Maintenance treatment in metastatic breast cancer

Metastatic breast cancer (MBC) occurs in 20–30% of women with breast cancer and is an incurable disease. Treatment is palliative and directed to prolong survival, decrease symptoms and improve patients’ quality of life. For patients with hormone receptor-negative disease or for hormone receptor-positive disease that has become resistant to endocrine therapy, or is progessing rapidly and life threatening, cytotoxic chemotherapy is indicated. However, the optimal duration of chemotherapy treatment for MBC is still a matter of debate. Studies using maintenance chemotherapy regimens standard in the 1990s showed a consistent benefit with a more prolonged time to progression, although an improvement in survival was only demonstrated in one study. Two recent trials with newer cytotoxic agents showed controversial results; whereas one study concluded that the policy of prolonging treatment in chemotherapy-sensitive patients, after aggressive, modern combination chemotherapy, cannot be recommended for women with MBC, the other study showed that maintenance therapy with pegylated liposomal doxorubicin significantly prolonged time to progression in MBC patients after first-line chemotherapy without significant clinical toxicity. Initial data regarding metronomic chemotherapy indicate that continuously low-dose cyclophosphamide and methotrexate is minimally toxic and effective in heavily pretreated breast cancer patients. In daily practice, maintenance chemotherapy is a reasonable strategy that prolongs time to progression in patients with MBC who did not show progression after first-line chemotherapy. However, this benefit should be considered together with toxicities of treatment and the patient’s preference.     

Metformin in early breast cancer: a prospective window of opportunity neoadjuvant study

Taxanes are a standard first-line option for metastatic breast cancer (MBC), but their utility may be limited by primary or acquired resistance. New microtubule-targeting agents have been developed to overcome taxane resistance and provide additional options for improving patient outcomes. This article reviews these alternative microtubule-targeting agents and their potential clinical benefits for MBC patients. Relevant clinical data were compiled through searches within PubMed and congress abstract databases. Ixabepilone, a novel microtubule-stabilizing drug approved by the US Food and Drug Administration (FDA), has proven efficacy across multiple lines of therapy, including patients with taxane-resistant/refractory disease. In phase III trials, ixabepilone plus capecitabine significantly improved progression-free survival compared with capecitabine alone in anthracycline/taxane-pretreated patients. Eribulin has recently been approved by the FDA and by the European Medicines Agency for the treatment of patients with MBC who have received at least two prior chemotherapy regimens for late-stage disease. In a phase III trial, eribulin extended overall survival compared with the physician's treatment choice in heavily pretreated MBC patients. In addition, several investigational microtubule-targeting agents may have therapeutic potential in MBC. The development of new microtubule-targeting agents helps to address the need for additional effective regimens for patients progressing after standard treatment with anthracycline- and taxane-containing regimens.     

晚期乳腺癌紫杉类耐药及其新型抗微管治疗

紫杉类药物原发性或继发性耐药已成为不可避免的棘手难题.伊沙匹隆对经多线治疗包括紫杉类耐药的乳腺癌患者有效.艾日布林用于治疗接受过二线以上化疗的晚期乳腺癌患者.新型抗微管药物有望成为既往接受过紫杉类药物标准化疗的晚期乳腺癌患者的有效方案.     

The Place for Eribulin in the Treatment of Metastatic Breast Cancer

Treatment of metastatic breast cancer (MBC) remains one of the major challenges in cancer care. Chemotherapeutic agents currently approved for the treatment of invasive disease may exhibit initial efficacy; however, the development of resistance to therapy and concerns over tolerability are common and generally limit treatment options available to physicians and patients. Novel chemotherapeutic agents are, therefore, necessary to increase survival, delay disease progression, and improve tolerability. Eribulin mesylate (E7389) is a novel microtubule dynamics inhibitor with a unique mechanism of action that has shown antitumor efficacy and a manageable tolerability profile in clinical trials. Importantly, eribulin is the only single agent to date that has been shown to prolong overall survival in patients with heavily pretreated MBC. This review will discuss eribulin, with focus on the potential it has to address the specific treatment needs of patients with MBC who are refractory to conventional chemotherapies.     

