Introduction

Neoplasia is the result of complex intracellular metabolic disturbances leading to errors in cytoplasmic/nuclear signaling [1]. Carcinogenesis includes the development of different malignant cell clones that evolve in time following patterns previously described in the evolutionary ecology [2]. Spatial and temporal domains in malignant tumors are now well recognized as main obstacles for the development of efficient therapies [3]. Four different models of tumor evolution have been very recently described (linear, branched, neutral, and punctuated) [4]. Fitness, an ecological term referring to the average contribution of a genotype to future generations, is a crucial issue in the development of this diversity. As a result, unique forms of intratumor heterogeneity (ITH) do develop. ITH is a generalized event in tumor evolution with important clinical implications. It has been associated to a poorer survival rate in a recent study of 3300 neoplasms of nine different tumor types [5].

Although displaying a dynamic behavior, tumors are frequently perceived by pathologists as static processes associated to the time where they are surgically removed from patients. In such a way, tumors appear under the microscope as mere fixed snapshots ready to be studied with more or less sophisticated tools with the aim of rendering a pathology report. Some tumors can be analyzed in toto by the pathologist (the ideal situation for thorough tumor knowledge). However, many tumors are too large and therefore making it unfeasible to carry out total sampling. In this particular setting, pathologists select samples for histological and molecular studies following internationally accepted protocols from referential books [6]. Previous studies, however, have demonstrated that currently accepted protocols of tumor sampling are insufficient for a reliable ITH detection and question their usefulness in daily practice [7,8,9,10,11]. Current protocols of tumor sampling give only a partial view of the total tumor complexity, missing in some cases relevant information for the patient, as recently acknowledged [12].

To overcome this problem, we have very recently developed a new sampling method (Fig. 1), the so-called multisite tumor sampling (MSTS). We have shown that MSTS outperforms routine sampling protocols (RP) in detecting ITH at no extra costs [13,14,15,16,17]. Here, we extend previous work by presenting an in silico study aiming to evaluate the performance of MSTS in detecting temporal (at early and late stages) ITH in all the previously described models of tumor evolution.

Fig. 1
figure 1

Slice of a clear cell renal cell carcinoma showing both sampling protocols. Multisite tumor sampling (MSTS) (upper figure) obtains 32 small fragments whereas routine sampling (RS) (lower figure) obtains 4 large fragments. Both protocols make use of four cassettes to analyze the tumor slice

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Material and methods

Multisite tumor sampling strategy

We test the four conceptual models (linear, branched, neutral, and punctuated) of tumor evolution [4] (Fig. 2) at different time points of the tumor progression, addressing at each time point the performances of MSTS and RP in detecting ITH. We have developed very simple computational modeling techniques for each specific time evolution tumor class. The modeling makes use of mathematical rules and constraints that imitate the time evolution of real tumors (detailed explanations of the model are provided in figures and supplementary material, as we believe that visual support helps to understand the specific explanations). The modeling approach allows us to repeatedly evaluate the performance of ITH detection along time for MSTS and RP. Although RP is adapted to every tumor type and topography [6], it always consists of selecting a large sample of tumor per centimeter of tumor diameter (meaning that a 6 cm in diameter tumor will select 6 samples to be included in six cassettes). By contrast, MSTS [13] consists in selecting many small tissue samples obtained from distant tumor areas and including them in groups of six to eight in the same number of cassettes (meaning that a 6 cm in diameter tumor will select 36 to 48 samples to be included in six cassettes).

Fig. 2
figure 2

Schematic view of linear (a), branched (b), neutral (c), and punctuated (d) models of temporal tumor evolution. A simulation approach of the four tumor evolution models allow to compare the performances of ITH detection at both early and late stages of the tumor evolution

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Ethical reasons in clinical practice impede an extensive regional analysis of the same tumor in different points of its temporal evolution (active surveillance is an option only in some cases). For these reasons, tumor evolution is traced by applying phylogenetic inferences [4]. The mutational history of tumors can in this way be partially deciphered at the precise time point of surgical removal. However, this methodology is imperfect because those clones that disappear during tumor progression are undetectable.

