Efficacy and safety of oral pentoxifylline on semen parameters and reproductive hormones in idiopathic male infertility: a systematic review and meta-analysis

Introduction

According to the World Health Organization (WHO), approximately 17.5% [95% confidence interval (CI): 15.0–20.3%] of individuals will experience infertility during their lifetime (1). Male factors account for nearly 50% of infertility cases, with male-specific causes contributing to 20–30% of all infertility cases (2,3). Sperm abnormalities—including oligozoospermia, asthenozoospermia, and teratozoospermia—represent major etiologies of male infertility (4,5). Current treatment options for impaired semen quality remain limited, primarily comprising lifestyle modification, pharmacological interventions, and surgical approaches (6). Assisted reproductive technologies (ART), such as intrauterine insemination, in vitro fertilization, and intracytoplasmic sperm injection are effective for some idiopathic cases, but these methods are often costly, invasive, or associated with adverse effects, and their efficacy is inconsistent in patients with idiopathic or unexplained semen abnormalities.

Empirical pharmacological therapies remain the most widely used and readily accepted treatment strategy, including antioxidants, prebiotic and probiotic supplements, and hormonal agents (6). Pentoxifylline (PTX), a methylxanthine derivative with hemorheological properties, was initially introduced for the treatment of intermittent claudication and later applied in peripheral vascular diseases. Its potential utility in male infertility has been investigated for decades. Early observational studies and preliminary randomized controlled trials (RCTs) suggested beneficial effects on sperm motility, leading to its use in ART laboratories to select viable sperm from immotile samples (7-9). However, PTX has also been shown to prematurely trigger the acrosome reaction and exert toxic effects on oocytes and early embryos (10).

These in vitro findings provide a strong rationale for exploring oral PTX as a systemic therapy. Pharmacokinetically, orally administered PTX is distributed to the testes, epididymis, and seminal plasma, establishing the physiological basis for the in vivo modulation of spermatogenesis and sperm maturation. Recent evidence from animal models demonstrates that systemically administered bioactive compounds with potent antioxidant and anti-inflammatory properties, such as Astragalus and curcumin, effectively ameliorate testicular damage and restore reproductive capacity (11-13). Given that PTX is a well-characterized hemorheological agent sharing comparable immunomodulatory and radical-scavenging profiles, it likely mitigates idiopathic male infertility through analogous multi-target pharmacological pathways.

Mechanistically, the potential therapeutic efficacy of systemic PTX on male infertility is hypothesized to be primarily mediated by the following pathways.

• Phosphodiesterase inhibition: PTX prevents the degradation of cyclic adenosine monophosphate (cAMP), leading to its intracellular accumulation. This elevation activates protein kinase A and triggers the tyrosine phosphorylation of flagellar proteins, fundamentally driving sperm capacitation, hyperactivation, and increased flagellar beat frequency (14).
• Mitigation of oxidative stress: excessive reactive oxygen species in seminal plasma induce lipid peroxidation of the sperm membrane and DNA fragmentation (15). As a potent free-radical scavenger (16), PTX neutralizes reactive oxygen species (ROS) to preserve membrane integrity and genomic stability, both of which are critical for normal morphology and fertilization success (17,18).
• Microcirculatory optimization: by improving erythrocyte deformability and reducing blood viscosity, PTX enhances testicular and epididymal perfusion (19). This hemodynamic optimization ensures a nutrient- and oxygen-rich microenvironment essential for efficient spermatogenesis and optimal Sertoli and Leydig cell function.
• Immunomodulation: PTX downregulates pro-inflammatory cytokines [e.g., tumor necrosis factor alpha (TNF-α)] and suppresses subclinical inflammation within the reproductive tract. This regulatory effect preserves the integrity of the blood-testis barrier and minimizes immune-mediated damage to developing spermatozoa (20,21).

Despite these theoretical and experimental rationales, the clinical evidence for oral PTX in male infertility remains inconclusive. Previous randomized trials have been limited by small sample sizes, heterogeneous methodologies, and insufficient data on critical outcomes such as pregnancy and live birth rates. Furthermore, comprehensive safety evaluations are lacking. A systematic review and meta-analysis of RCTs is therefore warranted to clarify the efficacy and safety profile of PTX in this population.