First-Line Treatment of Metastatic Breast Cancer

For many years, tamoxifen was the mainstay of treatment for hormone receptor-positive metastatic breast cancer (MBC). However, in recent years, newer endocrine agents, particularly aromatase inhibitors, have consistently proved their superiority over tamoxifen by improving clinical outcomes. These agents have therefore been incorporated into first-line treatment strategies for endocrine-responsive disease. The chemother-apeutic armamentarium has also been enriched with new agents and combinations that have played a role in improving breast cancer survival in recent decades. However, few chemotherapy clinical trials have claimed a clear survival benefit of one regimen over another. More recently, the development of biologic agents has further widened the spectrum of available therapies. Among these, trastuzumab, a monoclonal antibody against human epidermal growth factor receptor 2 (HER2), has significantly altered the lives of patients with HER2-positive MBC. The transfer of research findings to clinical practice is a delicate process that implies the ability to adequately tailor evidence obtained from well designed clinical trials to the individual patient. This article discusses landmark studies in the treatment of MBC, with emphasis on those treatments used as ‘first-line’ therapy following relapse.     

Targeting angiogenesis in metastatic breast cancer

Angiogenesis has become an important target in the treatment of several solid tumors, including breast cancer. As monotherapy, antiangiogenic agents have demonstrated limited activity in metastatic breast cancer (MBC); therefore, they have generally been developed for use in combination with chemotherapies. Thus far, the experience with antiangiogenic agents for MBC has been mixed. The results from one study assessing addition of the monoclonal antibody bevacizumab to paclitaxel led to approval of bevacizumab for MBC. However, the modest improvement of progression-free survival rates in subsequent MBC studies has led to reappraisal of bevacizumab. Phase III studies have not produced evidence supporting use of the multikinase inhibitor sunitinib alone or in combination with MBC chemotherapy. Experience with sorafenib in a phase IIb program indicates potential when used in select combinations, particularly with capecitabine; however, phase III confirmatory data are needed. Although antiangiogenic therapies combined with chemotherapy have increased progression-free survival rates for patients with MBC, increases in overall survival times have not been observed. Some studies have tried to combine antiangiogenic agents such as bevacizumab and sunitinib or sorafenib, but that approach has been limited because of toxicity concerns. Sequential use of antiangiogenic agents with differing mechanisms of action may be an effective approach. Despite setbacks, angiogenesis will likely remain an important target of treatment for selected patients with MBC.     

Achievements in systemic therapies in the pregenomic era in metastatic breast cancer

Over the last decades, the introduction of several new agents into clinical practice has significantly improved disease control and obtained some, albeit rare, survival benefits in metastatic breast cancer (MBC). Despite these results, the choice of treatment for the majority of patients is still empirically based, since the only two predictive factors with level 1 evidence for clinical use are hormonal receptor status for endocrine therapy and HER-2 status for trastuzumab therapy. Important improvements in the endocrine therapy of both pre- and postmenopausal women with hormone-responsive disease have been achieved. For premenopausal women, ovarian function suppression with luteinizing hormone-releasing hormone analogs combined with tamoxifen has become the standard treatment, although aromatase inhibitors plus ovarian function suppression are under evaluation. In postmenopausal patients, aromatase inhibitors have proved to be superior to standard endocrine therapies in either first- or second-line treatment and a novel antiestrogen compound, fulvestrant, has been introduced in clinical practice. Chemotherapy remains the treatment of choice for hormone unresponsive or resistant patients. Anthracyclines and taxanes have been used either alone or in combination as first-line chemotherapy, but with the more frequent use of these agents in the adjuvant setting, new standards are needed for first-line chemotherapy, and new and more efficacious treatments are required. In the subgroup of patients with tumors that overexpress HER-2, the use of trastuzumab alone or in combination with chemotherapy has modified the natural history of these tumors, even if only about one out of two patients obtains a clinical response. In this review we summarize the main achievements and the currently available treatment options for patients with MBC.     

State of the art therapy for HER2-negative metastatic breast cancer

Metastatic breast cancer (MBC) remains a challenging disease to treat with only a small minority of patients achieving long-term survival. Although great strides have been made in the fight against breast cancer, international consensus to the approach to treat the disease is lacking. Over the past few decades, the introduction of several new agents, including biologically-targeted agents, have impacted disease control as well as survival, albeit modestly. Despite these advances, treatment for the majority of breast cancer remains empirically based, especially in the approach to HER2-negative, endocrine non-sensitive disease. Taxane- and anthracycline-containing regimens continue to be a mainstay of MBC therapy; however, increasing use of these agents in the adjuvant and neoadjuvant settings provides a challenge for the treating oncologist. As such, this review will focus on state of the art therapy for patients with endocrine non-sensitive, HER2-negative MBC, highlighting recent advances offering new treatment paradigms.     

