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7/ m V The prognostic value of measuring the gross lineal radial growth of pulmonary metastases and primary pulmonary cancers The gross rales of growth of pulmonary cancers and pulmonary metastases may be reduced to clinically useful nomograms and graphs. The constructs are feasible because most neoplasms growing in the lung are observed only during a limited segment of their life history, often being observed too few times to permit the identification of the growth curve of best fit. Consequently, the parameter that can be calculated most quickly, namely linear radial growth rale in mm.lday, may be most useful. The linear radial growth rates are plotted against observed survival. The nomograms permit easy approximation of the volume doubling time and the exponential radial growth rate in mm.hnm.lday. The mean of the log normal frequency distributions of doubling times for common primary and metastatic cancers found growing in the lung is plotted on one nomogram to put the information in perspective. The more widespread reporting and tabulation of such data should lead to a highly useful kinetic staging and treatment evaluation system. John S. Sprat!, Jr., M.S.P.H., M.O., F.A.C.S., and John Arthur Sprait, B.A.. Columbia, Mo. Ti, he one characteristic known to be common to all cancers is growth. Until recently, this characteristic has been described in subjective terms like "fast'' or "slow," but the actual rate of growth has been re corded infrequently. A brief summary of the utility val ue of knowing the rates of growth is given in Table I. Growth of any cancer fits into a kinetic model determined by many variables acting simultaneously to effect a net rate of increase or decrease in the total mass of a cancer. The kinetic model is depicted in Fig. I. Beginning in the early 1960's, we have been able to accumulate considerable data from several roentgen files. Clusters of observed growth curves measured for 22 primary lung cancers of different histologic types and of pulmonary metastases have been previously From the Cancer Research Center and the Ellis hschcl Stale Cancer Hospital. Columbia. Mo. This investigation was supported by the Public Health Service Research Grant CA-08023 from the National Cancer Insiuuic Received tor pubiicauon May 28. 1V75. Address for reprints: John S. Spratt. Jr.. M l), Cancer Research Center. Business 70 and Garth Ave.. Columbia. Mo. 65201. `Director. Cancer Research Center, and Chief Surgeon. Ellis Fischel Stale Cancer Hospital. published.`"s The dimensions of roentgen shakiwl recorded at different times for growing cancers cask 1 measured by calipers. Though radiographic gcomcar j factors affect actual size, the rate of change is M significantly affected by these same factors if lucatfa] techniques remain constant. We have now measwd [ hundreds of different cancers growing in the lung, bones, the breast, the lymph nodes, and the cuU-^^^Hggufviy Furthermore, numerous review articles on compUl tions of similar observations are beginning to accuot I late. The more completely and comprehensively tail data are reported, the sooner it will be feasible a| establish a kinetic classification for benign malignant neoplasms that will explain many behatua characteristics of cancers not elucidated by atuloau and morphologic classification systems. Corrcuu between kinetics and morphology remains tugadesirable lo make maximum use of past diua] experience largely based on gross anatomic microscopic morphology. The gross rates of growth are measurable in ua>i^^BlkccDn segment of the entire period of growth. This sepal exists between the threshold diameter of radiog^al visibility and the prelethal diameter which 274 T. CAIM021492 /mij-ua . . . ,, " J * * w * tJ OT LA/V f.T.LG 17, U. .CODE) 6113 18097 r#'-' *-** 4ii - k "* -- ? '976 .I Growth ofpulmonary metastases and pulmonary cancers 27 5 Host detfmmoMs of growth Nutrition iTtmuno rMtromfs Chorocteristics of cHs of origin Endocrine factors - INCREASING MASS f\ GENETIC predis position induced ENVIRON MENTAL OR ENDOGENOUS CARCINOGEN AT NET GROWTH RATE 1t DETECTABLE SYMPTOMATIC 1 LETHAL Re. I. Kinetic model of an untreated cancer A solid cancer growing in the lung is a dynamic mass of tissue on which many factors are acting simultaneously These variable factors produce a net effect on growth which pnxiuecs grossly measurable growth talcs characterizing various cancers (and pulmonary metastases) and affecting longevity. * V.'-me obscured by confluent growth of multiple Pioases or by secondary events such as pneumonia .n shadow* sBM'. ad itelectasis in the lung. tcers can he ; A'previous report' indicated that the radiologist e geometric wh sees pulmonary metastases at sizes less than 6 tnge is not smK la size obtained by 26.7 net doublings of a 1,000 if roentgen ocrllfand never at sizes less than 3 mm. They arc not v measured utubHy visible until they reach 10 mm. in diameter, be lung, the nqSB- At these metastases grow, the untreated host will not the colon. 'W'urvivc the presence of pulmonary metastases or a a complies- frfonnary cancer larger than 10 cm. in greatest to accumu- dfobl dimension. Thus the segment of a growth curve tsivcly such <j9H fly and consistently measurable by thoracic feasible to 'UB nowtenography exists between 10 mm. ami 100 ocnign and *V^B * All patients will be dead by the time the diameter v behavioral .In reached 200 mm. (a size obtained by 40 H \v anatomic t doublings of a 1.000 cgi cell). Measurements Correlation -jjH 4 net growth rates are also possible for other organ tins highly .a| no. such as the skin,1 colon,9 hone.