The present study aims to systematically review and meta-analyze randomized trials to evaluate the efficacy of PTX supplementation compared with placebo in improving semen parameters (sperm motility, sperm concentration, and sperm morphology) and reproductive hormones in infertile men with abnormal semen analyses. We present this article in accordance with the PRISMA reporting checklist (available at https://tau.amegroups.com/article/view/10.21037/tau-2025-1-999/rc) (22).

Methods

Search strategy

The study protocol was prospectively registered in PROSPERO (CRD420251102594). The search strategy was developed according to the Population, Intervention, Comparator, Outcomes, and Study design framework. A comprehensive search was conducted in PubMed, Embase, Web of Science, and the Cochrane Central Register of Controlled Trials, covering all records from inception to July 19, 2025. Search terms included both Medical Subject Headings (MeSH) and free-text keywords: ‘pentoxifylline’, ’spermatozoa’, ’semen’, ’sperm’, ‘male subfertility’, ‘asthenozoospermia’, ‘oligozoospermia’, ‘teratozoospermia’, ‘OAT’, ’spermatogenesis’, ’seminal plasma’, and ‘RCT’. Reference lists of included studies and relevant reviews were also manually screened.

Two reviewers (W.Z. and Y.D.) independently screened titles and abstracts, and potentially eligible articles were assessed in full. Disagreements were resolved by consensus with a third reviewer (H.W.). Only English-language publications were included. The full search strategy is available in Appendix 1.

Inclusion and exclusion criteria

Studies were included if they met the following criteria: (I) RCT design; (II) participants were infertile men aged 23–50 years with infertility lasting ≥1 year, with female partners confirmed fertile; (III) intervention was oral PTX monotherapy; (IV) at least one outcome of interest (semen parameters, reproductive hormones, or pregnancy outcomes) was reported; and (V) publication in English.

Exclusion criteria were: (I) non-original articles (reviews, editorials, comments, case reports, protocols, animal studies); (II) combined therapies involving PTX; (III) studies lacking relevant clinical outcome data; (IV) duplicate or overlapping cohorts; and (V) inaccessible full text.

Endpoints

The primary outcomes were semen parameters: sperm concentration (10⁶/mL), total motility (%), normal morphology (%), and ejaculate volume (mL), which are established indicators of male fertility potential.

The secondary outcomes were reproductive hormone levels: testosterone (ng/mL), follicle-stimulating hormone (FSH, IU/L), and luteinizing hormone (LH, IU/L), reflecting endocrine regulation of spermatogenesis.

Mean values and standard deviations (SDs) were extracted for quantitative synthesis.

Data extraction

For the studies ultimately included, two reviewers (W.Z. and D.L.) independently extracted data using a standardized data extraction form. The extracted data mainly included the following information: first author, publication date, study period, study design, age, smoking, body mass index (BMI), infertility duration, intervention, treatment course, semen parameters and reproductive hormones.

Quality assessment

The Cochrane Risk of Bias 2 (RoB-2) tool was used to assess the risk of bias in included RCTs across five domains: selection, performance, detection, attrition, and reporting biases (23). Each study was rated as low, some concerns, or high risk of bias. Two reviewers (W.Z. and Y.D.) independently assessed risk of bias, with discrepancies resolved through discussion with a third reviewer (H.W.).

Statistical analysis

All analyses were performed using R (version 4.4.2) with the meta and metafor packages. For continuous outcomes, mean difference (MD) with 95% CIs was calculated. If studies reported medians and ranges, these were converted to means and SDs using established methods (24-26).

Heterogeneity was assessed using Cochran’s Q and the I² statistic. A fixed-effects model was applied when I²≤50%; otherwise, a random-effects model was used. Subgroup analyses were performed by treatment duration. Sensitivity analyses were conducted using leave-one-out methods. Publication bias was evaluated using Egger’s test and funnel plots. A two-sided P<0.05 was considered statistically significant.

Results

Literature search

The initial database search yielded 574 records. After removal of duplicates and screening of titles and abstracts, 15 studies were retrieved for full-text assessment. Ultimately, five RCTs met the eligibility criteria and were included in the meta-analysis (Figure 1).