Capecitabine monotherapy: review of studies in first-line HER-2-negative metastatic breast cancer

The goals of treatment for metastatic breast cancer (MBC) are to prolong overall survival (OS) while maximizing quality of life, palliating symptoms, and delaying tumor progression. For many years, anthracyclines and taxanes have been the mainstay of treatment for MBC, but these agents are now commonly administered earlier in the course of the disease. A recent meta-analysis revealed adverse effects on OS and overall response rates in patients with MBC receiving first-line anthracycline-based chemotherapy following relapse on adjuvant chemotherapy. Noncrossresistant cytotoxic agents and combinations that combine high clinical activity and acceptable tolerability while being convenient for patients are therefore needed for the first-line treatment of MBC patients. Capecitabine has substantial antitumor activity in the first-line treatment of patients with MBC in prospective, randomized, phase II/III clinical trials as monotherapy and in combination with biologic and novel agents. First-line capecitabine monotherapy has a favorable safety profile, lacking myelosuppression and alopecia, and does not compromise the administration of further lines of chemotherapy. Capecitabine is suitable for long-term administration without the cumulative toxicity that can limit the prolonged use of other chemotherapy agents. Here, we review the available data on capecitabine as a single agent for first-line treatment of patients with human epidermal growth factor receptor 2-negative MBC.     

Visceral Disease in Patients With Metastatic Breast Cancer: Efficacy and Safety of Treatment With Ixabepilone and Other Chemotherapeutic Agents

Patients with metastatic breast cancer (MBC) have poor prognoses and 5-year survival rates of approximately 20%. The site(s) and degree of metastatic dissemination are among the principal prognostic factors for patients with MBC. Patients with visceral metastases to the liver and/or lung have a very poor prognosis. Although good performance status, restricted disease dissemination, and limited extent of metastatic infiltration are associated with higher responses to chemotherapy, responses are generally short lived, with rapid disease progression after treatment failure. Thus, novel strategies for the management of patients with MBC with visceral disease are urgently needed. We have analyzed outcomes of trials that evaluated various chemotherapeutic agents as monotherapy or in combination with capecitabine in patients with MBC with primary visceral disease involvement. Treatment with microtubule inhibitors such as paclitaxel, docetaxel, and albumin-bound paclitaxel, generally administered in earlier lines of treatment, resulted in comparable responses. Lower response rates (RRs) were reported with other agents such as capecitabine, vinorelbine, and gemcitabine. Adverse events consistent with known toxicities of each agent were observed in the selected trials and related to dose and administration schedule. The epothilone B analogue ixabepilone has demonstrated clinical efficacy and manageable safety in populations of heavily pretreated patients with MBC with high visceral disease burdens to liver and/or lung (61%–86% of patients). Objective RRs ranging from 12% to 57% have been reported for ixabepilone, as monotherapy and in combination with capecitabine, depending on degree of pretreatment. Responses to ixabepilone in patients with visceral metastases were comparable to those observed in overall study patient populations.     

Ixabepilone plus capecitabine for breast cancer patients with an early metastatic relapse after adjuvant chemotherapy: two clinical trials

BackgroundDespite recent advances in treating patients with metastatic breast cancer (MBC), outcomes remain poor. Ixabepilone is a semisynthetic analogue of epothilone B with low susceptibility to multiple mechanisms of tumor-cell resistance. This review examined the results of 2 phase III clinical trials of ixabepilone in patients with drug-resistant or heavily pretreated, locally advanced breast cancer or MBC.Patients and MethodsIn both studies, women with locally advanced breast cancer or MBC pretreated with, or resistant to, taxanes or anthracyclines were randomly assigned to ixabepilone plus capecitabine, or capecitabine alone, until disease progression or unacceptable toxicity occurred.ResultsIxabepilone plus capecitabine significantly prolonged progression-free survival (PFS) compared with capecitabine alone. The median PFS was prolonged by 1.5 months and 1.8 months in the 2 studies (hazard ratio, < 0.8 in both studies; P ≥ .001). These observations remained valid within several patient subsets: those receiving ixabepilone as first-line therapy, those with taxane-resistant disease, and those with particularly poor prognostic features. Ixabepilone plus capecitabine significantly improved overall survival (OS) compared with capecitabine in patients with symptomatic disease (12.3 vs. 9.5 months, respectively; P = .015). Peripheral neuropathy with ixabepilone was generally reversible and was effectively managed by dosage reduction in most patients. Ixabepilone did not exacerbate capecitabine-induced hand-foot syndrome or diarrhea.ConclusionThe results of these 2 large phase III trials suggest that ixabepilone plus capecitabine may improve treatment outcomes for patients with locally advanced breast cancer or MBC resistant to, or heavily pretreated with, taxanes or anthracyclines, even in those with poor prognostic features.     

