consan SGR() ¼ SGR 0 during he sudied ime period and umour volume a he ime of herapy iniiaion is i ; (4) umour response is assessed a a ime poin D pos afer herapy iniiaion and umour volume a he ime of efficacy assessmens ; and (5) umour would coninue o grow wih SGR 0 if he growh was nonerruped and is volume would be a he ime of efficacy assessmen. Applicaion o paien daa Tumour response values were calculaed for reamen of non- Hodgkin s lymphoma paiens wih 131 I-labelled ani-b1 anibody, In() d Treamenniiaion Δ pre i Δ pos Time Efficacy assessmen Figure 1 Definiion of he parameers used in he sudy. d, i, and are umour volumes a diagnosis, herapy iniiaion, and ime of efficacy assessmen, respecively. Tumour volume would increase o a he ime of efficacy assessmenf herapy was no sared. ¼ umour response value derived in his sudy, LR ¼ log raio measure for quanificaion of reamen effeciveness, e1 and e2 ¼ underesimaion of if prereamen or pos-reamen growh of umour is negleced, respecively. ¼ overall underesimaion of if prereamen and pos-reamen growh of umour are negleced ( ¼ LR þ e1 þ e2). e2 e1 LR 683 Briish Journal of Cancer (2011) 105(5),

3 684 where daa were rerieved from a previously published aricle (Sgouros e al, 2003). The sudy was seleced based on he availabiliy of umour volumes and he ime of prereamen and pos-reamen volume esimaions in each paien, informaion necessary for calculaion. Toal umour burden was assessed by drawing conours around all lymphoma lesions idenified on whole-body CT or MRI. Two more paiens are included in he original aricle, where umours disappeared afer reamen. Those daa were excluded in his sudy. Average pos-reamen re-growh of umour volumes used as an esimaion of he naural growh rae of non-hodgkin s lymphomas in his sudy. Anoher se of daa were rerieved from he lieraure, where prosae-specific anigen (PSA) increase raes before and afer reamen wih a nuriional supplemen were available in 12 prosae cancer paiens (Guess e al, 2003). Tumour response values were calculaed using PSA levels before and afer reamen for assessmen of reamen efficacy. Tumour response values were calculaed for non-hodgkin s lymphoma paiens using oal umour burden as reference and for prosae cancer paiens using PSA level as reference, respecively. On he basis of he calculaed mean and sandard deviaion of and LR in each group of paiens, frequency disribuion of and LR were approximaed wih corresponding normal disribuion wih he same mean and sandard deviaion values in each group, respecively. RESULTS When he umour response model developed in his sudy (Equaion (5)) is applied o an exponenially growing umour, is relaed o umour volume and growh rae as follows (Figure 1): ¼ ln þ SGR 0 D pre þ SGR 0 D pos ð6þ fflfflfflfflfflffl{zfflfflfflfflfflffl} d fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} e1 e2 LR fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} The firs erm on he righ-hand side of he above equaion, LR, is he reamen effeciveness where he naural growh of umour is negleced and is equivalen o he LR measure suggesed by Karrison e al (2007). LR values less han 0.5, beween 0.5 and þ 1, and larger han þ 1 correspond o progressive disease, sable disease, and parial response according o RECIST, respecively. The second erm, e1, and he hird erm, e2, represen umour growh before and afer reamenniiaion, respecively. The overall effec of umour growh from he ime of diagnosis o he ime of efficacy assessmen, D, sums up as follows: ¼ ln þ SGR 0 D ¼ LR þ ð7þ d The above equaion indicaes ha evaluaion of reamen effeciveness by comparing he volume of reaed umour wih prereamen umour volume underesimaes he effec of herapy by. If a herapeuic drug has pure cyosaic effec, has, he drug inhibis umour growh, bu does no desroy exising umour cells, and if he drug can compleely block umour growh, he umour volume a he ime of efficacy assessmen will be he same as he umour volume a he ime of reamenniiaion, i. The cyosaic efficacy of reamens hen e2 ¼ ln( / i ) (Figure 1). If he drug can parially conrol umour growh, he umour volume a he ime of efficacy assessmen will be larger han i (closer o ) and he reamen efficacy will be less han e2 in Figure 1. Noe ha umour volume a he ime of efficacy assessmens, however, larger han umour volume a he ime of diagnosis, d. According o RECIST, a of more han 1.73 d (20% increase in diameer) will be considered as progressive disease. For a umour wih DT shorer han 27 days (SGR 42.6% per day) and a reamen ha compleely blocks umour growh, he drug will be considered wihou any effec and be caegorised as progressive disease according o RECIST. The frequency disribuions of and LR are shown in Figures 2A and B for non-hodgkin