Figure 1 PRISMA 2020 flow diagram. PRISMA, Preferred Reporting Items for Systematic Reviews and Meta-Analyses.

Study characteristics

The five included RCTs were published between 1983 and 2023, comprising a total of 455 infertile men. Participants were aged 20–48 years with infertility lasting over one year. All five studies were randomized, placebo-controlled trials administering oral PTX at 400 mg per dose, given either twice (21,27,28) or three times daily (24,29). Treatment duration ranged from 3 to 6 months, with one trial reporting a 24-week regimen, ensuring coverage of at least one spermatogenic cycle. Prior evidence indicates that PTX 600–1,200 mg/day for ≥6 weeks is sufficient to improve semen quality, suggesting that variations in treatment schedules were within an acceptable range (17,30). Reported outcomes included semen parameters (volume, concentration, motility, morphology) and reproductive hormones (testosterone, LH, FSH). The detailed characteristics and baseline data of the included studies are summarized in Table 1.

Meta-analysis results of all studies

Sperm concentration

Five studies reported data on sperm concentration. Overall pooled analysis showed no significant difference in sperm concentration with PTX supplementation compared to placebo (MD =9.16, 95% CI: −2.30 to 20.62; I²=95.2%; Figure 2A). Since I²>50%, a random-effects model was used. In the subgroup analysis, at 3 months, PTX supplementation was associated with a significant improvement compared with placebo (MD =16.31, 95% CI: 1.55–31.07; I² =95.9%; Figure 2A). However, this effect was not sustained at 6 months (MD =−0.23, 95% CI: −14.34 to 13.88; I² =95.9%; Figure 2A).

Figure 2 Effects of PTX on semen parameters. (A) Sperm concentration. (B) Sperm morphology. (C) Sperm motility. CI, confidence intervals; df, degree of freedom; MD, mean difference; mo, month; PTX, pentoxifylline; SD, standard deviation.

Sperm morphology

Four studies provided data on sperm morphology. Pooled analysis indicated that PTX significantly improved the percentage of morphologically normal sperm compared with placebo (MD =3.86, 95% CI: 1.01–6.71; I²=97.7%; Figure 2B). Due to the high heterogeneity (I²>50%), a random-effects model was employed. Subgroup analysis revealed a significant difference in the efficacy of PTX supplementation between the 3- and 6-month treatment groups (P<0.001).

Sperm motility

Three studies reported sperm motility. Overall pooled results demonstrated that PTX significantly increased total motility (MD =10.44, 95% CI: 3.57–17.30; I²=99%; Figure 2C), though heterogeneity was substantial. Therefore, a random-effects model was applied (I²>50%). Subgroup analysis showed a more consistent effect at 6 months (MD =10.29, 95% CI: 9.55–11.03; I²=0%; Figure 2C).

Semen volume

Only two included studies reported data on ejaculate volume. Given the scarcity of available data and the potential for methodological heterogeneity, these outcomes were considered unsuitable for quantitative pooling, and a descriptive synthesis was performed instead. The reported results across the two trials were highly inconsistent. Consequently, the current evidence remains insufficient to demonstrate whether oral PTX supplementation exerts any significant effect on ejaculate volume.

Serum hormones

Three studies reported serum reproductive hormone levels. PTX supplementation did not significantly alter testosterone (MD =0.22, 95% CI: −0.23 to 0.67; I²=28.6%; Figure 3A) or FSH levels (MD =−1.51, 95% CI: −4.16 to 1.14; I²=93.5%; Figure 3B). However, a modest but statistically significant reduction in LH was observed (MD =−0.97, 95% CI: −1.45 to −0.49; I²=0%; Figure 3C).

Figure 3 Effects of PTX on reproductive hormones. (A) Testosterone. (B) Follicle-stimulating hormone. (C) Luteinizing hormone. CI, confidence intervals; df, degree of freedom; MD, mean difference; mo, month; PTX, pentoxifylline; SD, standard deviation.

