Women and men exhibit anatomical and functional differences in their cardiovascular systems. For example, women have smaller heart sizes, stronger ventricular contractility, smaller blood vessels, and smaller overall blood volume in the circulation (1–3). The manifestations of cardiovascular diseases also differ by sex. During a heart attack, men often present crushing chest pain, spreading pain in arms, nausea and cold sweat, whereas women mostly exhibit pain under the breastbone, abdominal pain, shortness of breath, nausea, and extreme fatigue (4, 5). In recent years, clinical studies have raised awareness of these differences along with the need to account for them to improve patient outcomes (6).

In this work, we contribute to this important area of research by investigating the effect of sex anatomical and functional differences on the circulation by means of a validated closed-loop mathematical model of the cardiovascular system (7–9). The model here is used as a virtual laboratory to simulate and compare multiple scenarios where parameters associated with sex differences are varied, such as ventricular contractility and arterial geometry. The model is also used to quantify the impact of sex-related parameter differences on the distribution of blood volume through the cardiovascular system. The model-predicted volumetric outputs are found to be consistent with published clinical data. Interestingly, the model indicates that the balance between the contractile function of the left ventricle (LV) and the load opposed by the arterial circulation, represented by the ventricular-arterial coupling (VAC) ratio, attains similar levels in females and males. This balance, however, is achieved through a different combination of factors. In females, the higher LV contractility is met by reduced arterial diameters, and this coupling ultimately leads to similar VAC ratios as in males.

Another interesting aspect of this work is that the mathematical model used to simulate cardiovascular sex differences also allows us to predict the shape of the ballistocardiogram (BCG) pertaining to the specific simulated scenario. As a matter of fact, the BCG signal is directly related to cardiovascular volumes. At each heartbeat, the blood ejected from the ventricles moves across the vascular compartments of the body which, as a consequence, host different amounts of blood at different instants along the cardiac cycle. The repetitive motion of blood volumes within the cardiovascular system results in the repetitive motion of the center of mass of the human body at each cardiac cycle, which is the motion captured by the BCG (10). Since the body motion is transmitted to the objects with which the body is in contact, the BCG offers a natural opportunity for noninvasive, unobtrusive monitoring of cardiovascular function. In the last decades, many devices for BCG sensing have been proposed, such as bed sensors (11, 12), weighing scales (13, 14), and accelerometers (15, 16).

A recent study showed that different BCG waveforms may be indicative of different cardiovascular baseline characteristics (15). Given the differences that the cardiovascular system exhibits in women and men, it is reasonable to conjecture that the baseline shape of the BCG signal may also be different depending on sex. Within this work, we test this conjecture by comparing the shape of BCG waveforms predicted by the mathematical model upon sex-related changes in cardiovascular parameters with BCG waveforms experimentally acquired on healthy males and females. Our study indicated that sex-related differences in arterial diameter and length are the major determinants of sex-related BCG differences, which manifest primarily through a decrease in amplitude and an earlier occurrence of the peaks, especially in the systolic phase.

The approach proposed in this work consists of utilizing mathematical modeling to interpret clinical and experimental data on the grounds of fundamental principles of cardiovascular physiology. This approach provides valuable insights on how different factors contribute to determine the healthy baseline conditions in women and men, which is a fundamental step towards a deeper understanding of sex differences in cardiovascular disease. Furthermore, we envision that the sex-related analysis of the BCG waveform will facilitate the effective design and implementation of noninvasive cardiovascular monitoring based on BCG sensing that will enable early diagnosis and prevent the worsening of cardiovascular disease in both women and men. The work is organized as follows. Sex-related cardiovascular differences observed in clinical studies are reviewed in Section 2. The main features of the mathematical model for the cardiovascular system are illustrated in Section 3, with particular emphasis on its inputs, outputs, and methods for BCG computing. The details of the experimental BCG acquisition are also provided in Section 3. The comparison between model predictions and clinical and experimental data is presented in Section 4, while conclusions and perspectives are outlined in Section 5.