Based on this phylogenetical approach, four different models of tumor evolution have been defined very recently: linear, branched, neutral, and punctuated [4]. These models are not tumor-specific; in fact the same tumor, i.e., hepatocellular carcinoma [18] and colorectal adenocarcinoma [19,20,21,22], may pursue different patterns of evolution in different patients.

The four classes of tumor evolution

Linear evolution

This is a step-wise process made on successive driver mutations in which every clone that is newly created displaces the precedent one. For example, some colonic adenocarcinomas follow this tumor class, as at each following time-step generate a unique and different clone which is usually more aggressive than the previous one [19]. This pattern can be considered as the paragon of the Darwinian evolution, as a single clone dominates and replace the others as a result of its advantageous fitness. As a result, these neoplasms display a single taxon (understood as the unit of developed heterogeneity at the top of the phylogenetical tree).

Branched evolution

This tumor class is the result of the evolution of different clones originated from a common ancestor. Since multiple different clones evolve together in time, the final result leads to both time-dependent changing patterns and spatial regionalization of the tumor. ITH displays here a stochastic distribution across the whole tumor mass [23]. Subclonal lineages develop subsequently giving rise to different generations and also to a moderate-to-high number of taxa. Clones and subclones in branched tumor evolution may either compete or cooperate. On one hand, different clones do compete for resources and space following Lotka-Volterra equations [24], a promising research line for potential future therapeutic targeting [25, 26]. On the other, clones with higher fitness may decide not to eradicate the remaining, a fact that has promoted a specific inter-clonal cooperation proposal [27]. The branched model of tumor evolution has been extensively studied in several neoplasms, including carcinomas of the breast [28] and kidney [29]. In these neoplasms, truncal mutations are represented by the common trunk in the tumor evolution tree. The length of these trunks is directly related to the degree of divergence between the different branching subclones. Some truncal mutations are tumor type-specific, i.e., VHL gene mutations and clear cell renal cell carcinoma [30].

Neutral evolution

This tumor class represents an extreme example of a branched pattern. In this particular context, clone competition does not take place along the whole tumor temporal evolution, resulting in an increasingly atomized ITH distribution as time evolves. In contrast, ITH is the result of the sum of all the clones generated along the tumor life [4] and where taxa are very numerous in neutral evolution. This is a genuine model of non-Darwinian tumor evolution (in which clonal selection is not present) and that has been described more frequently in some cancers arising in the stomach, lung, urinary bladder, cervix, and colon [22]. On the other hand, glioblastomas, melanomas, and tumors of the kidney, pancreas, and thyroid characteristically do not follow a neutral evolution [22].

Punctuated evolution

This tumor class is somehow different to the rest as the genomic aberrations accumulate in the tumor at very early stages of progression and where ITH is much higher at the beginning of the carcinogenetic process than at the end, because one (or at most very few) dominant clones with high fitness appear very early in the tumor evolution, and after, they expand progressively throughout the entire neoplasm. As a result, punctuated evolution does not contain intermediate taxa and the phylogenetic tree is composed by a single root with one dominant clone. This pattern is representative of a gradual Darwinian tumor evolution and has been called the “Big Bang” model of tumor evolution [21]. Some colorectal, prostate, and ovarian tumors, among others, may display punctuated evolution [4].

In silico modeling

We extend previous modeling work [13] to the situation of ITH patterns evolving in time. At each time point (representing one snapshot in the time tumor evolution) the total tumor shape was modeled with a 2D square. For the modeling of the temporal evolution, we started in a common square and designed a specific growing pattern, modeled by simple rules and constraints, allowing us to imitate the real characteristics of the temporal evolution for each tumor evolution class (linear, branched, neutral, and punctuated). Next, after evolving these dynamics T time points, we evaluated the performances of MSTS and RP in detecting ITH for each of the time points.

We repeated N times (and separately) the two different strategies MSTS and RP for each time point and tumor evolution class. We also simulated M times the same tumor dynamics, each one starting at a different initial condition and mimicking to be a different tumor. For each time point and tumor evolution model, we calculated the number of successfully detected ITH sites for each of the C ITH types (similar to our previous approach in [13] we introduced different types of ITH, representing as C different values). The final performance results at each time point were averaged across the N repetitions and also across the M different tumors of the same tumor evolution model.