Considerations in treatment choice for metastatic breast cancer

Chemotherapy treatment choices for metastatic breast cancer (MBC) have become increasingly complex as therapeutic options multiply. In addition, the more frequent use of adjuvant chemotherapy coupled with the introduction of new standard adjuvant therapies has made these choices more difficult. Another issue that remains unsettled is whether to employ combination therapy or to use each agent singly until its value is exhausted. The results of recent studies investigating this issue have revealed higher response rates, time to tumor progression and, in some cases, improved overall survival with doublet therapy. However, there was no planned crossover in these trials and, as such, the absolute benefits of doublet therapy remain undetermined. The future of therapy for MBC appears to be combining effective single-agent chemotherapy with novel biologic agents. For example, compared with paclitaxel alone, therapy comprising paclitaxel plus bevacizumab produced a doubling of response rate and progression-free survival. However, similar data are required for both the first- and the second-line setting, and for other chemotherapy agents, for example, docetaxel and navelbine. Trastuzumab is the treatment of choice for patients with HER2-positive tumors. Its use in combination with chemotherapy, particularly the taxanes, is well established. However, much remains to be learned about biologic agents; for example, trials need to establish whether these therapies should be continued at the time of progression or whether other treatments should be given in their place. A recent study in patients whose disease had progressed after trastuzumab and chemotherapy and who were subsequently given lapatinib, has reported promising outcomes for this agent. When presented with the many options that are now available for the treatment of MBC, we must keep in mind the primary goal of such treatment: palliation of disease with minimal toxicity. Furthermore, a concurrent requirement for prolongation of survival is now commonplace. However, it is clear that there is currently no “gold standard” treatment for MBC, although the future of therapy appears to be the combination of effective single agents with novel biologic therapies. This article is based on an invited lecture delivered at the 15th Annual Meeting of the Japanese Breast Cancer Society, held in Yokohama June 29–30, 2007.     

Cytotoxic drugs for patients with breast cancer in the era of targeted treatment: back to the future?

BackgroundDespite current trend of targeted therapy development, cytotoxic agents are a mainstay of treatment of patients with breast cancer. We reviewed recent advances in cytotoxic therapy for patients with metastatic breast cancer (MBC).Materials and methodsMedline searches were conducted for English language studies using the term ‘MBC’ and ‘cytotoxic drugs’. The data search was restricted to the period 2000–2011.ResultsSeveral novel cytotoxic compounds, all microtubule inhibitors, have been approved for clinical use in MBC: (i) nab-paclitaxel, reported to improve tumour response and decrease hypersensitivity reactions in comparison with other taxanes; (ii) ixabepilone, shown to have clinical benefit in taxane- and anthracycline-resistant disease and (iii) eribulin, shown to improve overall survival in heavily pre-treated patients, when compared with best available standard treatment. Agents, such as larotaxel, vinflunine, trabectidin and formulations, including cationic liposomal paclitaxel or paclitaxel poliglumex, are currently under evaluation in phase II/III trials.ConclusionToxicity and chemotherapy resistance are still major limitations in the treatment of patients with MBC. Further research into new cytotoxic compounds is needed in order to maximise benefit, whilst minimising toxicity.     