The cardiovascular system exhibits a similar structure in women and men, but its dimensions and functions are distinctly different depending on sex (5). The female heart size is, on average, one-fourth smaller than the male heart (3). Independently from the body size, women showed to have smaller ventricular chambers and smaller arterial diameter and length compared to men of the same age and race (1, 17). Table 1 summarizes the main findings related to differences in healthy hearts and arteries of males and females. The findings are also discussed below.

The Left Ventricle (LV) in women is typically smaller than in men, leading to lower end-diastolic volume (EDV) and end-systolic volume (ESV). The stroke volume (SV) is also smaller in women, being approximately 22.9% less than that in men (3, 18). The higher heart rate (HR) typically observed in women reduces the gap difference in the cardiac output (CO) to approximately 12.5% (1, 3, 18, 19). LV ejection fraction (EF), a meaningful indicator of ventricular efficiency, is found to be approximately 6.5% higher in women than in men (20). LV end-systolic elastance (Ees), an important marker of LV contractility, is also found to be higher in the female heart, with Ees being approximately 22.4% higher in women than in men (21). The increased value of Ees in females is accompanied by an increased value of diastolic elastance, Ed, and arterial elastance, Ea. Specifically, Ed and Ea are found to be approximately 28.6% and 20.8% higher in women than in men (22, 23). In a healthy heart, an increase in Ees is usually accompanied by an increase in Ea; this maintains the ventricular-arterial coupling (VAC) ratio (Ea/Ees ratio) within the healthy human range, approximately between 0.6 and 1.2, to ensure overall cardiovascular efficiency and performance (24). Interestingly, despite the many differences in anatomy and function, both the female and male hearts are characterized by similar VAC ratios very close to 0.7 (25).

The Right Ventricle (RV) in women is also characterized by smaller size and higher contractility compared to men (20, 26). Similarly to the LV, EDV and ESV in the RV are lower in females by 16.1% and 19.4%, respectively. The SV and the CO in the right ventricle are also lower in females. The female RV is characterized by values of EF, Ees, and Ea that are higher than those found in males by 5.2%, 14.3% and 20%, respectively (18, 22, 27). The end-diastolic elastance Ed, on the other hand, has not been found to be significantly different between the right ventricle of males and females (26). The RV-Pulmonary Arterial (RV-PA) coupling estimated by RV Ees/Ea ratio is considered to be an indicator of RV efficiency. Its healthy range falls between 1.0 and 2.0 for healthy individuals; in males and females it is reported at 1.7 and 1.4, respectively (25, 28).

The Main Arteries also present important differences among women and men. Vessel diameters and lengths are usually smaller in females compared to males (1, 29). Diameter and length of the arterial root are, on average, approximately 10% smaller in females than in males. This difference, however, seems to vary along the aortic segments. Specifically, the female-male differences in the diameters of the ascending aorta, the aortic arch, the thoracic aorta, and the abdominal aorta are found to amount approximately to 8.8%, 10%, 8.0%, and 15.8%, respectively (17). The diameter of the carotid artery is approximately 6.2% smaller in females compared to males (30). Similarly, arteries are typically shorter in women, for whom the length of ascending aorta, the aortic arch, the thoracic aorta, and the abdominal aorta are approximately 9.5%, 13.5%, 9.8% and 11.1% smaller than in men (17). The carotid length is reported to be 9.6% smaller in women (30).

It is reasonable to assume that the female-male differences in the cardiovascular system will also manifest in BCG signals. We recall that the BCG waveform results from the motion of the center of mass of the human body as the blood volume redistributes within different vascular compartments at each heartbeat (10). Thus, anatomic and functional differences in the cardiovascular system may lead to different patterns in blood volume distribution, which could be picked up by the BCG. Indeed, it has been observed that the mean BCG amplitude in females is lower than in males by nearly 36% (3.56 N vs. 5.56 N) (31).