The four different tumor evolution classes were simulated in the following way:

Linear evolution: We first set up a specific Poisson distribution (modeling the fact that the more the time passes, the higher the probability for a new ITH to appear) for the initial spatial organization of ITH, ensuring the appearance of different predefined ITH sites. Next, as time evolves, the modeling strategy was based on keeping each ITH type growing with a uniform rate from the square center until the border. The only constraint was not having more than two types of ITH per tumor site at the same time-point.

Branched evolution: We first fixed a low appearance ratio of ITH, chosen randomly between all possible ITH types and starting randomly from any point of the square. Next, growing rates for ITH were proportionally decreasing as time evolved, thus, making ITH growing faster in the early stages and slower in the late ones. A non-rivalry growing constraint was defined to avoid two ITH types competing for space.

Neutral evolution: We first fixed a high appearance ratio by choosing randomly between all possible ITH types and starting randomly from any point of the square. The growing possibilities were the same for all ITH types at any time, but those ITH at the early stages could grow bigger than those starting at the late stages. ITH could compete for space before reaching their growing limit.

Punctuated evolution: Every three steps, a new ITH (with no repetition) was started from the square center while previous ITH sites were allowed to expand (with a uniform growing rate) until the first ITH reached the square border, stopping the growing of the rest.

Results

Similar to the strategy followed in [13], simulations were performed with the following parameters: L = 99 (side of 2D square), C = 4 (ITH types), N = 500 (repetitions number for the two MSTS and RP strategies), M = 15 (number of simulated tumors), T = 100 time points, d = 16 (for RP the block size; for MSTS 16 independent blocks). The ITH, performance, equal to the number of detected ITH sites divided by the total number of ITH sites × 100, for each tumor sampling strategy (MSTS and RP) was calculated and averaged at each time point over the N repetitions and M different tumors.

The ITH performance measured as the percentage of ITH detection per each time point for both different protocols and each tumor evolution class are shown in Fig. 3. For visualization purposes, only one type of ITH is shown. In all the cases, the MSTS sampling strategy outperforms RP. It is also important to note that the performance variability (i.e., standard deviation) of the MSTS was in general smaller for all time points and tumor evolution models in comparison to the variability achieved by RP, making the results of ITH detection not only more accurate but also more efficient (here, efficiency measured as the inverse of the variability). Figure 3 also illustrates the performances of MSTS and RP at two specific time points, early (t = 10) and late (t = 90) evolution stages. A dynamic view of the whole process is shown in the Supplemental file 1.

Fig. 3
figure 3

Results from the computational modeling for the temporal tumor evolution showing that MSTS performs better than RP. Four different classes of tumor evolution have been modeled, from top to bottom: linear, branched, neutral, and punctuated. At the first two columns, we plotted snapshots of the temporal tumor evolution at two stages: early (time = 10) and late (time = 90), represented also in Fig. 2. At the right column, we plotted the percentage of ITH detection (mean ± SD) as a function of tumor evolution time for MSTS (red) and RP (blue). Here, time is given in arbitrary units, although we wrote “months” just an indicative scale that might correspond to reality, but absolutely no time scale has been introduced in the modeling approach. We plotted only one ITH type for visualization clarity, but four classes of ITH types have been modeled. SD was calculated across N different repetitions of the same strategy and across M different tumors. Notice that, not only the mean of ITH detection was drastically enhanced by MSTS, but also the SD was substantially smaller, meaning that MSTS is more efficient (less variable) as compared to RP. Exact values for all simulated parameters are given in the text

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For the class of linear tumor evolution, we show that MSTS detects ITH earlier and faster than RP, while MSTS performance decreases later and slower when a different ITH type overwrites a previous one. Although performance differences along tumor evolution are small, the MSTS strategy outperforms RP in some of the time points.

Branched evolution is the clearest example of MSTS superiority, because the RP strategy breaks down when the tumor evolution finds different ITH types and the appearance rate is not high.

For neutral evolution, the performance of MSTS is also higher than RP. Although MSTS is significantly better than RP in all the stages of tumor evolution, MSTS performance is considerably higher in early stages.

Finally, for punctuated tumor evolution, MSTS works much better for late stages of the tumor evolution. MSTS and RP performances in early stages show small differences.

Differences in performance between MSTS and RP at early and late stages are shown in Fig. 4.