Extending survival with chemotherapy in metastatic breast cancer

Metastatic breast cancer (MBC) remains essentially incurable, and goals of therapy include the palliation of symptoms, delay of disease progression, and prolongation of overall survival time without negatively impacting quality of life. Anthracycline and taxane-based therapies have traditionally shown the highest degree of activity in MBC. Though numerous randomized clinical trials have shown improvements in overall response rates, few have found clear survival benefits. In recent years, however, there has been a small but growing series of clinical trials demonstrating modest, but meaningful survival advantages in metastatic disease. A common feature in many of these trials has been the use of a taxane, and more recently, a taxane combined with an antimetabolite. In addition, the development of targeted biologic agents active against MBC, such as trastuzumab and bevacizumab, has demonstrated great potential for enhancing the effects of chemotherapy and producing meaningful survival improvements. The role of the taxanes, antimetabolites, and biologics in extending survival in MBC is discussed.     

Landmark trials in the medical oncology management of metastatic breast cancer

Significant advances in the management of metastatic breast cancer (MBC) have guided more personalized treatment according to disease biology and led to improved survival outcomes and quality of life for patients. In this review, we discuss landmark clinical trials in medical oncology that have shaped the current standard of care for MBC. Combinations of endocrine therapy with cyclin-dependent kinase 4/6 inhibitors have led to substantial improvements in overall survival, thus becoming standard first-line treatment for patients with HR-positive MBC. Inhibition of the PI3K and mTOR pathway is another promising strategy to overcome resistance to endocrine therapy. HER2-targeted therapies have also evolved with the addition of pertuzumab to trastuzumab plus a taxane demonstrating remarkable overall survival advantage in patient with HER2-positive MBC. In second or later line therapies, novel anti-HER2 antibody-drug conjugates and TKIs have durable antitumor activity, survival benefit, and encouraging efficacy in the subgroup of patients with brain metastases. Triple negative breast cancer remains the most challenging subtype due to lack of druggable targets. Immunotherapy for patients with PDL-1 expression on tumor infiltrating immune cells and poly (ADP-ribose) polymerase inhibitors for those with germline BRCA1/2 mutations are the latest approved targeted strategies in this population. Numerous obstacles still exist in treating MBC, especially for patients whose disease develops resistance to available agents. Future research is eagerly awaited to address the optimal sequence or combination of therapies and to identify better biomarkers to guide precision medicine.     

Novel Cytotoxic Agents in the Treatment of Metastatic Breast Cancer

Breast cancer is the most common cancer affecting women worldwide, comprising approximately 20% of all cancers. Although many advances in the treatment of this disease have been made and mortality of early breast cancer improved over the past three decades, metastatic breast cancer (MBC) remains an incurable disease. Cytotoxic chemotherapy continues to play a major role in the treatment of MBC and has been recently combined with biologic agents such as monoclonal antibodies or kinase inhibitors. Over the past decade, several novel cytotoxic chemotherapies have been evaluated in clinical trials. Encouraging results have been observed with novel anti-microtubule agents, with recent US Food and Drug Administration approval of eribulin in 2010. Other novel cytotoxic agents currently under clinical development include novel anti-microtubule drugs, platinum compounds, and anti-angiogenic agents combined with chemotherapy. Here, we review all the major novel cytotoxic agents that have undergone clinical study over the past 5 years for the treatment of MBC.     

Capecitabine in combination with novel targeted agents in the management of metastatic breast cancer: underlying rationale and results of clinical trials

At present there is no established standard of care for metastatic breast cancer and prognosis remains poor, although the use of newer chemotherapeutic regimens has led to modest improvements in survival. Capecitabine, an oral prodrug of 5-fluorouracil, is a promising addition to these approaches, having already shown single-agent activity against metastatic breast cancer. Following a pivotal trial demonstrating that capecitabine confers increased survival when used in combination with docetaxel, it is being investigated intensively in combined regimens using other standard chemotherapeutic agents, as well as with novel molecularly targeted therapies. Among the novel agents, the most intensively studied in combination with capecitabine is trastuzumab. Despite preclinical data suggesting that these two agents might not show additive effects, clinical trials have been very encouraging for both heavily pretreated patients and for patients receiving first-line therapy in the metastatic setting. This work is being further extended in an ongoing trial in the neoadjuvant setting. An initial trial in combination with bevacizumab, enrolling heavily pretreated patients, was less successful, but following the example of the E2100 trial, this combination is being re-examined in less heavily treated patients. In addition, this review discusses ongoing trials with an array of newer molecularly targeted agents. Significant improvement in time to progression has already been demonstrated in the combination of lapatinib and capecitabine compared with capecitabine monotherapy; for the most part, however, these trials are still in early stages.     