Sensitivity analysis

A leave-one-out sensitivity analysis was performed to evaluate the stability of the pooled results (Figure S1). Repeating the meta-analysis by sequentially excluding each individual study demonstrated that the direction of the pooled effect remained consistent. However, this procedure did not materially reduce the substantial statistical heterogeneity. The persistence of high heterogeneity indicates that the variance is not driven by a single outlier, but rather reflects the inherent clinical and methodological diversity across the included trials. Consequently, while the overall trend of the effect is maintained, the pooled estimates should be interpreted with caution.

Furthermore, recognizing the uncertainty introduced by converting medians and ranges to means and SDs, an additional sensitivity analysis was conducted by temporarily excluding the studies that required such mathematical transformations. This exclusion did not significantly alter the primary outcomes, suggesting that the data conversion method did not unduly bias the final statistical trends.

Risk of bias assessment

The risk of bias assessment is summarized in Figure 4, alongside an expanded textual evaluation of the specific RoB-2 domains. Overall, three trials demonstrated a low risk of bias, one presented some concerns, and one had a high risk of bias. Regarding publication bias, Egger’s test was performed for each outcome (Figure S2), and all P values were >0.05. However, funnel plots and Egger’s tests lack adequate statistical power in meta-analyses comprising fewer than 10 studies. Therefore, although Egger’s tests yielded P>0.05 across outcomes, we cannot reliably rule out the possibility of publication bias, which remains a potential unmeasured confounding factor.

Figure 4 Risk of bias in randomized trials assessment.

Subgroup analysis

In an exploratory subgroup analysis, treatment duration was associated only with improvements in normal sperm morphology; no similar time-dependent differences were observed for the other endpoints. Because this evaluation relies on a small number of studies, the data are sparse and yield wide CIs. Consequently, these trends remain preliminary. They are currently insufficient to establish an optimal treatment timeline or to support any shifts in routine clinical practice.

Safety outcomes

Adverse events were reported in two studies. PTX was generally well tolerated, with the most common adverse effects being mild gastrointestinal symptoms (e.g., nausea, abdominal discomfort). However, since PTX acts as a peripheral vasodilator and may induce hypotension, blood pressure monitoring during treatment should be considered (21). No serious adverse events were documented, and treatment discontinuation rates did not differ significantly between groups.

Discussion

Male infertility is a widespread health problem, responsible for nearly half of infertility cases worldwide. Beyond the biological inability to conceive, its impact extends to psychological distress, reduced quality of life, strained partner relationships, and considerable healthcare costs. With infertility rates rising in many regions, the development of effective and accessible treatments remains an urgent clinical need.

This systematic review and meta-analysis evaluated the efficacy and safety of oral PTX supplementation in infertile men with abnormal semen parameters. Previous studies and narrative reviews (20,31) have indicated potential benefits of PTX in male infertility, yet the absence of quantitative synthesis has limited the strength of the evidence. By synthesizing evidence from five RCTs involving 455 participants, we found that PTX may significantly improved sperm motility and normal morphology, whereas its effects on sperm concentration appear to be time-dependent and less inconsistent. No significant alterations in testosterone or FSH levels were observed, though it was associated with a modest reduction in LH. Importantly, PTX was well tolerated, with primarily mild gastrointestinal adverse events reported.

Our findings support and expand upon earlier narrative reviews and small-scale trials suggesting that PTX enhances sperm motility, morphology, and the acrosome reaction (21,32). Unlike laboratory studies where PTX is directly added to semen samples, oral administration exerts systemic effects, potentially improving testicular microcirculation, reducing oxidative stress (16,17), and enhancing intracellular cAMP signaling (33). The consistent improvement in morphology, in particular, suggests that PTX may positively influence spermatogenesis and sperm maturation, rather than merely exerting short-lived pharmacological stimulation.

In contrast, the effect of PTX on sperm concentration was less consistent. Short-term benefits were observed at 3 months but not sustained at 6 months, which may reflect differences in study populations, baseline semen profiles, or treatment regimens. Given that spermatogenesis requires approximately 74 days, longer treatment and follow-up may be necessary to capture the full impact of PTX on sperm production. Alternatively, PTX’s primary benefit may lie in enhancing motility and morphology rather than increasing sperm counts, which could still translate into meaningful clinical improvements.