* breast.-1 and ast clinical iH v-ph nodes.1 itomic and :S||| when the growth rate is calculated over such a short selected segment, the calculation of the line f best le in only 1 trtecomes hypothetical in most cases. Actually, the his segment segment of growth between If) mm. and 10 cm. radiographic approximates straight line growth and may he which may *H'Tt,ed as a straight line when a site is measured two times, before and after a span of time adequate for growth, as is the situation in many cases. Thus arguments over whether the growth is logarithmic, Gompertzian, linear, or other are often impossible to resolve in the clinical setting because of the short period of observation relative to the total life history of the neoplasm. Furthermore, there arc good animal models of solid tumors which suggest that radial growth really is linear during this segment of spherical cancerous growth if continued ceil duplication is re stricted only to an advancing margin of active growth while the center becomes dormant and necrotic. In fact. Mayncord4 provides very sound observations that the radial growth of at least some cancers is linear. He observes that Jensen's rat sarcoma increases linearly with time, not exponentially. He developed a mathematical theory that satisfactorily explains the observed linear growth. The explanation hinges on the observation that active cellular proliferation occurs only in a thin outer shell of a spherical cancer with the central cells being either dormant or necrotic. With these points in mind, we re-examined data previously reported. Several years ago. the foremost concept was doubling time. We have recalculated the growth in millimeters per day of radial growth and correlated that growth with observed survival from a BCCZ.742 LAM021493 6113 18098 276 Spratt and Spratt The Jour* 1 Thorace and Caidava*.** I.- *rf7 Fig. 2. This scalier diagram compares the corrclalum between the linear radial growih rale of ihe lasicsi growing pulmonary metastasis with the duration of host survival. The duration of survival has been corrected lor the observed rate so that survival is plotted from a common si/c. a greatest chordal diameter of 10 mm. The scatter diagram defines the limits of lethality based on the linear growth rate. Table I. Clinical value of knowing the growih rate of pulmonary neoplasms <metastatic and primaryI Differential diagnosis Prediction of longeviiy Evaluating and planning effective detection programs Planning therapy Evaluating therapy Correlation of gross rates of growih with cellular kinetics Improving understanding of the natural history ol cancers wnh prevention or suppression of neoplasiie growth being the ultimatc objective common point. The common point is a radiographic density with a diameter of 10 mm. (Fig. 2). To calculate the linear radial growth of a cancer, one need only use a standard rate formula. radial growth rale (nun./day! where the diameter at the first measurement Id,) a. subtracted from the diameter of the second measuremem (d*). The difference is divided by 2 lu give ire radial change. This, in turn, is divided by the nunfct . of days elapsing between the first and second observa tion io give the linear growth rate m mm./day. With exponential or geometric growth, the lineal radial rate increases as the sphere e llarges. If the radial rale is expressed as a geometric rale (mm./mm./dau, ihis apparent increase in growth ate wuhinctcwcj size remains constant. Several simple nomograms are needed to displav iu interrelations among litnc. size, tales of growth, aid survival. The first nomogram developed relates tadul growth rale in mm./mm./day and doubling titnow tumors of different radii to the linear radial growth r*i (mm./day) (Fig. 3). This nomogram will permit the crude but ra|l approximation of the exponential growth rate J spherical cancers for which two measurements J diameter or radius are available at two different p>hu in time. Time intervals must be great enough to pctu measurable growth. To use, calculate the linear radii growth in mm./day. Next, add the diameters measure* at points n and h and divide by 2 to obtain the mitlpuis diameter. Divide ihis diameter by 2 again to obtaintk midpoint radius. Select the point on the nontogua where a vertical line from the mm./day intersects at line most closely approximating the midpoint radi<* lixtend a line horizontally to intersect the equtvarf exponential growth scales giving the exponential rau growth of ihe cancer in mm./ntm./day and the s.re giving the doubling tune in days. The relation between the number of doublings s survival for pulmonary cancers and mciasiascv u been published previously.9 A scatter diagram shuai the relation between linear radial growth (mm. vi and host survival is given in Fig. 2. This diagram particularly useful for predicting the minimum. maximum duration of survival of persons luvj( pulmonary metastases of known linear growih rale A second nomogram with added data of clou value is given m Fig 4. This nomogram permit fc direct conversion ol the exponential radial gruwat mm./mm./day) and host survival is given in Fig I This diagram is particularly useful for predicting * muiiimim and maximum duration of survival < persons having pulmonary metastases of known l.io growih rale. A second nomogram w ith added data of de value is given in Fig. 4. This nomogram permit-ft direct conversion of Ihe exponential radial gws 6113 18099 BCC2743 Growth of pulmonary metastases and pulmonary cancers 1 277* 1976 Cl ! r it rapid: rate of| i.'nts i p<>int*J i permit j r radial j ensured^ lidpoinl j tain the i nogram i cts the | radio*r i i valent 1 .1 radial i ie scab Fig. 3. To use this nomogram. s.ikulatc the linear radial growth rale in mm./day as described in the text. Similarly, determine the length <>! the itulms iimlpntm between the two measurements of tumor size. ITc slanted lines are the nomograms for the midpoint radii Protect a vertical extension from the calculated growth rate Imm./dav) to intersect the line most closcls approximating the midpoint radius. From this intersect, extend a line honzontally to obtain an approximation of the doobhne time on the left. By extending the horizontal line to the nght, one can obtain the exponential radial growth in mm./mm^day. Fig. 2.'j ing the , ival of clinical mits the owth in Fig. 4. This nomocram relates die lone ie,|in,cd in das s lor a crow me spherical cancer to double its volume to the exponential radial growth rate in mm ...... . d.i\ Hv mnliiplung the exponential radial rate by 3 and moving the decimal place to the right three places, still an additional parameter is obtained--the net gain in cancer cells per Ihousand existing cancer cells per das LAM021495 BCC2744 6113 18100 2 7 8 Spran and Sprait Th JOwn\j 3 Thoracic and Cardovast-* < mm./mm./day to the time required for the volume to double, but the line of intersection reports (he mean rates for various types of cancers and meiastases that have been observed to grow in the lung.*-" As a basis of comparing the linear radial growth rate of cancers to the linear growth of a non-neoplastic epithelial tissue in an adult, we can look at the data on the growth of William Bean's left thumbnail. Secular trends in growth of my thumbnail arc reported. Various observations, including slowing on the rale of growth with infections, arc recorded. The slowing of the rate of growth has progressed in somewhat irregular phases. This is a phenomenon that most people observe if they care to introspect themselves as they participate in the aging process. The average daily rate of growth has varied I mm 0.123 mm. per day when 1 was 32 to 0.100 nun. when 1 was 61.* Throughout a 30 year period the growth was much faster than that observed for the cancers measured in this study. Cancer tissue may frequently grow more slowly than normal tissues, rather than more rapidly. The difference between cancerous and normal tissue is more a matter of control and organization than of rate. During the period of clinical observation, it might prove useful to be able to quantitate a slowing of growth rate as a parameter of effective therapy. This might be particularly useful with chemotherapy. A slowing of rate might be an indication for continued therapy. An acceleration of rate would certainly merit a consideration of stopping the treatment. In the case of surgical resection of metastases. survival in excess of the maximum survival to be expected for a metastasis with a known growth rate would serve as an Index of therapeutic success. The data in this study all apply to untreated cancers. Short-term betterment of survival in categories of cases of similar size and linear growth rale would be From Bean, W. B.: Arch. Intern. Med. 134. 497. eepvn^ht H04. Amcncan Medical Association. necessary to show the longevity benefit of new typo if therapy. When present, many of these benefits are term. For example, 200 days of comfortable life at uc end stage of cancer is superior to only 100 days of.'* progressive dyspnea produced br the sustained gtu4 ' of cancer. However, such short-term evaluation uoui' be facilitated by a kinetic staging1 system based <; growth rate and mass that is applicable to indivalud*./ Kl l b. R T. NCtS 1 llean. W. B.: Nail Growth: 30 Year, of Obserwu*; Arch IiiIcmi. Med. 134: 407, l74. 2 Hc.iii. W If.: Nail Growlh: A 7 wcnly-Year Study. AiJlI: Inicin Med. Ill: 476, 1063. t Kiis.mia. S . Sprait. J. S,. Jr.. Doncgan. W. L-.Watxrtw. I- K . and Cunningham. C.: The Gross Rales of GmiH Human Mammary Carcinoma. Cancer 30: 594. 1912. 4 Masncmd. \V. V.: On a Law of Growth of Jensen'tSJ, Sarcoma. Am. J. Cancer 16: 8-1, 1932.' . 5 Sprait. J. S., Jr.. Ter-Pogossian. M.. and Long. R. T.L-2 I lie I Vkciion and Growlh ot Intralhoracic Neopla>; l.osser l.mills ol Radiographic Distinction, the Amen*1 leiii Si/e. the Duration, and he Pattern of Gnmd ' Determined by Direct Mensuration of Tumor DiantfA. Prom Random Thoracic Roentgenograms, Arch. Surf in. 2H3. 1963. (i Sprait. J. S . Jr.. Spjut. H.'J.. and Roper. C. L. Hr Frequency Distribution of the Rates of Growlh and* I.climated Duration of Primary Pulmonary Cofunuc*. Cancer 16: 687. 1963. 7 Spintl. J S.. Jr., and Spratt. T. L.: Rates of Grmu* Pulmonary Metastases and Host Survival, Ann. Surg lik 161. 1964. 8 Sprait. J S.. Jr.: The Rales of Growth of Sian* Saicoinas. Cancer 18: 14. 1965, 9 VVcIin. S . Yourkcr. J.. and Sprait. J. S.. Jr.: Rato* Patients ol Growth ol 375 Tumors of Large Intestine *a Rccium Observed Serially by Double Contrast lre* Study iM.ilmo Technique). Ant. J. Roentgenol. R*4j IIki Nucl. Med. 90: 673, 1963. LAM021496 BCCC745 6113 *.. 18101