Fig. 4
figure 4

Differences in ITH detection between MSTS (red) and RP (blue) for four different ITH types (ITH1-ITH4) and at two temporal tumor evolution stages: early (t = 10) and late (t = 90). MSTS performed slightly better than RP for linear evolution and much better for the rest (branched, neutral and punctuated). ***p value <0.001 after t test comparison

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Discussion

A malignant tumor is the result of the interaction between billions of cells, each one following signaling pathways that are largely unknown. As a result of these interactions different clones with specific genomic and metabolomic profiles constantly appear and disappear along the natural history of neoplasms [31]. However, pathologists have a biased perception of this reality because they analyze tumors at one precise temporal snapshot of their evolution. Previous events in the tumor, although important for the patient, remain unknown because they are not shown in the biopsy. In other words, pathologists usually have not in mind the temporal dimension of a given tumor when making its diagnosis. However, as mentioned in this manuscript, tumors do evolve in a continuous fashion and sometimes they do in very different ways. Even more important, totally different tumors may have identical spatial representation at one time point of their evolution, as acknowledged recently [3].

Although the practical consequences of ITH have been recently highlighted [12, 32], the adequacy of sampling protocols to current needs remains suboptimal right now and is still pending for modern pathology. However, the acknowledgement of this limitation is not new [12, 33, 34].

Recent data obtained first in silico [13] and later from a clinical validation [15], have shown the practical advantages of performing MSTS in detecting ITH in large tumors as compared to RP. The fact that many areas of the tumor are sampled with small tissue cubes fitting in the same number of cassettes increases diagnostic efficiency at no extra costs in Pathology Labs [13, 14]. We also have demonstrated that MSTS strategy must be adapted for an optimal performance to the anatomical peculiarities of the sites where the tumors arise [17], such it happens in hollow viscera (gastrointestinal tract, urinary bladder, etc). Because these tumors have natural barriers (muscularis propria) impeding to expand as 3D-spheroids, they tend to grow as plaque-like masses. For this reason, such tumors are better sampled by selecting tumor tissue bars involving the full thickness of the tumor together with the viscera wall [17] (Fig. 5). In summary, we conclude that MSTS outperforms RP in discovering ITH in any large tumor placed at any site and in which total sampling is not affordable. This body of information [13,14,15,16,17] should help pathologists to detect ITH more efficiently, a point that is being widely claimed by oncologists [35].

Fig. 5
figure 5

MSTS strategy in a colonic adenocarcinoma. Tumor tissue bars involve the full thickness of the bowel wall ensuring ITH detection

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Modern oncology in clinical practice has two main challenges when facing ITH detection: First, the tumor representativeness of small diagnostic biopsies: does less than 1% of the tumor (as it happens in reality many times) represent the entire tumor? Second, the sampling reliability in large neoplasms: how large and in what manner the tumor sampling must be performed? Although the answer to the first question is obviously no, nobody has found an efficient alternative so far, so this question remains open for discussion. With respect to the second question, the answer remains largely unknown, although some authors have pointed out to these questions very recently. Bettoni et al. [11] asked if single small biopsies were representative of the tumor entirety in rectal cancers. Similar problems of supposedly incomplete tumor representativeness have been detected in small specimens from prostate [7] and ovarian [9] cancers. In this context, liquid biopsy appears as a promising tool in the next future but performances in detecting ITH right now are very limited and restricted to only some types of tumors [36,37,38].

The present study focuses specifically on surgical specimens and on the impact of temporal tumor changes in the performance of two sampling strategies: MSTS and RP. Early detection of tumors is a pillar of modern medicine to improve patient survival. The implementation of different prevention campaigns leads to discover more and more tumors at early developmental stages. Some aggressive mutations can be present in a tumor at very early stages (for example, neoplasms following punctuated evolution). For this reason, pathologists must also decide the best tumor sampling strategy in these early developmental stages.

To shed some light into this problem, we have compared here the performances of MSTS and RP in detecting ITH at both early and late stages of tumor evolution and MSTS outperformed RP in all the cases. Not only the MSTS performance in detecting ITH is higher, but its efficiency as well, as MSTS provides a smaller detection variance. Our results show that the MSTS strategy is better as compared to RP regardless the moment the tumor is sampled.