This study utilizes a validated mathematical model for the cardiovascular system to predict and quantify how the distribution of blood volume within the body is impacted by differences in specific cardiac and vascular parameters associated with males and females (Section 2). The cardiovascular model leverages the analogy between the flow of a fluid in a hydraulic network and the flow of current in an electric circuit and translates fundamental principles of cardiovascular physiology into mathematical equations, a comprehensive description of the cardiovascular model, with full details, is provided in (7). Here we focus on describing which parameters are used as model inputs (Section 3.1), which quantities are computed as model outputs (Section 3.3), and which numerical strategies are used to solve the equations (Section 3.4). The model-predicted BCG waveforms are compared with experimental BCG waveforms acquired on human subjects by means of an accelerometer placed on a suspended bed. The details of the experimental BCG acquisition are given in Section 3.5.

The outputs of the cardiovascular model obtained for the various versions illustrated in Section 3.2 are compared in terms of volumetric outputs (Section 4.1), cardiovascular indexes (Section 4.2), and BCG waveforms (Section 4.3). BCG waveforms estimated from the model are then compared with the BCG signals obtained experimentally (Section 4.3). We recall that, starting from the idealized male model version based on the model parameters reported in (7), we vary specific parameter values individually (i.e. HR, ELS, ELD, ERS, arterial diameter and length), thereby yielding six additional model versions. All changes are simultaneously incorporated into a single version called idealized female model version. Since the specific values of the modified parameters reported in Table 2 may vary from person to person, we also tested the cases in which such values were altered by ±5%.

This study provides novel insights on the effect of sex-related anatomical and functional differences on blood circulation. Theoretical predictions based on a mechanism-driven cardiovascular model were used to interpret clinical and experimental data and describe how different factors contribute to determine the healthy baseline conditions in women and men. This is a fundamental step towards a deeper understanding of sex differences in cardiovascular disease. Our results indicate that the balance between LV contractile function and arterial impedance is achieved differently in females and males, with higher LV contractility in females being met by smaller arterial diameters. This difference in cardiovascular balance is captured by the BCG waveform, where the reduced arterial diameters lead to smaller amplitudes and earlier timing of the BCG peaks. These insights help deepen our understanding of sex-related baseline differences in cardiovascular function and could enable better tailoring of therapeutic and monitoring approaches to cardiovascular disease in women and men. Thanks to its noninvasiveness and strict relationship with blood volume distribution, sex-informed BCG sensing could be used to monitor cardiovascular changes in many different situations, spanning from optimizing physical exercise (37, 38) to detecting risks during pregnancy (39, 40).

Noninvasive cardiovascular monitoring based on BCG waveforms can provide advantages with respect to accessibility and cost-effectiveness when compared to other techniques such as echocardiography, making BCG-based devices suitable for routine monitoring in home and ambulatory settings. Routine monitoring could potentially lead to early diagnosis of cardiovascular complications, facilitating timely interventions and reducing the burden of cardiovascular diseases. While BCG waveforms hold great promise, a critical challenge for widespread clinical use is the standardization of BCG waveform acquisition. To-date, several devices and methods have been used to measure the BCG in various settings, and these are not always comparable. Therefore, the great challenge is to standardize BCG measurement to ensure that data collected from different sources can be consistent and comparable.

The results presented in this work should be contextualized within the limitations of the methods utilized to obtain them. The model simulations have been compared with published values of cardiac volumes and related parameters. These values, however, should be considered more as general indicators than as exact numbers since they may vary depending on the particular subjects under consideration. The cardiovascular model considered here does not include a detailed description of the atria, which could affect the ability to capture post-systolic events in the distribution of blood volumes and, consequently, in the BCG waveform. Furthermore, the comparison between experimentally-measured and model-predicted BCG waveforms could benefit from a larger pool of subjects. A larger cohort spanning across ages would better facilitate insights into how aging may affect cardiovascular function in women and men. These are very important directions of research that could be explored by extending the approach presented here.