The biological plausibility of PTX’s effects is supported by both its pharmacokinetic profile and known mechanisms of action. PTX is highly water-soluble, rapidly absorbed after oral administration, and distributed uniformly throughout the body, including reproductive tissues and secretions (17). Importantly, it can penetrate the blood–testis barrier, reaching the testes, epididymis, and seminal plasma (34), thereby establishing the necessary conditions for in vivo improvement of semen quality. At the molecular level, PTX functions as a phosphodiesterase inhibitor, preventing the breakdown of cAMP. Since sperm capacitation, hyperactivation, and motility are highly cAMP-dependent processes (35), elevated intracellular cAMP induced by PTX activates protein kinase A-mediated phosphorylation cascades. These cascades, in turn, trigger tyrosine phosphorylation of key flagellar proteins such as AKAP3, AKAP4, FSIP2, CABYR, and VCP (36), ultimately enhancing the frequency and amplitude of sperm flagellar beating. This mechanism provides a plausible explanation for the consistent improvements in motility observed in our analysis.

To further substantiate the biological plausibility observed in our clinical analysis, the efficacy of systemic PTX aligns closely with preclinical evidence demonstrating its protective role. In murine models of cyclophosphamide-induced reproductive toxicity, intraperitoneal administration of PTX reversed the decline in sperm motility, viability, and daily sperm production. Concurrently, PTX supplementation restored total antioxidant capacity and serum testosterone levels while attenuating lipid peroxidation, thereby mitigating chemotherapy-induced testicular oxidative stress (37). Similar protective mechanisms have been reported in testicular torsion-detorsion models (16), where systemic PTX administration elevated superoxide dismutase and catalase activities, which sequentially preserved seminiferous tubule morphology and germ cell survival following ischemia-reperfusion injury. Furthermore, prophylactic PTX administration in 3,4-methylenedioxymethamphetamine-treated rats significantly improved testicular histological scores, reduced the frequency of TUNEL-positive apoptotic bodies in the seminiferous epithelium, and downregulated active caspase-3 expression (38). Collectively, these in vivo studies indicate that systemic PTX modulates testicular health and preserves spermatogonial function primarily through the suppression of oxidative stress and apoptosis cascades. Such mechanistic pathways provide a biological rationale for the improvements in semen parameters and potential fertility outcomes observed in clinical settings.

Beyond its localized influence on intracellular cAMP signaling, we also evaluated the potential systemic endocrine impact of oral PTX. Regarding reproductive hormones, the observed changes were marginal and derived from only three trials. The lack of significant alterations in testosterone and FSH indicates that PTX does not substantially disrupt the hypothalamic-pituitary-gonadal axis. While the modest decline in LH could theoretically relate to improved testicular perfusion or reduced inflammation (39), any such mechanistic explanation remains entirely speculative. Given the sparse and heterogeneous nature of the available data, these hormonal findings are insufficient to draw definitive conclusions and should be viewed strictly as hypothesis-generating.

From a clinical perspective, improvements in sperm motility and morphology are highly relevant, as these are key determinants of natural fertility and ART success (40,41). PTX thus emerges as a potentially useful adjunctive therapy for idiopathic male infertility, particularly in cases of asthenozoospermia or teratozoospermia. Its low cost, oral availability, and favorable safety profile further strengthen its appeal. However, the optimal dosing regimen and treatment duration remain undefined due to a lack of data, and most importantly, the lack of robust data on pregnancy and live birth outcomes limits the translation of these findings into clinical practice.

Clinically, the safety profile of PTX is reassuring. Across the included trials, no serious adverse events were reported, with only mild gastrointestinal symptoms documented—a finding consistent with its long-standing clinical use in vascular disorders (42). Nonetheless, the small sample sizes and short follow-up durations of existing studies preclude definitive conclusions regarding its long-term safety in the context of male infertility. Beyond systemic tolerability, it is also crucial to contextualize the historical concerns regarding the potential reproductive toxicity of PTX observed in in vitro settings. As previously noted, in vitro studies have indicated that direct exposure of spermatozoa to high concentrations of PTX can prematurely trigger the acrosome reaction and exert detrimental effects on oocytes and early embryos (43). However, our findings and safety data suggest that these in vitro adverse effects do not readily translate to in vivo scenarios following systemic administration. Oral supplementation involves complex pharmacokinetic processes—including absorption, extensive first-pass metabolism, and systemic distribution—that dictate that the concentration of PTX reaching the reproductive tract microenvironment is significantly lower and more physiological than the acute, supraphysiological doses typically utilized in ART laboratories. Consequently, systemic PTX likely provides a moderate, sustained modulation of intracellular cAMP rather than an acute biochemical spike. This steady-state regulation enhances sperm motility and morphology during spermatogenesis and epididymal transit, without inducing premature capacitation or acrosomal exocytosis before the spermatozoa interact with the oocyte within the female reproductive tract.