s lymphoma and prosae cancer paiens, respecively. The resuls show ha LR largely underesimaes umour response compared o. DISCUSSION Tradiional quanificaion mehods used in oncology can give conradicory resuls o mahemaically accurae and biologically relevan mehods (Mehrara e al, 2007, 2009). In his aricle, we presen a dimensionless coninuous quaniy for objecive assessmen of, regardless of umour ype, clinical measures oher han umour response, and he mechanism of he effec of herapy Frequency Frequency LR LR Figure 2 Frequency disribuions of and LR based on reamen resuls of (A) 11 non-hodgkin s lymphoma paiens and (B) 12 prosae cancer paiens. The mean and sandard deviaion values were obained for each group and he corresponding normal disribuions were drawn. : mean ¼ 4.16 and 0.35, s.d. ¼ 1.69 and 0.06; LR: mean ¼ 1.02 and 0.1, s.d. ¼ 1.03 and 0.02 for non-hodgkin s lymphoma and prosae cancer paiens, respecively. and LR values were calculaed from changes in umour volume and PSA level in non-hodgkin s lymphoma and prosae cancer paiens, respecively. Briish Journal of Cancer (2011) 105(5),

4 on umour: cyooxic and/or cyosaic. Sudies have shown ha umour growh rae is a valuable parameer for, for example, predicion of recurrence afer surgery (Cucchei e al, 2005) and survival of paiens (Blankenberg e al, 1995), and he change in umour growh rae can serve as a surrogae end poin for deerminaion of herapy response (Haney e al, 2001). In his sudy, a simplified formula was derived based on he effec of herapy on kineics of umour growh. Tumour response was measured by he logarihm of he raio of pos-reamen umour volume o he volume of umour (a he ime of efficacy assessmen) if herapy was noniiaed. ¼ 0 indicaes no effec, and he larger value he more effecive herapy. A negaive value indicaes pos-reamen umour swelling or growh enhancemen. values are larger han corresponding LR values, which were used by Karrison e al (2007). The value of LR is calculaed as he logarihm of he raio of pos-reamen umour volume o he prereamen umour volume. The naural growh of umour during diagnosis and herapy iniiaion as well as afer herapy is negleced in he LR value. There migh be a few weeks or longer delay beween umour diagnosis and iniiaion of herapy due o pracical limiaions or necessiy of furher evaluaions. Tumours coninue o grow during his period. As an example, he volume of a umour wih DT of 70 days will increase 23% during 3 weeks. Repopulaion of umour cells during herapy, for example, beween cycles of chemoherapy, is also an imporan facor ha should no be negleced (Davis and Tannock, 2000; Kim and Tannock, 2005). The overall underesimaion of reamen effeciveness by LR () is larger when umour is rapidly growing or he ime beween prereamen and pos-reamen volume assessmens is long. The relaive imporance of also depends on dose response relaion, has, for a more effecive drug LR is less affeced by his error. The generally used mehods when comparing he pos-reamen volume of umour wih he prereamen volume will hus resuln underesimaion of reamen effeciveness. I has already been shown ha RECIST underesimaes he effec of imainib on measaic gasroinesinal sromal umour (Choi e al, 2007). The fac ha reamen effeciveness is underesimaed by LR or RECIST has imporanmplicaions on assessing he efficacy of new anicancer drugs or combinaions of herapies. I has been demonsraed ha clinical rial designs based on LR are feasible (Karrison e al, 2007), which suggess ha can also be used for such sudies. The main difference beween and LR is he reference volume of umour for efficacy assessmen, which is he volume of corresponding unreaed umour or prereamen volume of umour for and LR, respecively. The saisical aspecs of using such coninuous variables in clinical rials, for example, handling exreme cases as complee disappearance of lesions in wo paiens in his sudy, are discussed elsewhere (Karrison e al, 2007). Here we discuss he advanages and limiaions of using as a quaniy for umour response. The main limiaion wih using, compared o LR, is he esimaion of he volume of an unreaed umour a he ime of evaluaion, which needs he naural growh model of umour. In his sudy, we assumed an exponenial model for naural growh of umours. However, he presened formula for calculaion of (Equaion (5)) can be used for any growh model, provided ha he non-exponenial growh characerisics of umour and can be esimaed. The naural growh rae of umours can be esimaed by appropriae echniques according o he available daa in each sudy. Owing o lack of informaion, we esimaed he growh rae of unreaed non-hodgkin s lymphoma umours from he average re-growh rae of umours afer herapy, which migh be differen from he rue growh rae of umours