Beyond cytotoxic chemotherapy for the first-line treatment of HER2-negative, hormone-insensitive metastatic breast cancer: current status and future opportunities

As reflected in its varied clinical behavior, appearances under the light microscope, and differential patterns of gene expression, metastatic breast cancer (MBC) is a heterogeneous disease. Systemic treatment decisions are guided by specific tumor characteristics and individual patient factors. For patients with hormone receptor (HR)-negative MBC and for those whose HR-positive disease has become refractory to hormonal therapies, cytotoxic chemotherapy has been the mainstay of systemic treatment. For hormone-insensitive, HER2-positive MBCs, the addition of trastuzumab to chemotherapy has resulted in improved outcomes. Hormone-insensitive MBC lacking HER2 overexpression includes the subset of patients with estrogen receptor/ progesterone receptor/HER2-negative (so-called triple-negative) disease, which represents a significant minority of all breast cancers. Therapeutic options for such patients are limited by the lack of specific targeted approaches, and this heterogeneous group will be considered collectively as well as separately in this overview of existing and emerging treatment strategies. Conventional cytotoxic chemotherapy, alone or in combination, has been the standard first-line treatment for patients with MBC not amenable to antiestrogen or trastuzumab therapy. The recent evaluation of new targeted therapies in combination with cytotoxic agents has created a new type of combination regimen. Agents targeting angiogenesis, the epidermal growth factor receptor, and various signal transduction pathways have been combined with chemotherapy and possess biologic activity in MBC. As these combinations are being investigated, parallel correlative studies aimed at enriching the population who will benefit most are under way.     

Advances in the management of metastatic breast cancer: options beyond first-line chemotherapy

This article provides an overview of recent advances in chemotherapy that may be used for the treatment of patients with locally advanced or metastatic breast cancer (MBC). Key phase ii and iii trial data for eribulin mesylate, ixabepilone, and nab-paclitaxel, published since 2006, are discussed on the basis of recency, depth, and quality.Eribulin mesylate is the first monotherapy to significantly increase overall survival in patients with pretreated MBC, but nab-paclitaxel offers a novel and safer mode of delivery in comparison with standard taxanes. By contrast, the use of ixabepilone will be limited for now, until the associated neurotoxicity can be better managed. Alongside a brief overview of the other major chemotherapies currently in use, we have aimed to provide a Canadian context for how these novel agents may be integrated into clinical practice.     

Evolving nonendocrine therapeutic options for metastatic breast cancer: how adjuvant chemotherapy influences treatment

Patients with metastatic breast cancer (MBC) represent a very heterogeneous population and several factors are important for therapeutic decision: patients' characteristics including age, comorbidities, performance status, tumor biological profile, site and extension of metastatic spread, previous adjuvant therapies, and disease-free interval. New cytotoxic agents, new endocrine agents, and targeted therapies are becoming the new mainstay of adjuvant treatment. The growing understanding of the biology of breast cancer cells has led to the identification of key molecular points that represent possible targets for target-specific agents. Trastuzumab, the monoclonal antibody against the HER2 receptor, represents the standard treatment of high-risk early-stage breast cancer overexpressing HER2. With increasing use of very active drugs in the adjuvant setting, there is a greater need for effective therapy at the time of relapse. In endocrine resistant disease, a treatment-free interval > 12 months after adjuvant chemotherapy has been shown to be an important factor for drug sensitivity. If the tumor has been exposed to an anthracycline and a taxane in adjuvant setting and the treatment-free interval is > 12 months, the rechallenge with the same agents might be an option. If the treatment-free interval is < 12 months, it is preferable to use a different agent. Capecitabine, gemcitabine, and vinorelbine have demonstrated substantial activity in MBC. Novel cytotoxic agents including epothilones and vinflunine are currently in clinical development for taxane-resistant disease. Lapatinib, a new target agent that simultaneously inhibits both HER2 and epidermal growth factor receptor tyrosine kinases has been shown to be active in trastuzumab-resistant MBC. Moreover, several new agents targeting HER2 are currently under clinical development. There are no data on rechallenge with trastuzumab in patients who had received this agent as adjuvant treatment and relapsed after a long treatment-free interval, and this issue is a new area of research.