The clinical relevance of in vitro embryotoxicity findings warrants cautious evaluation. Although laboratory assays suggest that premature acrosomal exocytosis could impair fertilization and early embryogenesis (44), clinical data indicating adverse effects of systemic PTX on ultimate reproductive outcomes—such as clinical pregnancy rates, embryo viability, or long-term offspring development—are currently lacking. Instead, systemic administration may optimize gamete integrity prior to fertilization by improving baseline semen parameters, as physiological pharmacokinetics prevent the exposure of spermatozoa to the acute high concentrations typical of in vitro models. Nonetheless, to address these toxicological concerns and establish clinical safety, future prospective trials should systematically evaluate longitudinal reproductive endpoints, including embryo morphokinetics during ART cycles, miscarriage rates, and the incidence of congenital anomalies.

Interpretation of our findings should take into account the substantial statistical heterogeneity observed across several outcomes. Such variability likely arises from differences in study populations, underlying infertility etiologies, baseline semen parameters, PTX dosing regimens, and methodological factors such as the use of different WHO manuals for semen analysis. Despite subgroup and sensitivity analyses, residual heterogeneity remained, suggesting that unmeasured confounders may have contributed. As a result, pooled estimates should be regarded as average effects across heterogeneous populations, rather than precise predictions for individual patients.

Several limitations must also be acknowledged. First, the number of included RCTs was small and sample sizes were modest, reducing statistical power. Consequently, this paucity of trials precluded the feasibility of conducting more granular subgroup analyses to further explore potential sources of heterogeneity or dose-response relationships. Second, treatment regimens varied in terms of PTX dose and duration, which may have influenced outcomes. Third, none of the trials reported live birth rates, and data on pregnancy outcomes were scarce, although these represent the most clinically meaningful endpoints. Fourth, the methodological quality of included trials was variable, with concerns regarding allocation concealment and blinding in some studies. Finally, the restriction to English-language publications may have excluded relevant trials.

Future research should focus on large, high-quality RCTs with standardized dosing protocols, longer treatment and follow-up durations, and clinically relevant endpoints such as pregnancy and live birth rates. Mechanistic studies are also needed to clarify the precise pathways by which PTX exerts its beneficial effects on sperm function. Addressing these gaps will be essential to determine whether PTX can be incorporated into routine clinical practice as an effective therapy for male infertility.

Conclusions

This systematic review and meta-analysis indicates that oral PTX supplementation may significantly exert beneficial effects on sperm motility and morphology in infertile men. However, its inconsistent effects on sperm concentration and the lack of substantial impact on the hypothalamic-pituitary-gonadal axis (e.g., testosterone or FSH levels). PTX appears to be generally well tolerated within the evaluated timeframes, though long-term safety data and its impact on offspring remain limited. While these findings highlight PTX as a promising adjunctive therapy for specific phenotypes such as asthenozoospermia or teratozoospermia, large-scale, high-quality trials with reproductive endpoints are essential to establish its clinical utility.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the PRISMA reporting checklist. Available at https://tau.amegroups.com/article/view/10.21037/tau-2025-1-999/rc

Peer Review File: Available at https://tau.amegroups.com/article/view/10.21037/tau-2025-1-999/prf

Funding: This research was supported by the State Administration of Traditional Chinese Medicine High-level Key Disciplines of Traditional Chinese Medicine (No. zyyzdxk-2023238), The Beijing High-Level Innovation and Entrepreneurship Talent Support Program Young Top Talent Projects (No. G202524104) and Scientific and Technological Innovation Project of China Academy of Chinese Medical Sciences (No. CI2026A02221).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://tau.amegroups.com/article/view/10.21037/tau-2025-1-999/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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