before reamen. However, hese daa were used only for demonsraion, and no clinical inerpreaion of he resuls should be made. If umour volumes a wo occasions before sar of herapy are available, for example, having wo CT scans a diagnosic invesigaion and an invesigaion jus before herapy iniiaion, naural SGR of umour and consecuively can be calculaed using Equaion (1). Taking boh iner- and inra-operaor as well as iner-scan variabiliy ino accoun, an increase of he measured volume by more han 25% is needed for a 95% likelihood of being a rue growh, raher han measuremennaccuracy. For an exponenially growing umour, increase of he measured volume will be more han 25% if he measuremen ime inerval beween wo invesigaions is longer han 0.32 DT. If umour volume before reamens only available a one occasion, for example, he firs diagnosic imaging, umour volume a he ime of herapy iniiaion can be esimaed by backexrapolaion of volume regression curve during herapy, which migh be described by exponenial model (Sein e al, 2008). Tha measure ogeher wih he firs umour volume available can be used for esimaion of he naural SGR of umour. However, we used PSA level as reference, insead of umour volume, for calculaion of and LR in prosae cancer paiens and he resuls were similar o when umour volume was used for calculaions in non-hodgkin s lymphoma paiens. This indicaes ha values calculaed based on umour marker level can be used for quanificaion of reamen efficacy in some ypes of umours. Measuremen of umour marker level before he iniiaion of reamens usually more pracical in clinical research and pracice. However, oher facors ha may affec umour marker level, for example, PSA decline due o dediffereniaion of he umour as i becomes anaplasic, mus be considered, when pos-reamen changes of umour marker level is sudied. Tumour srucure can be raher non-homogeneous, consising of, for example, differen clones of cancer cells (wih differen sensiiviies o an anicancer agen), sroma and necroic areas. The value of SGR of he umour may hen be obained from he spaial disribuion of SGR wihin umour, sgr(x,y,z): SGR ¼ 1 I sgrðx; y; zþdxdydz: ð8þ An effecive reamen can reduce sgr(x,y,z) differenly in differen pars of he umour depending on, for example, pharmacokineics and dose response of a sysemically used agen. This will accordingly cause a reducion in SGR of umour as was used in he presened model (Equaion (4)). Sudies have shown ha funcional imaging variables migh be correlaed wih umour growh rae, for example, using PET (Duhaylongsod e al, 1995; Tann e al, 2008). Furher developmens in his field can faciliae umour SGR esimaion by funcional imaging before reamen as well as inegraion of daa based on anaomical changes in umour wih oher means of umour response assessmen by funcional imaging wih MRI (Chenever e al, 1997) or PET (Sroobans e al, 2003; Boss e al, 2008). In his sudy, we assumed ha is evaluaed a a specific occasion afer reamen, as is usually done in clinical sudies. However, emporal changes of umour SGR afer reamen can also give valuable informaion such as progression due o he resisan clones of umour, which can be idenified wih he poin ha SGR sars rising. However, his remains o be sudied. Time o even, for example, ime o progression (TTP) or progression-free survival (PFS), is an end poin has also recommended for assessmen of herapeuic efficacy (Scher e al, 2008; Eisenhauer e al, 2009). An ineresing aspec of he presened mehod in his sudy is ha Equaions (1) and (5) imply ha TTP is linearly relaed o. I should be noed han his conex, he TTP refers o he progression of he umour(s) under sudy, whereas from a clinical perspecive, appearance of new measaic lesions may be considered as disease progression. However, he measases migh have been seled before he sar of 685 Briish Journal of Cancer (2011) 105(5),

5 686 reamen or he effec of reamen migh be differen on he primary umour and measases. In conclusion, a number of flaws can be idenified in quanificaion mehods of used in available sandards, for example, neglecing he naural growh rae of umour, which leads o underesimaion of reamen effeciveness. The logarihm of he raio of reaed umour volume (umour marker level) o he volume (umour marker level) of corresponding non-reaed umour is a general coninuous quaniy for umour response o boh cyosaic and cyooxic agens. I can also accommodae inegraion of daa from anaomical changes of umour wih daa from changes in oher biological characerisics of umour afer herapy. These resuls are valuable for clinical sudies, revision of curren sandards for assessmen of, and also a deerminisic approach for individualised herapy in oncology. 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